On the Need for a Language Describing Distribution Shifts: Illustrations on Tabular Datasets
Authors: Jiashuo Liu
Tianyu Wang
Peng Cui
Hongseok Namkoong
Venue: NeurIPS 2023 Datasets and Benchmarks Poster (2023)
Keywords: distribution shift types
natural distribution shifts
tabular datasets
TL;DR: We build a tabular benchmark with specified distribution shift patterns, which highlights the importance of future research that builds an understanding of how distributions differ.

Abstract: Different distribution shifts require different algorithmic and operational
  interventions. Methodological research must be grounded by the specific
  shifts they address.  Although nascent benchmarks provide a promising
  empirical foundation, they \emph{implicitly} focus on covariate
  shifts, and the validity of empirical findings depends on the type of shift, 
  e.g., previous observations on algorithmic performance can fail to be valid when
  the $Y|X$ distribution changes.  We conduct a thorough investigation of
  natural shifts in 5 tabular datasets over 86,000 model configurations, and
  find that $Y|X$-shifts are most prevalent.  To encourage researchers to
  develop a refined language for distribution shifts, we build
 ``WhyShift``, an empirical testbed of curated real-world shifts where
  we characterize the type of shift we benchmark performance over.  Since
  $Y|X$-shifts are prevalent in tabular settings, we \emph{identify covariate
  regions} that suffer the biggest $Y|X$-shifts and discuss implications for
  algorithmic and data-based interventions.  Our testbed highlights the
  importance of future research that builds an understanding of why
  distributions differ.

On the Need for a Language Describing Distribution Shifts: Illustrations on Tabular Datasets
Tianyu Wang"*,, Peng Cui', Hongseok Namkoong" Department of Computer Science and Technology, Tsinghua University
Jiashuo Liu';
Department of Industrial Engineering and Operations Research, Columbia University
Decision, Risk, and Operations Division, Columbia Business School
1 1iuj iashuo778gmail com, tw28378columbia. edu cuip@tsinghua. edu. en, namkoongōgsb.c sta.koongggsb.oolubb...... columbia. edu
Abstract
Different distribution shifts require different algorithmic and operational interven- tions. Methodological research must be grounded by the specific shifts they address. Although nascent benchmarks provide a promising empirical foundation, they im- plicitly focus on covariate shifts, and the validity of empirical findings depends on the type of shift, e.g., previous observations on algorithmic performance can fail be valid when the Y|X distribution changes. We conduct a thorough investigation natural shifts in tabular datasets over 86,000 model configurations, and find are most prevalent. To encourage researchers to develop refined language for distribution shifts, we build WHYSHIFT, an empirical testbed of curated real-world shifts where we characterize the type of shift we benchmark performance over. Since Y X-siffts are prevalent in tabular settings, we identify covariate regions that suffer the biggest Y X'|x-hhife and discuss implications for algorithmic and data-based interventions. Our testbed highlights the importance future research that builds an understanding of why distributions differ
that
Introduction
The performance of predictive models has been observed to degrade under distribution shifts in
wide range of applications, such as healthcare 9
95 76 93,, economics [36] (55,, education [6].
vision 77 63 86 28, and language [62] 77. Distribution shifts vary in type, typically defined as either a change in the marginal distribution of the covariates (X-shifts) or the conditional relationship between the outcome and covariate (Y X-shifts). Real-world scenarios comprise of both types of shifts. In computer vision 662 47 81 38 IOI). Y|X-shiffe are less likely to occur as Y is constructed from human knowledge given an imput X, unless the labeling noise severe. For tabular datasets, Y|X -hiffs can be more common because of missing variables and hidden confounders. For example, the prevalence of disease may be affected by unrecorded covariates whose distribution changes across domains, such as lifestyle factors and socioeconomic status
39
103 93].
Different types of distribution shifts require different solutions. When facing X-shifts, the implicit goal of many researchers is to develop a single robust model that can be generalized effectively across multiple domains. Various algorithms have been developed align the marginal distributions (Px), including domain adaptation and importance sampling methods. However, under X|S-sissts, there may be fundamental trade-off between learning algorithms: to perform well on a target distribution, a model may have to necessarily perform worse on others. Algorithmically, typical methods for
Equul contribution
MMore information the data, codes and python packages about WHYSHIFT available at https 7/g gitthb..c.ooo httpt//////onooooaaaaaaaa-a--e layhhhihi
37th Conference on Neural Information Processing Systems (NeurIPS 2023) Track on Datasets and Benchmarks.

---

200%
Relative Regret
100%%
2216
0%
Adult:
DOMIPA
AUS Pub.
ACS Inc.
ACS5 Inc.
ALS Pub.
AUS Pub. (NE-LA)
ACH Mob.
Tans
Los Aect.
ACS Iac. (CA-PP)
(sex. eaXe)
(sex S: (aar) (sex de (ood) (sox noee)
Jaex & O00
(MS-III) (NYC-BOG) (CA-OR)
Figure 1. Relative regret (I.I in typical benchmarks [26] 31 (left burs) and seven settings designed in our benehmark (right bars). We use XGBoost FF here for illustration.
addressing Y| -shiisss include distributionally robust optimization (DRO) 13 85 28
80 27 and Operationally, the modeler can identify and collect an unobserved confounder C such that Y Y|X, K C' Cremains invariant across domains, or resort to overhauling the entire model development pipeline to collect more samples from the target.
causal learning methods 772
46
However, existing distribution shift benchmarks only focus on X-shifts 74
[01]. To
illustrate this concretely, consider popular tabular datasets used to benchmark model performance over demographic subgroups: Adult, BRFSS, COMPAS, ACS Public Coverage, and ACS Income 3 We take the largest demographic group training P and the smallest as target Q to simulate subgroup shifts, c.g., in Adult, P =white men and Q =non-white women. We measure the optimality gap of the model fe trained on P as measured on the target Q using the relative regret
102 31.
Bole(Y, minzer (ole(Y. ((X)) 1, where fr E argmin Ep E,(((Y, fEF
(1.1)
and ((...) .) is the 0-1 loss. For these widely-used benchmarks, the relative regret is small (left 5 bars in
Figure D. suggesting the Y|X distribution is largely transferable across those demographic groups.
To study diverse distribution shift patterns, we consider real-world tabular datasets constructed from the US Census (as proposed by Ding el al. (25) and traffic measurements [64 65 D. We focus on spatiotemporal shifts to model most common natural shifts. Our full benchmark covers 22 settings (see Table in Appendix D). where each setting includes one source (e.g.. California) and a number of possible targets (c.g., other states). For illustration purposes, we focus on settings covering 169 possible source-target pairs (see Table 2 and carefully select one target per setting to represent a wide range of Y Xh-sifst (right bars in Figure D].
We find -shifsssts constitute substantial proportion of real-world distribution shifts, yet previous (unqualified) empirical findings in the literature only hold over mild X-shifts and fail to hold over Y|X-shifte (Section?) 2). Out of 169 source-target pairs with significant performance degradation (> percentage points of accuracy drop), 80% them are primarily attributed to -shifsss Y|X- shifts introduce considerable performance variations on the target distribution, leading to different relationships between in- and quttof-distribution performances across settings and datasets. This in stark contrast to the recently observed accuracy- seerracy-onthh--eee oonthee-line phenomenon [63], where the in- and -f-tssirbrittoinnnnn performance have been posited to exhibit a strong linear relationship. In Figure 2 showcase how the accuracy-on-the line trend fails to hold when Y X X-shiftt are strong. Our results imply that the standard practice of blindly evaluating performance over various shifts is only justified over X-shifts, where we expect there be a single model that is robust across domains.
For severe -hh-shifss, the training data may not even be informative for modeling the Y|X rela- tionship in the target. To inform algorithmic and data-based interventions, we must understand why the distribution changed. In Section 3 we illustrate the need for more methodological research that builds a deep understanding of distributional differences. As a concrete example, we show that simple approach for identifying covariate regions with strong Y X -hiffss can suggest data-based interventions. Our case study shows it can be usefuul to collect target data over particular covariate region, or features C' such that the Y|X, C distribution is more stable across source and target.
In Section 4 we provide the details of our benchmark, WHYSHIFT. We use five datasets to construct 7 spatiotemporal distribution shifts, and evaluate 22 methods over 86,000+ model configurations. We compare broad range of algorithms including tree ensembles, DRO, imbalance, and faimness methods and summarize our key findings below.
Rankings of model performance change over different shift patterns. As the validity of empirical findings implicitly depends on the type of shift, any methodological development must be grounded by the specific shifts it addresses.
Tree ensemble methods are competitive, but still suffer from significant performance degradation.

---

10 R² = 0.191
160 R² = 0.371
R² = 0.511
R² = 0.379
y-x
y-x Paline
yex
y=x
Fi tine
Fii Sm
Fw tine
Target Ase
lurget 80
8
Ace Drop 10.3, Yp. 89%
Acc Diop 83, MP: 82% 70
Ace Drop 16.1, M.C: 100%
Ace Deop 16.5, YJK 02% 70
100 %
TO
200
162
Source Ace
Source Ace
Source Ace
Source Are
ACS (CA-4 PR)
(b) ACS Mobility (MS HD)
Taxi (NYC-+ BOG)
(d) ACS
Pub.Cor (NE- LA)
R'
0,038
y-x 1it
50 R' - 0,749
y-x
R" 0.841
--x
Fix
Acc 1rop11.6, YIX: 60%
Ace Drop 5.4. YJK: 13%
Adc Drop 112. YJ:
1he 2%
120
Souree Ace
Source Aee
Source Ace
(c) US Accident (CA-+ OR) ACS Pub, Cov (2010-22017)
Income (Young-> Old)
Figure 2. Target vs. source accuracies for 22 algorithms and datasets in our benchmark. A linear (green line) and its corresponding R² value is reported on the top left of each figure. Each blue point represents one hyperparameter configuration. (a)-(f): six examples of ACS Income, ACS Mobility, Taxi, ACS Pub. Cov, US Accident datasets. (g): simulated covariate shifts on on sub-sampled ACS Income dataset.
DRO methods sensitive configurations and exhibit significant performance variations.
Imbalance and faimess methods show similar performance with the base learner (XGBoost).
A small validation data from the target distribution goes a long way, and more generally, non- algorithmic interventions warrant greater consideration.
2 Distribution Shifts in Tabular Settings
To illustrate how complex distribution shift patterns arise tabular data. we compare 22 algorithms including tree ensemble methods, robust learning, imbalance, and fairesss methods. On 5 real- world tabular datasets (ACS Income, ACS Public Coverage (ACS Pub. Cov). ACS Mobility (25). US
Accident [64 65 and Taxi 11. we consider the natural spatial shifts between states/cities, e.g.. California to Puerto Rico. For the ACS Pub.Cor dataset, we also consider temporal shifts, e.g., from 2010 to 2017. Since all natural distribution shifts we consider are largely induced by Y|X-shifts, we construct synthetic subgroup shift from younger people to older people in order to simulate X-shifts. Deferring detailed summary to Section 4.1 this section.
we focus on introducing representative phenomena in
In Figure 2 we present the source (in (in-distribution) and target nuut-of-distributoon performances of 22 algorithmss, each with 200 hyperparameter configurations. To understand shift patterns, we utilize the recently proposed DIstribution Shift DEcomposition (DISDE) framework [16] which decomposes the performance degradation into components attributed to YJX- and X-shifts. Using the best XGBoost configuration as the baseline model for each source-targes pair, we present the total performance degradation and the proportion attributed to Y|X-shifts.
Distribution shifts are predominantly Y -shifts in our empirical study We find performance degradation under natural shifts is overwhelmingly attributed to Y|X-shifts, as illustrated in the curated list in Figure 2] More generally, out of the 169 source-target pairs whose performance degradation is larger than 8 percentage points, 87.2% of them have over 50% of the performance degradation attributed to Y -ssiftss (70.2% of them have over 60% of the gap attributed to Y|X- shifts). We conjecture that X|X are prevalent in tabular data due to missing features. For example, in the context of income prediction, individual outcomes may change due to unobserved economic and political factors whose distribution changes over geographical locations (25). In contrast, in vision and language tasks, the input (e.g., pixels and words) often encapsulates most of the necessary information for predicting the outcome, making strong Y| "1]-ssh -hiffs less likely unless the labeling noise is severe. Consequently, compared to vision and language data in domain generalization
3

---

Target Ace
Shift X|X Shift
Y|X Shift X Shift
LR
MLP
XGBooot
Improces- DP
SVM
X-DRO
SUBG
ACS Income (Young-1OM)
ACS Pub.Cov
ACS Pub.Cov
CS Accident (CA-OR)
ACS Income (CA-PR)
ACS Mobility (MS-HI)
Taxi (NYC-BOG)
(2010-2017)
(NE-LA)
Figure 3: Performances of typical algorithms of 7 settings in our benchmark.
tasks, tabular data exhibits more pronounced real Y|X-shifts. Our findings highlight the importance of understanding the cause of the distribution shift.
Accuracy-on-the-liee fails to hold over X-siftts We find significant variation in the relation- ship between source and target performance throughout all natural distribution shifts presented in The correlation between source and target performance is relatively weak, and we tend to poor linear fits (low R²) when the bulk of the performance degradation is attributed to X|X-shifts. That is, we see in Figures 2 (a)-(f) that the relationship between the two performances exhibits significant fluctuations across different source-target pairs. In Figure 3 observe that performance rankings of algorithms substantially vary across different Y X --shifts. Our finding highlights the inherent complexity associated with real distribution shifts in tabular datasets, which stands in sharp contrast to the in tabular data highlight how empirical observations must be qualified over the range of shifts they remain valid over. This is particularly important for Y|X-shiffe shifts which introduce larger variations in the relationship between source and target performance.
phenomena [63]. The varied shift patterns
Source and target performances are correlated when X- X-shifts dominate Across all natural shifts we study, we find X-shifts are only prominent in temporal shifts (ACS Time dataset; Figure 21 To better investigate the role X-shifts, we subsample the data to artificially induce strong covariate shifts over individual's age. Specifically, we focus on individuals from California and form two groups according to whether their age is 2 25. The source data oversamples low age groups where 80% is drawn from the age < 25 group: proportions are reversed in the target data.
On this synthetic shift we construct, the DISDE [6] method attributes the bulk of the performance degradation to X-shifts in Figure 2g Our finding confirms the intuition that unobserved economic factors remain relatively consistent for individuals from the same state (CA). In this synthetic example with X-shifts, we observe a relatively strong correlation between source and target performance. Moreover, the large performance degradation on these datasets suggests that existing robust learning methods are still severely affected by covariate shifts, indicating the need for future research that addresses covariate shifts in tabular data.
Case Study: Understanding Distribution Shifts Facilitates Interventions
Typical algorithmic approaches to handling practical distribution shifts aim to optimize performance over a postulated set of distribution shifts. Causal learning assumes the underlying causal structure can be learned to withstand distribution shifts [72 83 82 77 while DRO methods explicitly optimize 27 Despite progress algorithm design, there are few efforts that examine the patterns of real-world distribution shifts. It remains unclear whether the data assumptions made by algorithms hold in practice, and this mismatch often
worst-case performance over a set of distributions
13
leads to poor empirical performance [40 95 76 19 46).
Complementing the active literature on algorithmic development, we present an empirical study that underscores the practical significance of tools that provide a qualitative understanding of the shift hand. In light of the prevalence of Y --siftts effective approach for identifying covariate regions that suffer strong Y X-shitts. We demonstrate our approach on the income prediction task (ACS Income), and show that can guide operational interventions for addressing distribution shifts. Our case study is not meant to be a rigorous scientific analysis, but rather (heuristic) vignette illustrating the need for future research on methodologies that can generate qualitative insights on distributional differences.
tabular data, we introduce a simple yet

---

3.1 Identifying Regions with Strong Y| Xh-sfssts
Here we propose a simple yet effective method for identifying covariate regions with strong X|X- shifts. Despite its simplicity, we demonstrate in the following subsections that our method can inspire operational and modeling interventions. Letting (X; Y) be random variable supported on the space X' x J/ consider a model f X + y that predicts outcome Y E ) from covariates X E X with the associated loss function & E(f(X),Y) Given samples (X, Y) drawn from the source and target distributions P and Q, our goal is to identify a region R S X' where Pr|x differs a lot from Qyjx.
Since Pyix and Qy x are undefined outside of the support of Pxx and Qx respectively, the com- parison can only be made on a subset of the common support. To aid comparisons on the common support, Cai et al. [66] introduced shared distribution approach. The shared distribution has high density when both Px and qx are high, and low density whenever either is small. Following Cai et al. [6], we choose a specific shared distribution Sx over X from the likelihood ratio:
sx (x) px
px(x)) (x) (z)/ (px (z) qx (x)).
(3.1)
We provide more discussion on the choices of Sx and other technical details justifying the correctness of 8x in Appendix C.3 Since we do not have access to samples from the shared distribution Sx, we reweight samples from Px and Qx using the likelihood ratios 8x (x)/px( (x())) x qx (a)/ (2) qx (x)) and x (x(x)/o qx (x) x P.x (x) /px (z) + qx (z)). The ratio can be modeled as the probability
that input is from Px vs Qx. Denote a' as the proportion of the pooled data that comes from Qx and x² (x) == P(X from Qx r)), we can express the likelihood ratios as:
x (x)
(x)
(1 a- TT (x) a² - x<))) wp =p(TT(x),
(3.2)
px
1- (x) qx (1 a* ) a0 (x=)
(x)
wQ( (z), )x))
(3.3)
With the likelihood ratios, we estimate the best prediction model under P and Q over the shared distribution Sxx (using XGBoost as the model class F):
Esx (LL((((())))))X) (- (E, (e
fu arg min feJ
for μ = P. P.Q.
(3.4)
Then, for any threshold b E [0. fxr E X [f((#) so(x)) b} suggests a region that may suffer model performance degradation with at least b due to Y|X-shifts. Without evaluating the performance on the shared distribution Sx, it is hard to distinguish the source of the model performance degradation, i.e. from X-shifts or Y -shifss
Empirically, given samples {(=F' wxt" )iemnn from P and ((xg MM BeEma) from Q, we estimate à un+nn and then train a binary "domain" classifier axx) to approximate the ratio x" (z). Note that the "domain" classifier can be any black-box method, and we use XGBoost throughout. Then we plug these empirical estimands in to obtain the estimated likelihood ratios (*((), à:) and learn prediction models fp and fo in Equation (.4p. To investigate the model difference under Sx. we pool samples from P and Q together and set sample weights as:
ng
Wp wp(# (+ &)) (t
( (1))) a)
A,-
Vi [np], AJ Exe(aa) we (f(((x)))))
Vj E [nq]. (3.5)
Ekelppl (P(
which are used to learn prediction model h(x) to approximate [fr(z) fo(z)) on the shared distribution 5x- The pseudo-code is summarized in the Algorithm D To allow simple interpretation
and efficient region identification, we use shallow decision tree h(x) and consider the region R corresponding to the feature range of a leaf node within the tree. More details could be found in Appendix and Appendix ( We show that the node splitting criterion in a standard decision trees training procedure is equivalent with our goal of finding regions with the largest discrepancy in Appendix C.4
3.2 Data- Interventions
Using Algorithm I we now demonstrate how better understanding of distribution shifts can facilitate the design of interventions. We focus the ACS Income dataset where the goal is to predict whether
5

---

Algorithm 1: Identify Regions with Strong -Shifsss..
Source samples {(xf", uf )efmn)) iid P and target samples ((T), Mi) (i) sEmml ~
Lid
Input:
Model discrepancy threshold
Estimate (xx R P(X ~ Q21x = x) by training a classifier on the source and target samples.
Calculate density ratios wr, (xr), ái) according to Equation (3.2) and (3.) for μ = P, Q.
3 Fit prediction models [u according to Equation (3.4) replacing wy (T (x), o*) there with
(f)), â) for P.
Fit model h(x) to predict ( fa(x)) using samples {(r, ) Die[m)) and {(x]. U3 ]e([o)) each with the weight Xo" (or 2 respectively), according to Equation (3.5)
Output: Region R fr E X: h(x) 2 b}.
an individual's income exceeds 50k (Y) based on their tabular census data (X). We train an income classifier on 20,000 samples from California (CA, source), and deploy the classifier in Puerto Rico and South Dakota (PR& & SD, target), where we get 4,000 samples from PR and SD after deployment. Given the considerable disparities in the economy, job markets, and cost of living between CA and PR/SD, we observe substantial performance degradation due to distribution shifts.
In Figure 4a we first decompose the performance degradation from CA to PR to understand the shift and find Y|X--shifts are the predominant factor. The calculation of X-shifts and Y| X--siftts is deferred to Appendix [.I] We dive deeper into the significant Y ||X -siffts and identify from CA to PR for the XGBoost and MLP classifier. From the region shown in Figure 44c and Figure 4dl we find college-edus educated individuals in business and educational roles (such as management, business, and educational work) exhibit large Y|X differences.
To illustrate how our analysis can inspire subsequent operational interventions to enhance performance on the target distribution, we study two operational interventions.
Collect specific data from the target To improve target performance, the most natural operational
intervention is to collect additional data from the target distribution. While rich body of work on domain adaptation 669 23 30, 90 89] study how to effectively utilize data from the target distribution to improve performance, there is little work that discusses how efficiently collect supervised data from the target distribution to maximize ofitt--distributtin generalization. To highlight the need for future research in this space, use the interpretable region identified by Algorithm [ as shown in Figure 4c to simulate a concerted data collection effort.
Since indiscriminately collecting data from the target distribution can be resource-intensive, we concentrate sampling efforts on the subpopulation that may suffer from YJ Y|X-shite X-shifts and selectively gather data them. For five base methods (logistic regression, MLP. random forest, lightGBM, and XGBoost), we randomly sample 250 points from the whole target distribution and the identified region suffering prominent Y | XS-ifftts, respectively. We report the test accuracies in Figure 4c, and observe that incorporating data from this region is more effective in enhancing OOD generalization While preliminary, results demonstrate the potential robustness benefits of efficiently allocating resources toward concerted data collection. Future methodological research in this direction may be fruitful; potential connections may exist with active learning algorithms [84] 96 [9].
Add more relevant features We now illustrate the potential benefits of generating qualitative insights on the distribution shift at hand. Our analysis in Figure 4c suggests educated individuals in financial, educational, and legal professions tend to experience large ||h-shifts from CA to PR. These roles typically need communication skills, and language barriers could potentially affect their incomes. In California (CA), English is the primary language, while in Puerto Rico (PR), despite both English and Spanish being recognized official languages, Spanish is predominantly spoken. Consequently, for a model trained on CA data and tested on PR data, incorporating a new feature that denotes English language proficiency (hereafter denoted "ENG") might prove beneficial in improving generalization performances. However, this feature is not included in the ACS Income dataset.
To address this, we went back to the Census Bureau's American Community Survey database to include the ENG feature in the set of covariates. In Figure 4bb we observe that the inclusion of this feature substantially reduces the degradation due to Y -hhffts, verifying that the originally missing

---

$1.4
$1.5
Alco
Work Hour 2 34.5
Rules
Accuracy
drgratatien
Sex:fonale 51
Work Hour 6(34,5,99.5
Education 2 College
Education College
Occupation
71.8
BUS, FIN, LGL, EDU, ENT
Occupation E.
YIX
YI
X shirt
X sun
CA PR
Difference
CA
PR
Difference
Risk Region
(a) Raw setting: drop 10.3
(b) Add ENG: drop 2.1
(c) Region with Y|X shifts (XGBoost)
Education C College
Rules
Original Setting
Add Region Data
Sex: female Age 2: 39
Test Accuracy
Add Target Data
Work Hour 35.5
Hour
Edueation a College
Sex: female
BB
Risk Region
LR
MLP
RF
LightGBM XGBoost
(d) Region with X|X shifts (MLP)
(c) Test accuracies of different ways to incorporate data.
Target Aee
80
ENG
Add ENG
Source Acc
Source Ace
Add ENG (CA-+PR)
(g) Add ENG (CA- SD)
Figure 4. Case study illustrations. (a)-(b) Decomposition of performance degradation for the XGBoost classifier from CA to PR. Figure (a) is for the original setting and (b) corresponds to the results post- integration of the "ENG" feature. (c)-(d) Demonstration of Algorithm [ an interpretable version of the region with strong Y X -siftts for the XGBoost and MLP models, respectively. (e) Test accuracies of five typical base methods trained and 250 observations from the identified risk region. (f)(() Performances of all algorithms prior and following the addition of the "ENG" feature. Figure corresponds the CA CA to SD.
the source, post addition of 250 randomly selected target observations,
Figure (g)
Table 1: Overview of datasets and selected settings.
#ID
Dataset
Type
#Samples
#Fcatures
Outcomec
#Domains
Selected Settings
Shift Patters
ACS Income
Natural
1,599,229
Income 250k 50k
California Puerto Rica
X
X
ACB Mobility
620.937
Residential Address
Mississippi
3
Taxi
Natural
1,506.769
7
Duration time 30 min
New York City Bologá
Y 2
ACS Cov
Natural
1,127,446
Public Ins. Coverage
Nebruska Louisians
Y S
297.132
Severity Accident
California- Oragen
ACS Pub.Cov Cov
Natural
859,632
Public Ins. Coverage
2010 (NY) 2017 (NY)
Y
ACS Tncome
Synthetic
195.665
Income250k
Younger- Older
Y.X
ENG feature may be one cause of Y X-shifts. Figure contrasts the performances of 22 algorithms (each with 200 hyperparameter configurations with original features with those that additionally use the ENG feature. The new feature significantly improves target performances across algorithms; roughly speaking, we posit that we have identified a variable C' such that Y|X, C' remains similar across CA and PR. However, when we extend this comparison the source-target pair (CA - SD), we observe no significant improvement (Figure 4g). This highlights that the selection of new features should be undertaken judiciously depending on the target distributions of interest. feature that proves effective in one target distribution might not yield similar results in another.
7

---

PIX & X
xX
YIX x
LR
MLP
Tree Ensembles
Fairness Methods
Target Acc
SVM
DRO Methods
Iubalance Methods
ACS Tocoiee
ACS Poh,Cov
ACS Pub.Cov (NE-LA)
US Accident (CA-OR)
ACS Income (CA-PII
ACS Mobility (MS- III)
Taxi INYC-BOG,
(Young -Old)
2010-2017)
Figure 5: Overall performances of all algorithms on the target data in our selected 7 settings.
4 WHYSHIFT: Benchmarking Distribution Shifts on Tabular Data
In this section, we detail our benchmark and summarize the main observations. Our finding highlights the importance of future research that builds an understanding of why the distribution has shifted.
4.1 Setup
We explore distribution shifts on real-world tabular datasets from the economic and traffic sectors with natural spatiotemporal distribution shifts. For economic data, we use ACS Income, ACS Mobility, and ACS Public Coverage datasets from the US- ACS PUMS data (25). where the outcome is whether an individual's income exceeds 50k, whether an individual changed the residential address one year ago, and whether an individual is covered by public health insurance, respectively. We primarily focus on spatial shifts across different states in the US. To complement spatial shifts, we derive an ACS Time task based on the ACS Public Coverage dataset, where there are temporal shifts between different years (2010 to 2021). For traffic data, we use US Accident [64 655 and Taxi 2 [. where the outcome whether an accident severe and whether the total ride duration time exceeds 30 minutes, respectively. We focus on spatial shifts between different states/cities. We summarize the datasets in Table I and defer a full description to the Appendix D.I
Datasets
Algorithms We evaluate 22 algorithms that span a wide range of learning strategies on tabular data, and compare their performances under different patterns of distribution shifts we construct. Concretely, these algorithms include: (1) base learners: Logistic Regression, SVM, fully-connected neural networks (MLP) with standard ERM optimization; (2) tree ensemble models: Random Forest, XGBoost, LightGBM; (3) robust learning: CVaR-DRO and x²-DRO with fast implementation (53)
CVaR-DRO and 2DRO of outlier-robust enhancement 105
Group DRO 77); (4) imbalanced 51 and (5) fuirness-enhunne
methods: inprocessing method 4 with demographic parity, equal opportunity, error parity constraints, postprocessing method (37 with exponential and threshold controls. For DRO methods (i.c. (3)), use MLP as the backbone model. For other algorithms compatible with tree ensemble models (i.e. (4-5)), we use the XGBoost model due to its superior performance on tabular data [34.. For algorithms requiring group labels,
learning: JTT (57 SUBY, RWY, SUBG, RWG 42). DWR
'hour' for US Accident and Taxi, and 'sex' for the others. Detailed descriptions for each algorithm can be found in Appendix [D.]]
Benchmarks We conduct experiments with more than 86,000 model configurations on various source-target distribution shift pairs, and carefully select 7 selected pairs with different distribution shift patterns. In Table [T] we characterize the shift patterns of these 7 source-target pairs, which contain different proportions of Y [X Xhshifts and X-shifts corresponding with plots in Figure The natural shifts. In the last setting,
first six settings introduce covariate shift, where we focus on individuals from CA and form two groups according to whether their age is > 25. The source data over-samples the low age group where 80% is drawn from the group where the individual's 's age 2 25, and the proportions are reversed in the target data.
sab-sample the dataset according age to
In Figure 5 and Figure 6 we plot the performance of algorithms using their best hyperparameter configuration on the validation dataset (i.i.d. with the source distribution). Additional results with various source distributions are in the Appendix. Our benchmark is designed to support empirical research, including new learning algorithms and diagnostics that provide qualitative insights on distribution shifts.
8

---

Performance Drop
LR
SVM
MLP
DRO Methods
Tmisulanco Methods
Tree Ensemiles
Fairness Methods
Lid performan performance on source
10-
YIX
YIX
YIX
ACS Income
ACS Pub. Cuv (2010 22017)
ACS Pub.Cov (NE :LA)
US Accident
ACS Income (CA PR)
ACS Mobility [MS .II)
Taxi (NYC BoC)
(Young :Old)
(CA :OR)
Figure 6. Performance drop between source and target data of all algorithms in our selected 7 scttings.
100
Methadd
Inciadurs Micltsbe
SVM
The Fowembix
Faimmos Mathods
MLP
Tagee Ase
Targer
220
Source Ace
Subgroup Discrepancy
Subgroup
(a) DRO & 1mh. Methods
(b) Performances under different validations on ACS Income dataset.
Figure 7. (a): Sensitivity of DRO methods and Imbalance Methods w.r.t configurations. (b) Target performances of 22 algorithms under different validation protocols ACS Income (CA (C)+PR) setting.
Hyper-parameter Tuning For each model, we conduct a grid search over a large set of hyper- parameters. See Appendix D.3 for the complete search space for each method. When method includes another as a "base" learner (e.g., DRO with MIP, RWY with XGBoost), we explore the full tuning space for the base model (e.g., the cross-produse of all MLP hyper- prrrae-prraeeerss with all DRO (rper-parameters). To control for computational effort, each method is run with 200 configurations for each source-target pair and we select the best configuration according the i.i.d. validation performance, In Figure 7b we further compare different choices of validation protocols.
Evaluation Metrics In our benchmark, we include different metrics for thorough evaluation. Specifically, we use Average Accuracy (micro-average). Worst-group Accuracy, and Macro-Fi score in our main results where
only have one target distribution. For the results with multiple target distributions (i.c. in Taxi, 13 in US Accident and 50 in the others), we present all target accuracies and Macro-F1 scores, as well the worst-distribution accuracy and Macro-F1 score among all target distributions Appendix D.6
D.7
D8
D.9
4.2 Analysis
Different algorithms do not exhibit consistent rankings over different shift patterns. In Fig- ure observe the rankings across different shifts are quite different, especially for ACS Income (CA PR) and ACS Mobility (MS-HHI where Y|X-shists dominate. This observation reaffirms the phenomena in Figure 2 that as -shishists become stronger, the relationship between source vs target performances becomes less consistent. In Appendix [D3] we also show that even for a fixed source distribution in fixed prediction task, algorithmic rankings of performances different target distributions vary lot.
Tree ensemble methods show competitive performance, but do not significantly improve the generalization drop between source and target data. From Figure SS] tree- ensembles (yellow bars) show robust and competitive performance the target distribution in 6 out of 7 settings. However, in Figure 6 which plots the performance degradation between source and target, tree ensembles do not show improved robustness. This suggests that they do not actually achieve better robustness against real-world distribution shifts, and their better performances on target data may simply be due better fitting the source distribution.
DRO methods are sensitive to configurations, with rankings varying significantly across different settings. From Figure 5, DRO methods exhibit competitive performances on ACS Mobility (MS+HI) Taxi (NYC-BOG), and ACS Income others. This sensitivity to configurations, as shown in Figure 7a (red points), could be attributed to
yet underperform in

---

Imbalance methods and fairness methods show similar performance with the base learner (oGBo) In our experiments, we choose the XGBoost model as the base learner for imbalance and fairness methods due its superior performance on tabular data [34]. However, from Figure and Figure 6 imbalance methods and fairness methods do not show a clear improvement upon their the worst-car case optimization that perturbs the training distribution within pre-defined uncertainty set, without any information regarding the target distribution. However, when target information is incorporated for hyper-parte pperr-paramtter tuning, as shown in Figure 7b there is notable improvement in the performance of DRO methods. Our observations suggest potential avenues for building more refined uncertainty sets in DRO methods.
base learner (XGBoost, last yellow bar). Further, as shown in Figure 7 imbalance methods (green) are also quite sensitive to configurations, and their performances do not improve much when their hyperparameters are tuned over the target data (Oracle).
Target information matters validation. Based on the ACS Income (CA-+PR) dataset, we compare different validation protocols, including the best average accuracy, minimum subgroup discrepancy, and best worst-subgroup accuracy on validation data generated from the source dis- tribution. We also use the Oracle validation that chooses the configuration with the best average accuracy on validation data generated from the larget distribution. In Figure 76, we find the first three protocols do not show a significant difference. However, oracle validation with target information substantially improves the effectiveness of both DRO and tree ensemble methods. We conclude using target information for model selection can provide robustness gains even with a small target dataset.
Non-algorithmic interventions warrant greater consideration. Reflecting on Section 3 it is clear that operational interventions yield significant enhancements for various methods, demon- strated in Figure 4e and Figure 4f In comparison to algorithmic interventions, such as designing different algorithms (e.g., DRO, Imbalance methods), data-centric approach can be more effective in addressing distribution shifts. For instance, research on feature collection and feature engineering methods may prove impactful. Another avenue for future work is developing methods that can optimally incorporate expensive samples from the target distribution.
5
Discussion
We explore the complexity of distribution shifts real-world tabular datasets in depth. Using natural shifts from 5 real-world tabular datasets across different domains, we specify each shift pattern and evaluate 22 methods experiments with over 86k trained models. Our benchmark WHYSHIFT encompasses various distribution shift patterns evaluate the robustness of the methods. We propose a simple but effective algorithm to identify regions with large Y X|X X-shifts, and through a comprehensive case study, demonstrate how a better understanding of distribution shifts facilitates algorithmic and bata- interventions. Our findings highlight the importance of future research to understand how and why distributions differ in real-world applications.
Our study leaves many open directions for improvements in future work. Our benchmark only includes tabular datasets from the economic and transportation domain. Considering datasets from other domains such as the medicine or those involving feature embeddings may highlight different types of distribution shift. On the algorithmic side, our angionnidentification target data to identify risky regions and cannot be used in cases where the target distribution is completely unknown. Furthermore, targeted data collection regions of X| X-shifts may be pose ethical and privacy concerns for marginalized groups. We provide more discussion in Appendix]] B
algorithm requires some
10

---

Acknowledgement
We thank Tiffany Cai for her help with implementing the DISDE method on our benchmarks. Peng Cui was supported in part by National Key R&D Program of China (No. 2018AAA0102004), National Natural Science Foundation of China (No. U1936219, 62141607). Hongseok Namkoong was partially supported by the Amazon Research Award.
References
[1] Other
taxi
dataset.
taxi rroutes-eeese forttes--o---eee www.moeeiiiiiyy-ee quito
[2] Us taxi
dataset.
http:://wwwkaagg http:///www.a.gggl..coo//co
nyc-taxi- ciip-duration/daae
[3] Robert Adragna, Elliot Creager, David Madras, and Richard S. Zemel. Fairness and robustness in invariant learning: A case study in toxicity classification. CoRR, abs/201 1. .06485, 2020.
[4] Alekh Agarwal, Alina Beygelzimer, Miroslav Dudík, John Langford, and Hanna Wallach, reductions approach to fair classification. In International Conference on Machine Learning. pages 60 69. PMLR, 2018
[5] Kartik Ahuja, Karthikeyan Shanmugam, Kush Varshney, and Amit Dhurandhar. Invariant risk minimization games. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 145-155. PMLR, 13-18 Jul 2020.
[6] Evelin Amorim, Marcia Cançado, and Adriano Veloso. Automated essay scoring in the presence of biased ratings. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pages 229-237, 2018.
[7] Shushan Arakelyan, Rocktim Jyoti Das, Yi Mao, and Xiang Ren. Exploring distributional shifts in large language models for code analysis. CoRR, abs/2303.09123 2023.
[8] Martin Arjovsky, Léon Bottou, Ishaan Guirajani, and David Lopez-Paz. Invariant risk mini- mization. arXiv preprint 190.:0997..02893 2019.
Peter Bandi, Oscar Geessink, Quirine Manson, Marcory Van Dijk, Maschenka Balkenhol, Meyke Hermsen, Babak Ehteshami Bejnordi, Byungjae Lee, Kyunghyun Paeng, Aoxiao Zhong, al. From detection of individual metastases to classification of lymph node status at the patient level: the camelyon17 challenge. IEEE transactions on medical imaging. 38(2):550-566 560, 2018
[10] Sara Beery, Arushi Agarwal, Elijah Cole, and Vighnesh Birodkar. The iwildcam 2021 compe- tition dataset. arXiv preprint arXiv:2105.03-49, 2021.
[11] Rachel K. E. Bellamy, Kuntal Dey, Michael Hind, Samuel C. Hoffman, Stephanie Houde, Kalapriya Kannan, Pranay Lohia, Jacquelyn Martino, Sameep Mehta, Aleksandra Mo- jsilovic, Seema Nagar, Karthikeyan Natesan Ramamurthy, John T. Richards, Diptikalyan Saha, Prasanna Sattigeri, Moninder Singh, Kush R. Varshney, and Yunfeng Zhang. Al faimess 360: An extensible toolkit for detecting and mitigating algorithmic bias. IBM Res. Dev., 63(4/5):4:1-4:55 2019.
[12] Sarah Bird, Miro Dudík, Richard Edgar, Brandon Horn, Roman Lutz, Vanessa Milan, Mehrnoosh Sameki, Hanna Wallach, and Kathleen Walker. Fairlearn: A toolkit for assessing and improving fairness in ai. Microsoft, Tech. Rep. MSR-7R-2020-32. 2020.
[13] Jose Blanchet, Yang Kang, and Karthyek Murthy. Robust wasserstein profile inference and applications to machine learning. Journal of Applied Probability, 56(3):830-857, 2019.
11

---

[14] Daniel Borkan, Lucas Dixon, Jeffrey Sorensen, Nithum Thain, and Lucy Vasserman. Nuanced metrics for measuring unintended bias with real data for text classification. In WWW, pages 491-500, 2019.
[15] Kailash Budhathoki, Dominik Janzing, Patrick Bloebaum, and Hoiyi Ng. Why did the distribution change? In Proceedings of The 24th International Conference on Artificial Intelligence and Staristics, pages 1666-1674. PMLR, 2021.
[16] Tiffany Cai, Hongseok Namkoong, Steve Yadlowsky, al. Diagnosing model performance under distribution shift. arXiv preprint arXiv:2303.0201/ 2023.
[17] Shiyu Chang, Yang Zhang, Mo Yu, and Tommi Jaakkola. Invariant rationalization. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 1448-1440 1458. PMLR, 13-18 Jul 2020.
[18] Rita Chattopadhyay, Wei Fan, Ian Davidson, Sethuraman Panchanathan, and Jieping Ye. Joint transfer and batch-mode active learning. In International conference on machine learning, pages 253-261. PMLR, 2013.
[19] Lu Cheng, Ruocheng Guo, Raha Moraffah, Paras Sheth, K Selçuk Candan, and Huan Liu. Evaluation methods and measures for causal learning algorithms. IEEE Transactions on Artificial Intelligence, 3(6):224-943, 2022.
[20] David A Cohn, Zoubin Ghahramani, and Michael I Jordan. Active learning with statistical models. Journal of artificial intelligence research, 4:129-145, 1996.
[21] Ian C Covert, Scott Lundberg, and Su-In Lee, Explaining by removing: A unified framework for model explanation. The Journal of Machine Learning Research. 22(1):9477-9566 2021.
[22] Elliot Creager, Joem--Henrik Jacobsen, and Richard Zemel. Environment Inference for Invariant Learning. In Proceedings of the 38th International Conference on Machine Learning, pages 1189-2200, PMLR, 2021.
[23] Gabriela Csurka. A comprehensive survey on domain adaptation for visual applications. In Gabriela Csurka, editor, Domain Adaptation in Computer Vision Applications, Advances in Computer Vision and Pattern Recognition, pages 1-35. Springer, 2017.
[24] Peng Cui and Susan Athey. Stable learning establishes some common ground between causal inference and machine learning. Nat. Mach. Intell., 1(2):110-115, 2022.
[25] Frances Ding, Moritz Hardt, John Miller, and Ludwig Schmidt. Retiring adult: New datasets for fair machine learning. Advances in neural information processing systems, 34:6478 -4940,6690, 2021.
[26] Dheeru Dua and Casey Graff. UCI machine learning repository, 2017.
[27]
John Duchi, Tatsunori Hashimoto, and Hongseok Namkoong. Distributionally robust losses for latent covariate mixtures. Operations Research, 71(2):649-664, 2023.
[28] John C Duchi and Hongseok Namkoong. Learning models with uniform performance via distributionally robust optimization. The Annaly of Statistics, 378-)11378-1400 2021.
[29] Chen Fang, Ye Xu, and Daniel Rockmore. Unbiased metric learning: On the utilization of multiple datasets and web images for softening bias. In ICCV, pages 1657-1664, 2013.
[30] Abolfazl Farahani, Sahar Voghoei, Khaled Rasheed, and Hamid R. Arabnia. A brief review of domain adaptation. CoRR, abs/2010.03978, 2020.
[31] Josh Gardner, Zoran Popović, and Ludwig Schmidt. Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation, 2022.
[32] Amirata Ghorbani and James Zou. Data shapley: Equitable valuation of data for machine
learning. In International Conference Machine Learning, pages 2242-2251. PMLR, 2019.
12

---

[33] Amirata Ghorbani, James Zou, and Andre Esteva. Data shapley valuation for efficient batch active learning. In 2022 56th Asilomar Conference on Signals, Systems, and Computers, pages 1456-1462. IEEE, 2022.
[34] Léo Grinsztajn, Edouard Oyallon, and Gaël Varoquaux. Why do tree-based models still outperform deep learning on tabular data?, 2022.
[35] Ishaan Guirajani and David Lopez-Paz. In search of lost domain generalization. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
[36] David Hand. Classifier technology and the illusion of progress. Statistical Science, 2006.
[37] Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning. Advances in neural information processing systems, 29, 2016.
[38] Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang. Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, Dawn Song, Jacob Steinhardt, and Justin Gilmer. The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization, 2021.
[39] Miguel A Hernán, Sonia Hernández-Diaz and James M Robins, A structural approach to selection bias. Epidemiology, pages 615-625, 2004.
[40] Weihua Hu, Gang Niu, Issei Sato, and Masashi Sugiyama. Does Distributionally Robust Supervised Learning Give Robust Classifiers? In Proceedings of the 35th International Conference on Machine Learning, pages 2029-2037. PMLR, 2018.
[41] Ahmed Hussein, Mohamed Medhat Gaber, Eyad Elyan, and Chrisina Jayne. Imitation learning: A survey of learning methods. ACM Computing Surveys (CSUR), 50(2):1-35, 2017.
[42] Badr Youbi Idrissi, Martin Arjovsky, Mohammad Pezeshki, and David Lopez-Paz. Simple data balancing achieves competitive woost-rroup-accurae In Proceedings of the First Conference Causal Learning and Reasoning, pages 336-351. PMLR, 2022.
[43] Bertrand looss and Paul Lemaître. review on global sensitivity analysis methods. Uncertainty management in imnuaation-optimiaaai of complex systems: algorithms and applications. pages 101-122, 2015.
[44] Ruoxi Jia, David Dao, Boxin Wang, Frances Ann Hubis, Nick Hynes, Nezihe Merve Gürel, Bo Li, Ce Zhang, Dawn Song, and Costas Spanos. Towards efficient data valuation based on the shapley value. In The 22nd International Conference on Artificial Intelligence and Statistics, pages 1167-1176. PMLR, 2019.
[45] Alistair EW Johnson, Tom J Pollard, Lu Shen, Li-wei Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G Mark. Mimic-iii, a freely accessible critical care database. Scientific data, 3(1):1-9, 2016.
[46] Jean Kaddour, Aengus Lynch, Qi Liu, Matt J Kusner, and Ricardo Silva. Causal machine learning: survey and open problems. arXiv preprint S.Ki::2206.1577.. 2022.
[47] Pang Wei Koh, Shiori Sagawa, Henrik Marklund, Sang Michael Xie, Marvin Zhang, Akshay Balsubramani, Weihua Hu, Michihiro Yasunaga, Richard Lanas Phillips, Irena Gao, Tony Lee, Etienne David, Ian Stavness. Wei Guo, Berton Earnshaw, Imran Haque, Sara M. Beery, Jure Leskovee, Anshul Kundaje, Emma Pierson. Sergey Levine. Chelsea Finn, and Percy Liang. WILDS: A Benchmark of in-the- -ild Distribution Shifts. In Proceedings of the 38th International Conference on Machine Learning, pages 5637-5664. PMLR, 2021.
[48] Ksenia Konyushkova, Raphael Sznitman, and Pascal Fua. Learning active learning from data. Advances in neural information processing systems, 30, 2017.
[49] Masanori Koyama and Shoichiro Yamaguchi. When invariance useful in an out-of-
distribution generalization problem ?, 2021.
13

---

[50] David Krueger, Ethan Caballero, Dinghuai Zhang, Remi Le Priol, and Aaron Courville. Out-of-distribution generalization via risk extrapolation (rex). In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning. volume 139 of Proceedings of Machine Learning Research, pages 5815-5822 PMLR, 18-24 Jul 2021.
Jacobsen, Amy Zhang, Jonathan Binas,
[51] Kun Kuang, Ruoxuan Xiong, Peng Cui, Susan Athey, and Bo Li. Stable prediction with model misspecification and agnostic distribution shift. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 4485-4492 2020.
[52] Sean Kulinski and David I. Inouye. Towards explaining distribution shifts. Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors, Proceedings of the 40th International Conference on Machine Learning. volume 202 of Proceedings of Machine Learning Research, pages 17931-17952, PMLR, 23-29 Jul 2023.
[53] Daniel Levy, Yair Carmon, John C Duchi, and Aaron Sidford. Large-scale methods for distributionally robust optimization. Advances in Neural Information Processing Systems, 33:8847-8860. 2020.
[54] Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy M Hospedales. Deeper, broader and artier domain generalization. In ICCV, pages 5542-5550, 2017.
[55] Richard Liaw, Eric Liang, Robert Nishihara, Philipp Moritz, Joseph E Gonzalez, and Ion Stoica. Tune: A research platform for distributed model selection and training. arXiv preprint arXiv:1807.055: 0118807.51188 18, 2018.
[56] Justin Lim, Christina X. Ji, Michael Oberst, Saul Blecker, Leora Horwitz, and David Sontag. Finding Regions of Heterogeneity in Decision-Making via Expected Conditional Covariance. https://anxivvorr/ab//111 10. 14508v. 2021.
[57] Evan Z. Liu, Behzad Haghgoo, Annie Chen, Aditi Raghunathan, Pang Wei Koh, Shiori Sagawa, Percy Liang, and Chelsea Finn. Just Train Twice: Improving Group Robustness without Training Group Information. In Proceedings of the 38th International Conference on Machine Learning, pages 6781 6781-6792. PMLR, 2021.
[58] Jiashuo Liu, Zheyuan Hu, Peng Cui, Bo Li, and Zheyan Shen. Heterogeneous risk minimization. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18-24 July 2021, Virtual Event, volume 139 of Proceedings of Machine Learning Research, pages 6814- PMLR, 2021.
[59] Zhuoming Liu, Hao Ding, Huaping Zhong, Weijia Li, Jifeng Dai, and Conghui He. Influence selection for active learning. In 2021 IEEE/CVF International Conference on Computer Vision, ICCV 2021, Montreal, QC, Canada, October 10-17, 2021, pages 9254-9266 9263. IEEE, 2021.
[60] Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions. Advances in neural information processing systems, 30, 2017.
[61] Rafid Mahmood, Sanja Fidler, and Marc T. Law. Low-budget active learning via wasserstein distance: An integer programming approach. In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022.
[62] John Miller, Karl Krauth, Benjamin Recht, and Ludwig Schmidt. The effect of natural distribution shift question answering models. In International Conference Machine Learning, pages 6905-6916. PMLR, 2020.
[63] John P. Miller, Rohan Taori, Aditi Raghunathan, Shiori Sagawa, Pang Wei Koh, Vaishaal Shankar, Percy Liang, Yair Carmon, and Ludwig Schmidt. Accuracy on the Line: On the Strong and In-Distribution Generalization. In Proceedings Correlation Between Conference on Machine Learning, pages 7721-7735. PMLR, 2021. of the 38th International
[64] Sobhan Moosavi, Mohammad Hossein Samavatian, Srinivasan Parthasarathy, and Rajiv Ram- nath. A countrywide traffic accident dataset. CoRR, abs/1996.05409, 2019.
14

---

[65] Sobhan Moosavi, Mohammad Hossein Samavatian, Srinivasan Parthasarathy, Radu Teodor- escu, and Rajiv Ramnath. Accident risk prediction based on heterogeneous sparse data: New dataset and insights. In Farnoush Banaei Kashani, Goce Trajcevski, Ralf Hartmut Güting, Lars Kulik, and Shawn D. Newsam, editors, Proceedings of the 27th ACM SIGSPATIAL. International Conference on Advances in Geographic Information Systems, SIGSPATIAL 2019, Chicago, IL, USA, November 5-8, 2019, pages 33-42. ACM, 2019.
[66] Jianmo Ni, Jiacheng Li, and Julian McAuley. Justifying recommendations using distantly- labeled reviews and fine-grained aspects. In EMNLP-IJCNLP, pages 188-197, 2019.
[67] Michael Oberst, Fredrik D. Johansson, Dennis Wei, Tian Gao, Gabriel Brat, David Sontag, and Kush R. Varshney. Characterization of Overlap in Observational Studies, 2020.
[68] Art B Owen. Sobol'indices and shapley value. SIAM/ASA Journal on Uncertainty Quantifica- tion, 2(1):245-251, 2014.
[69] Sinno Jialin Pan, Ivor W. Tsang, James T. Kwok, and Qiang Yang. Domain adaptation via transfer component analysis. In Craig Boutilier, editor, IJCAI 2009, Proceedings of the 2 International Joint Conference on Artificial Intelligence, Pusadena, California, USA, July 11-17, 2009, pages 1187-1192, 2009.
[70]
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Z. Yang. Zachary De Vito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang. Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high- peeg-peffrmance deep learning library. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d' Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information P Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pages 8024-8035 2019.
[71] Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, Jake VanderPlas, Alexandre Passos, David Cournapeau, Matthieu Brucher, Matthieu Perrot, and Edouard Duchesnay. Scikit-lcarn: Machine learning in python. Mach. Learn. Res., 12:2825- 2830, 2011.
[72] Jonas Peters, Peter Bühhmann, and Nicolai Meinshausen. Causal inference by using invariant prediction:
identification and confidence intervals. Journal of the Royal Statistical Society. Series B (Statistical Methodology), pages 947-1012, 2016.
[73] Veselin Raychev, Pavol Bielik, and Martin Vechev. Probabilistic model for code with decision trees. ACM SIGPLAN Notices, (1110))7117747 2016.
[74] Benjamin Recht, Rebecca Roelofs, I Ludwig Schmidt, and Vaishaal Shankar. Do imagenet classifiers generalize to imagenet? In International conference on machine learning, pages 5389-5400 PMLR, 2019.
[75] Marinka Zitnik Yuxiao Dong Hongyu Ren, Bowen Liu Michele Catasta Jure Leskovec, Weihua Hu, and Matthias Fey. Open graph benchmark: Datasets for machine learning on graphs. arXiv preprint arXiv:2005.0063 00687, 2020.
[76] Michael Roberts, Derek Driggs, Matthew Thorpe, Julian Gilbey, Michael Yeung, Stephan Ursprung, Angelica I Aviles-Rivero, Christian Etmann, Cathal McCague, Lucian Beer, et al. Common pitfalls and recommendations for using machine learning to detect and prognosticate for covid-19 using chest radiographs and scans. Nature Machine Intelligence, 3(3):199-217, 2021.
[77] Mateo Rojas-Carulla, Bernhard Schölkopf, Richard E. Turner, and Jonas Peters. Invariant models for causal transfer learning. J. Mach. Learn. Res., 19:36:1-36:34, 2018.
[78] Elan Rosenfeld, Pradeep Kumar Ravikumar, and Andrej Risteski. The risks of invariant risk minimization. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
15

---

[79] Shiori Sagawa, Pang Wei Koh, Tatsunori B. Hashimoto, and Percy Liang. Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization. arXiv: 1.08711, 2020.
[80] Roshni Sahoo, Lihua Lei, and Stefan Wager. Learning from a biased sample. arXiv preprint arXiv:2209.01754, 2022.
[81] Shibani Santurkar, Dimitris Tsipras, and Aleksander Madry. Breeds: Benchmarks for subpop- ulation shift. In International Conference on Learning Representations, 2021.
[82] Bernhard Schölkopf, Dominik Janzing, Jonas Peters, Eleni Sgouritsa, Kun Zhang, and Joris M. Mooij. On causal and anticausal learning. In Proceedings of the 29th International Conference on Machine Learning. ICML 2012, Edinburgh, Scotland, UK. June 26- - July 1, 2012. ieml.cc / Omnipress, 2012.
[83] Bernhard Schölkopf, Francesco Locatello, Stefan Bauer, Nan Rosemary Ke, Nal Kalchbrenner, Anirudh Goyal, and Yoshua Bengio. Toward causal representation learning. Proc. IEEE, 10965)=612-634, 2021.
[84] Burr Settles. Active learning literature survey. 2009.
[85] Soroosh Shaficezadeb--Abadeee Daniel Kuhn, and Peyman Mohajerin Esfahani. Regularization via mass transportation. Journal of Machine Learning Research, 20(103):1-68, 2019.
[86] Vaishaal Shankar, Achal Dave, Rebecca Roelofs, Deva Ramanan, Benjamin Recht, and Ludwig Schmidt. Do image classifiers generalize across time? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9661-9669, 2021.
[87] Jic-Jing Shao, Yunlu Xu, Zhanzhan Cheng, and Yu-Feng Li. Active model adaptation under unknown shift. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1558-1566, 2022.
[88] Jong-Chyi Su, Yi-Hsuan Tsai, Kihyuk Sohn, Buyu Liu, Subhransu Maji, and Manmohan Chandraker. Active adversarial domain adaptation. In Proceedings of the IEEE/CVE Winter Conference on Applications of Computer Vision, pages 739-748, 2020.
[89] Baochen Sun, Jiashi Feng, and Kate Saenko. Return of frustratingly easy domain adaptation. In Proceedings of the AAAI conference on artificial intelligence, volume 30, 2016.
[90] Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7167-7176, 2017.
[91] Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In CVPR, pages 5018-5027, 2017.
[92] Qing Wang. Jiechao Xiong, Lei Han, Han Liu, Tong Zhang, et al. Exponentially weighted imitation learning for batched historical data. Advances in Neural Information Processing Systems, 31, 2018.
[93] Andrew Wong, Erkin Otles, John P Donnelly, Andrew Krumm, Jeffrey McCullough, Olivia DeTroyer-Cooley Justin Pestrue, Marie Phillips, Judy Konye, Carleen Penoza, et al. External validation of widely implemented proprietary sepsis prediction model in hospitalized patients. JAMA Internal Medicine, 18 1816))106551000 2021.
[94] Hua Wu, Nontawat Charoemphakdee, Han Bao, Voot Tangkaratt, and Masashi Sugiyama. Imitation learning from imperfect demonstration. In International Conference on Machine Learning, pages
PMLR, 2019.
[95] Laure Wynants, Ben Van Calster, Gary Collins, Richard D Riley, Georg Heinze, Ewoud Schuit, Elena Albu, Banafsheh Arshi, Vanesa Bellou, Mare MJ Bonten, et al. Prediction models for diagnosis and prognosis of covid-19 19: systematic review and critical appraisal. bmj, 369, 2020.
16

---

[96] Binhui Xie. Longhui Yuan, Shuang Li, Chi Harold Liu, and Xinjing Cheng, Towards fewer annotations: Active learning via region impurity and prediction uncertainty for domain adaptive semantic segmentation. In IEEF/CVE Conference Computer Vision and Patlern Recognition, CVPR 2022, New Orleans, LA, USA, June 18-24, 2022, pages 8058-8066 8068.008. IEFE, 2022.
[97] Linyi Yang. Shuibai Zhang, Libo Qin, Yafu Li, Yidong Wang, Hanmeng Liu, Jindong Wang. Xing Xie, and Yue Zhang. Glue-x: Evaluating natural language understanding models from an out-of-distribution generalization perspective, 2023.
[98] Yuzhe Yang, Haoran Zhang, Dina Katabi, and Marzyeh Ghassemi. Change is hard: A closer look at subpopulation shift. CoRR, 0bs/2302.122544 2023.
[99] Yuzhe Yang. Haoran Zhang, Dina Katabi, and Marzyeh Ghassemi. Change is Hard: A Closer Look at Subpopulation Shift, 2023.
[100] Huaxiu Yao, Caroline Choi, Bochuan Cao, Yoonho Lee, Pang Wei Koh, and Chelsea Finn. Wild-time: A benchmark of in-the-wild distribution shift over time. In NeurlPS, 2022.
[101] Huaxiu Yao, Caroline Choi, Bochuan Cao, Yoonho Lee, Pang Wei Koh, and Chelsea Finn. Wild-time: A benchmark of in-the-wild distribution shift over time. Advances in Neural Information Processing Systems, 15:10399-10324, 2022.
[102] Han Yu, Peng Cui, Yue He, Zheyan Shen, Yong Lin, Renzhe Xu, and Xingxuan Zhang. Stable learning via sparse variable independence. AAAI, abs/2212.00992. 2022.
[103] John Zech, Marcus A Badgeley, Manway Liu, Anthony B Costa, Joseph Titano, and Eric Karl Oermann. Variable generalization performance of deep learning model to detect pneumonia in chest radiographs: cross- sectional study. PLoS medicine, 15(1 10026668 2018.
[104] Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair represen- tations. In International conference on machine learning, pages 325-333, PMLR, 2013.
[105] Runtian Zhai, Chen Dan, Zico Kolter, and Pradeep Ravikumar. DORO: Distributional and Outlier Robust Optimization. In Proceedings of the 38th International Conference on Machine Learning, pages 12345-12355 PMLR, 2021.
[106] Haoran Zhang, Harvinect Singh, Marzyeh Ghassemi. and Shalmali Joshi. "Why did the Model Fail?": Attributing Model Performance Changes Distribution Shifts, 2023.
[107] Xingxuan Zhang, Yue He, Tan Wang, Jiaxin Qi, Han Yu, Zimu Wang. Jie Peng, Renzhe Xu, Zheyan Shen, Yulei Niu, et al. Nico challenge: -uttof-distiibution generalization for image recognition challenges. In Computer Vision-ECCC 2022 Workshops: Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part VI, pages 433 4500 Springer, 2023.
[108] Sicheng Zhao, Bo Li, Xiangyu Yue, Yang Gu, Pengfei Xu, Runbo Hu, Hua Chai, and Kurt Keutzer. Multi-source domain adaptation for semantic segmentation. arXiv preprint arXiv:1910.12188 2019.
17

---

Appendices
Relevant Work
18
On Distribution Shifts
18
A.2 Connection between Non-al alorithmi Interventions and Algorithmic Interventions
19
Discussion on Limitations
21
Case Study Details
22
DISDE to -hshifts and Y shiifts
22
Prevalence of XShiffs
22
Details of Algorithm
22
Analysis of Decision Tree
24
Details of Non-algorithmic Interventions
25
C.6 Potential Alternative Approach of Identifying Risk Region
25
Benchmark Details
26
D.1
Datasets Settings
26
D.2
Algorithms & Implementations
................................
27
D.3
Parameter Search Space
................................
28
D.4
Training Details
30
D.5
Detailed Results of Selected Settings in Main Body
30
D.6
Full Results of 22 Settings
32
Worst-Domain Accuracy
32
D.8
Average Macro-Fi Score
32
D.9
Worst-Domain Macro-F1 Score
32
D. 0.10 Agreement and Maintenance Plan
38
Relevant Work
A.1 On Distribution Shifts
Distribution Shift Benchmarks. Existing distribution shift benchmarks primarily concentrate
on image and language datasets [74
47
107
101 to assess the robustness and efficiency of 8]
algorithms in real applications.
We briefly review benchmarks that address distribution shifts across various data types, including image and language data. For image data, several datasets capture natural distribution shifts, such as spatial and temporal variations. PACS [54) and Office-Home [91] categorize environments to be image styles. VLCS [9] and iWildCam
their primary environments as data sources. DomainNet [108) is built on PACS and provides a more extensive selection with additional domains and categories. recent developments, Koh et al. [47] collect several datasets to establish WILDS, setting new structure for OOD generalization. Similarly. Yao et al. [100] introduced Wild-Time, highlighting temporal distribution shifts across diverse real-world scenarios. For language data, Civi 1ommeents [14] and Amazon [66] consist of individual comments collected from different users and distinctive groups (e.g. male and female). GLUE-X [97] provides a unified benchmark for evaluating OOD robustness in NLP models. For other types of data, OGB-MOIPCBA [75 collects
[TO]
18

---

molecular graphs in over 100,000 scaffolds and formulates a molecular property prediction task across different scaffolds. Towards auto-engineering, Py150 77 contains codes from 8,421 1 git repositories for code completion generalization.
However, these datasets/henchmarks do not specify investigate in-depth the distribution shift patterns, and there is a noticeable lack of benchmark papers that specifically address real-world tabular datasets. These tabular datasets often present distinct patterns compared image/language datasets, including prevalent methods +
and shift patterns.
Therefore, it is important to understand detailed distribution patterns among these datasets develop corresponding methodologies to address specific shifts, which is also observed a recent bench- mark [TOI]. Yang et al. [99] recently introduce one benchmark characterizing different patterns of subpopulation shift. This benchmark focuses on the relationship between a specific attribute and covariates, such as spurious correlation, which can be challenging to identify in tabular datasets. Besides, they focus on changes in the subpopulation, which is a subset of distribution shift patterns. For example, individuals in different states may suffer from little subpopulation shifts but still incur large distribution shift. Individuals' demographic features are similar but the income level differs greatly between CA and PR in ACS Income, demonstrated in Table 2 Besides, Kulinski and Inouye [52] use optimal transport to explain the shift between two distributions recently. But their method could not explicitly decompose the performance degradation as in our work. Motivated by the challenges above, our work hopes to fill in the gap by demonstrating one benchmark on tabular datasets with detailed analysis.
Table 2: Descriptive Characteristics under different states in ACS
income dataset
State
CA
MA
NY
NE
MT
SD
PR
Total Size
195665
40114
103021
10785
5463
4899
9071
White Man
0.3311
0.4161
0.3687
0.4822
0.4959
0.4691
0.3526
Nonwhite Man
0.1969
0.0878
0.1379
0.0454
0.0428
0.0492
0.1818
White Woman
0.2873
0,4066
0.3464
0.4318
0.4221
0.4297
0.3124
Non White Woman
0.1847
0.0895
0.1471
0.0404
0.0392
0.0521
0.1532
P(Y= 0)
0.589
0.532
0.585
0.688
0.707
0.730
0.894
Choice of Domains in Distribution Shifts Although it is popular in the fairness literature to set each demographic subgroup in the adult and ACS dataset as one domain [04] [2] 25), the relative regret of models trained on these domains is quite small shown in Figure empirically. This implicitly shows that Y| X-hiffts are not strong across different demographic subgroups. In contrast, the model usually experiences relatively large X-hiisssss under different spatial domains, which corresponds to the right-hand side of Figure Besides, from the practical perspective, machine learning models often need to be deployed in spatialtemporal domains (by city, state, and country-wise; by year) only with few observed data while the model is trained with abundant data from the source domain. This why we mainly choose spatiotemporal domains benchmark distribution shifts in our case.
A.2
Connection between Non-algorithmic Interventions and Algorithmic Interventions
Here we discuss the connections between our non-algorithmic interventions and several branches of methods addressing the distribution shifts, including active learning, imitation learning, causal learning, feature sensitivity analysis, and feature importance analysis.
Active Learning. Active learning aims to improve model performance by acquiring a limited number of labels from the target distribution. See the survey [4] for detailed reference. The challenge here to quantify the value of unlabeled data so that we can select samples better. The selection criterion of existing approaches includes estimated variance (20]. influence on the model
performance (59), and Shapley value
32 33 44, or source-target distance metrics through the
importance weighting [18 61). Some work also proposed running regression problem for the query procedure based on learning strategies from the existing dataset [48]. Specifically, the target
distribution where query data and aim to evaluate the model subsequently differs from the source
19

---

distribution. Some work also develops active learning methods on domain adaptation to select additional samples from the target distribution [8] 87 However, these works usually assume some restricted distribution structures between the source and target distribution such as only X-shifts oceur, which may not hold in the tabular data. contrast, we assume we have a few labeled target data but impose no restrictions on the two distributions. And we sample data in specific regions after identifying regions where we experience the largest Y sshitts.
Imitation Learning Imitation learning aims to mimic the behavior of the expert with some off- policy data. This usually occurs in the reinforcement learning setup where a learner aims to learn the best action given each state [1].. Here, distribution shifts occur due to the mismatch of the state coverage between the observed data (source domain) and the environment to deploy (target domain). This raises the need for the importance sampling method match the two distributions in imitation learning 192 94]. In fact, the underlying conditional distribution does not change only with covariate (state) shifts in the imitation learning setup. Therefore, thiis does not fit into our where the conditional distribution between the source and target domains differ.
Causal Learning Causal learning methods receive much attention in the field of machine learning.
The core idea of causal learning [72 8 is to learn causally invariant relationships across multiple pre-defined training environments. Arjovsky et al. [8] propose Invariant Risk Minimization (IRM)
49 5 (50 propose variations with similar invariant regularizations. However, the effectiveness of these methods are challenged both theoretically and empirically. Theoretically, Rosenfeld et al. (78) illustrate that IRM could fail in nonlinear context, and Liu al. (58) demonstrate that the learned invariance property largely depends on the quality of pre-defined environments. Empirically, Guirajani and Lopez- -Paz 35 show that when carefully implemented and tuned, ERM still outperforms the state-of-the-a methods in terms of average performance.
to learn invariant representations across environments, and follow-up works [17
Compared with the simple non-algorithmic interventions in this work, causal learning methods rely heavily on the invariance assumptions and have strict requirements on the quality of multi- environment data. This restricts their applicability in practice, since modern datasets are often collected without explicit environment labels, and in many scenarios, it is quite hard to pre-define meaningful environment labels. Our proposed non-algorithmic interventions (collecting features and data) do not rely on the invariance assumption, and it could serve as a "solution" when observing performance degradation, which helps analyze the model failure and to direct further improvements. And we hope that these simple data-centric interventions could inspire future research in this direction to mitigate the effects of distribution shifts.
Since we are also considering other missing features to improve the performance under distribution shifts, there are some works providing insights on the feature / region importance to the final output.
Feature Analysis: Sensitivity and Importance. There are two streams of literature measuring the relationship between input features and the response variable. These feature sensitivity analysis and feature importance. Feature sensitivity analysis aims to quantify the sensitivity of the performance metrics to each input. This helps understand the impact of variations in input features on the output of a simulation system. Classical metrics include ANOVA, Sobol indices (68) and Morris methods
43). Mcanwhile, feature importance aims to understand the performance decomposition of different algorithms. Shapley value-based approaches gain the most popularity in understanding the attribution of predictions to each input feature [60, 21].. Some work leverages these ideas to understand the difference in distribution shifts to each existing input feature in the data [15] 106). They decompose the shift on the joint distribution to particular X,-shifts or the condition X,I XX,-shfst (X, and X; denote different features) under a known causal graph. In contrast, we investigate the additional missing feature beyond existing datasets and aim to reduce the performance drop under distribution shifts in our paper. Specifically, we focus on the local regions where the distribution incurs the largest shifts and add the feature ENG in our main body due to our prior knowledge that "ENG" feature would yield the largest difference in that subpopulation between two distributions. Our region-based
20

---

approach, in fact, can be further rigorously extended to investigate the marginal distribution of what features would yield the largest difference in that region between two distributions. We hope this can inspire researchers to apply refined tools in this line such as Shapley value to help understand and mitigate distribution shifts.
Region Analysis: Attribution of Distribution Shifts. Similar to our algorithmic goal in Sec- tion of identifying regions where model learners are different, Oberst et al. [67] and Lim et al. [56] developed specific methods to identify specific covariate regions where model learners different. The difference between their setup and ours lies in the sampling and assumption of observed data. In their approach, the observed data is sampled ii.d. actoss various prediction models, without any distribution shift. Besides, they can observe only one selected prediction result per sample from all the model learners. However, in case study, the models are built datasets from two domains that experience distribution shifts. As a result, we can further isolate the model difference based on the shared input space X and differentiate it from the total difference, specifically focusing the Y|X- shifts.
B Discussion on Limitations
We discuss some limitations of our work.
For Benchmark First, only consider the source-target transfer pairs from datasets including the economic and transportation domain, and we leave the detailed pattern evaluation of these datasets in other domains such as the medical area (e.g. MIMIC-III (45) as interesting direction of the future work. Besides, we only consider the source and target from one fixed domain (i.e. one state or city). In practice, it is reasonable to extend this benchmark to consider the source and target distribution with multiple domains of varying proportions. Our results of characterizing the distribution shift patterns highlight the importance of utilizing other refined tools. These tools help us understand the difference between real-world distribution shifts and enable further investigation and analysis.
Our Algorithm is proposed to identify risky regions with large Y| X-hiftss when observing severe model degradation between the source target distributions. Therefore, one limitation that requires target data to identify the risky regions with large Y X -hifts. This algorithm cannot evaluate the generalization performance when the target distribution is completely unknown.
For Algorithm] 1
Furthermore, when conducting non-algorithmic interventions based on the risky regions learned by researchers should be careful and incorporate more background knowledge to find
Algorithm [ the proper way. For example, in Section 3.2 we analyze the risky regions and find that the "ENG" feature may be important mitigate the Y X-siifts. This is from prior knowledge that the official language between the two states different. Also, when Algorithm is misused (e.g., the learned risky regions are used without destination not being checked carefully), it might harm some vulnerable groups
For Data-Collection In Section 3.2 we propose two simple non-algori interventions to mitigate the -shifts,, one of which is to efficiently collect target data from the risky region. It achieves much better results combined with several typical methods on our benchmark. However, in practice, we acknowledge that this technique could only be used when we can obtain data from the target distribution and the data collection procedure does not raise any privacy concerns and predatory inclusion.
Applicability Across Different Data Modalities In this work, we focus on real-world distribution shifts in tabular data settings. We propose Algorithm to find the risk regions and come up with some simple data-based interventions. Therefore, we do not investigate in-depth the applicability of the proposed methods across other data types. However, we argue that our proposed Algorithm I could generalize to complicated data types (c.g., image data) with corresponding deep models.
21

---

Specifically, both the domain classifier (to estimate P(X from Qx(X)) and region learner h(X) should be replaced by deep neural networks, And our data-based interventions also have the potential to incorporate with more complicated data types. We leave this investigation to future work.
C Case Study Details
In this section, we provide more details about our case study in the main body.
C.1 DISDE to X-shifts and Y|X-shifts -shiffts
When facing performance degradation under distribution shifts, one direct idea is to figure the reasons why the performance drop. To this end, Cai et al. [16] propose DIstribution Shift DEcomposi- tion (DISDE) to attribute the total performance degradation to -|X-shifts and X-shifts. Specifically, given samples (X, Y) from distributions P' and Q, to quantify the discrepancy between Pyix and Qyjx. they first control the marginal distribution on X' by introducing the shared distribution Sx. From that, we can estimate the performance degradation caused by Xssiiiss and that caused by X-shifts could also be estimated by comparing Sx with Px and Qx respectively. Note that DISDE could be used in image datasets (see Section 4.2 in [16). The official code for DISDE could be found at battps://gitee
com namkoong lab/disde disde
We specify the formula of DISDE as follows:
Eql((fr(X), Y)]
Ep Ep(e(fr(X),)])
Es [X]( Ep Ep(Rp (X))
(I)
+ Exx (X) - [X)(
(II)
+ (x Esx [XQ
(III)
where := E,,((((X Y)IX = x]] for P.Q is denoted as the conditional risks on P and Q. 8x is the share distribution with support contained in both Px and Qx. Then we see the sum of the two terms (1) and (III) as the performance drop auributed to X -shifts and the term (II) as the performance drop attributed to Y|--shifts. Besides, we also implement DISDE in our released package named WHYSHIFT, which could be found at https: bttps://gtt github........ com/ com/namkoong lab/ whyshift
C.2 Prevalence of XSS-fissss
For each of the settings in Table we only select one target distribution in the main body, while our benchmark supports multiple target distributions. Specifically, for ACS Income, ACS Mobility, ACS Pub.Cov, we have 50 target distributions (the other 50 American states) in total for each setting; for Taxi, we have target distributions (other cities Mexico City, Bogotá, Quitio); for the temporal shift version of ACS Pub (i.c. setting 6), we have 3 target distributions (i.c. the year 2014, 2017, and 2021); and for US Accident, we have 13 target distributions (13 American states). Therefore, we have 169 source-targer transfer pairs in total for these 7 settings.
We use XGBoost classifier and calculate the decomposition of performance degradation via DISDE We calculate the "|X -shift ratio from the source distribution to the target distribution Q:
16
Esx (Sx]|R(XX: - Rp(X)]
X|S-shift ratio-
EQ [((s((())))))) Y) Ey [()((([(X)))))
where (X) is defined in Appendix C We first focus on pairs with relatively strong distribution shifts (i.e. performance degradation larger than 8 percentage points). Across these pairs, we find that 70.2% pairs have over 60 % Y|X -shifts, and 87.2% % pairs have over 50% Y|X-shiftis indicating the prevalence of Y|X shifts. To visualize the result better, in all 22 settings in our benchmark (as shown in Table 3). we focus on transfer pairs with performance degradation larger than 5 percentage points and plot the histogram of the ratio of Y [X- [S-siifts in Figure From Figure 8 Thifftss are prevalent in real-world distribution shifts.
we could see that
C,3 Details of Algorithm i
In this section, we provide more detailed introduction of our proposed Algorithm I We propose a simple yet efficient method to identify data regions with strong Y|X shifts, and could inspire operational and modeling interventions as shown in Section 3.2
22

---

Density
0.0
0.2
0.4
0.6
0.8
1.0
YIX Ratin
Figure 8: Histogram of Y|X shift ratio in our benchmark.
Consider a model f X + y that predicts outcome Y from covariates X. Let ((f(x), y) be loss function denoting notion of predictive error (c.g., cross-entropy loss, mean-square error). Our goal to identify a region S S X where P(Y ()) differs a lot from Q(Y order to directly compare X) and Q( (X), we must do apples-to-apple comparison: we cannot know Q( XX) for X's that are primarily observed in (and vice versa).
To address this, we first construct shared distribution Sx over X whose support is contained in that of both Px and Qx- We choose specific shared distribution Sx over whose support is contained in that of Px and Qx (following [16]). Ideally, the chosen shared distribution would exhibit higher density when both Px and Qx densities are high, and a lower density when either of the two possesses low density. This strategy effectively allows regions of shared density to be more pronounced. Recall that px. qx, sx are the densities of X under P. Q and S, we formulate s as
xx (I) x px(x) (x) ax (x)).
(C.1)
Choices of Sx Here would like to discuss different choices of Sx provide more intuitions. As demonstrated in [16), we can use many forms of the shared distribution. For example, we could choose the following form:
(x x min(px(x)) gx (x)},
(C.2)
which guarantees that the support of Sx is contained in that of both Px and Qx Another choice is:
1x (x) if minfaxle) (x(1)) 0
ex(m)) px(7) px(r) 2 c,
xx (x)
(C.3)
otherwise,
for some 6 2 0. This form of Sx defines shared samples as those with high likelihood ratios. Notably, for all the three forms of Sx, Px = Qx then Sx = Px = Qx. And when px (x: >> qx (x) or Px(x) (x) < 9x (x), Equation [CI1 and Equation (C.2 become similar. In our Algorithm 1 we use the
form of Equation [C.I). and Cai et al. [66 observe that practice the qualitative conclusions are not very sensitive to the specific choice of shared distribution.
Intuitions behind Algorithm I Sx, we reweight samples from Px and Qx using the likelihood ratios:
Since we do not have access to samples from the shared distribution
Sx (x)
9x
SX (x) x
Px (x
and
(C.4)
(x + (x)
px (x + (x)
Then we define à as the proportion of the pooled data that comes from distribution Q:
niQ
and *(x)) = T from Qx x)),
(C.5)
n. + nQ
23

---

where A (x) denotes the probability of sample to come from Qx Using Bayes' rule, we have:
[ P(X x X from Qx PP( from Qx)
ág(z) 0g + (1 -a)p(a)
P(())
(C.6)
&
â + (1 p( (())
Noting that the ratio (xx) can be modeled as the probability that an input came from Px vs Qx we train a binary "domain" classifier to estimate the ratios. (The "domain" classifier can be any
black-box method, and we use XGBoost throughout.)
Then the likelihood ratios that we care about could be reformulated as:
Px (xx
8X
(x)
X
and
8X
(z)
(C.7)
Px
(x
qX
(at
(z)
9x (ar
which gives that:
8x (x) (1 (1- ()) + a(1 म (x))
((x)
8X (x)
1-#
and
(C.8)
Px
qx
-1-
())())(()))) + a(1 - +(x))
After obtaining the likelihood ratios sx (ar) and Ex (x), could do apples-to-apples comparison: we estimate Pr|x and Qrix over the shared distribution Sx (using XGBoost F))
px
2x
dSx dPx (x)
fr == arg min feJ
Esx Ee(e(T(X))
= Er ((((X),)) Y)
(C.9)
So = arg min FEJ
Esx
(ole((())))))
= Eg ((((())))
dSx dQx (x)
(C.10)
Then, for any threshold 6 E [0, 1], fa E X
2 b} suggests region that may suffer
model performance degradation due to Xshifits..
C.4 Analysis of Decision Tree
In Algorithm 1. we use a shallow decision tree l((x) to approximate y= [fr(x) [Q(x) on the shared distribution Sx find the covariate region with highest discrepancy. In our decision tree, we use the squared error as the splitting criterion. And below we demonstrate that this criterion is equivalent to maximizing the discrepancy between two children nodes.
Suppose there are N samples with outcomes JEEN belonging to tree node fa, and these samples are split into two children nodes 81, 82, where the node 81, 82 denote the set of sample indices in the two children nodes respectively. The squared error criterion to split fa into 81 and 82 is:
min ((1, $1,82
1 N
Σ (ys -Y,1) + Σ (y: mY:2)) } 18
(C.11)
iE82
where
Σ Ci (ies) ΣN 1(ie)))
Σ Dizt y (ie
NY2 ==
(C.12)
EN ((iss))
denote the mean values of the outcome Y with samples in children nodes and 82. Denote the distribution of the outcome follows the empirical distribution over the N samples {y, {y.hee]]-
Simplifying C..II have:
C(31, = P(Y E Var,, (Y) + P(Y E Var,, (Y) EEs (ar(Y
(C.13)
where Var, (Y) denotes the variance of the outcome variable Y node 8, S (81, 82 is the variable representing the children nodes. Therefore, given that Var (Y)(== Vars (E((())))))) + E. Var(Y ()))
constant, the minimal [s[Varr( Var(Y| corresponds with the largest Vars (E which maximizes the discrepancy of the outcome between two children nodes.
24

---

C.5 Details of Non-algorithmic Interventions
In Section 3.2 we propose two potential non-algorithmic interventions to mitigate the performance degradation. In this section, introduce in detail the intervention of collecting specific data from the target.
Experiment Setup We focus on the income prediction task using the ACS Income dataset. Con- sider practical scenario where the training consists of 20,000 samples from California (CA) and the trained model was deployed in Puerto Rico (PR) trial. After the trial deployment in PR, we got small amount of samples from PR with labels and observed performance degradation. Under this setting, we investigate the effect of non-algorithmic interventions.
Collect specific data from the target We first identify the regions with high discrepancy between source and target. Note that the sample size of the target state is small compared to the training samples. Then for typical algorithms like logistic regression (L.R), MLP, random forest (RF), LightGBM and XGBoost, compare the performances of:
original setting (only 20,000 samples from the source);
original setting with N additional random samples drawn from the whole target state;
original setting with N additional random samples drawn from the risk region of the target
state.
In this experiment, we first select the best configuration of each method according to the i.i.d validation set in the original setting (only samples from CA), and fix it for the other two interventions. We vary N as 100, 200, 300 and the results are shown Figure g From Figure g incorporating data from the risk region leads to a stable improvement on typical algorithms even for small target sample sizes. However, we observe that LightGBM and XGBoost would easily overfit fo on the target data, and we use random forest under this setup alternative. It is worth investigating approaches to find risk regions effectively under small/imbalanced sample sizes the future. The approach mentioned here is simple way of non-algorithmic and explainable interventions and we hope could inspire further research in this direction.
Original Setting
Region
Original Seking
Region
Tost Accusay
Add Target Data
Teat Accurcy
Add Targer Data
LightGBM XGBoost
MLP
RF
LightGBM XGBoost
(a) N 100
(b) N 200
Otiginal Setting
Add Region Data
Test Accurncy
Add Targot Data
MLP
LightGBM XGBoost
(c) N 300
Figure 9: Test accuracies of different ways incorporate data.
C.6 Potential Alternative Approach of Identifying Risk Region
In Algorithm we propose simple way to identify the risk region to explain the cause of Y|X -shiffs. And the identified region could be used to guide the collecting process of target data, which could help to further reduce the effects of performance degradation. However, in practice, when the amount of target samples is quite small, it may be hard to train the fo only with target samples accurately.
25

---

Therefore, it may be better to propose method that does not need fo to fit Q( on the target distribution.
Following this idea, we propose an alternative way of Algorithm 1 it is feasible to fit fo the shared distribution Sx
Since the training data is enough,
dSx
(((X),))
Sp argmin Ep fEF
(C.14)
dPx
Then for no samples from target distribution Q. we could use prediction model h(x) to approximate |Y -Yfp(XX) on the shared distribution (by reweighting density ratio d5x). Note that this method does not need train fq on target samples, but the quality of the density ratio dSx / /dPx and the prediction model hxx) still depend on the target samples. We hope the estimation of the ratio and the residuals YY fx( can be less affected by the low sample size no. This nonaalgoii intervention is not the main focus of this work, but we hope this idea could help to promote this line of research.
aQx
D Benchmark Details
In this section, we provide the details of our benchmark. our benchmark, we explore distri- bution shifts on 5 real-world tabular datasets from the economic and traffic sectors with natural spatiotemporal distribution shifts. We carefully design 22 settings utilizing these datasets, and the overview of 22 settings is shown in Table 3 Note that in our main body, due to space limitations, we only pick typical settings and select only one representative target domain for each setting, Detailed introductions of all datasets, algorithms, and experiment settings will be given in the following sections. A Python package for our benchmark can be found at https: // / www.tttub.oooooooeeee www.w/ooo/mooo.....o largg-lab/whhhhh lab/whyshihttt
as shown in Table
Table 3. Overview of datasets and the whole 22 selected settings. In our benchmark, each setting has multiple target domains (except the last setting). In our main body, select only target domain for each setting. o: report the "Dom. Ratio" to represent the dominant ratio of Y ||X--si [Ssifffsts X X-sifft in source-target pairs with performance degradation larger than 5 percentage points each setting. For example, "Y|X: 13/14" means that there are 14 target pairs in Setting with degradation larger than percentage points and 13 out of them with over 50% degradation attributed to Y|X shifts. We
use XGBoost to measure this.
AID
Dataset
Type
#Features
Outcome
Source
#Train Samples
#Tet Damains
Dom, Ratio"
ACS
Incone
Sputial
1ncome250k
California
195 665
50
XIx: 13/14
ACS
Incone
Spatial
Income 250k
Connectiut
19,785
50
Y X| 24/24
ACS
Income
Spatial
Income250k
Masachusett
40,114
50
Y 21/22
Incoma
Spatial
Income250k
South Dakota
4,899
50
X :99
ACS
Mobility
Sputial
21
Residential Address
Mississippi
5,318
50
Y YIX 28/34
Kobility
Sputial
Residential Address
New York
40,463
50
Y 30031
7
ACS Mobility
Sputial
21
Residential Address
California
$0,329
50
Y YIX 9/17
Mobility
Spatial
Residential Address
Pennsylvamia
Taxi
Spatial
Duration time 30 min
Bogolá
3,063
3
X 1/2
10
Taxi
Spatial
Duration time min
New York City
1,488,646
Y 3/3
11
Pub.Com
Sputial
Public Ins. Coverage
Nebraska
6,332
50
Y X 32/39
12
ACS Pub. Cay
Sputial
18
Public Ins. Coverage
Florida
71,297
50
Y X 28/29
Spatial
Public Ins. Coverage
Texas
98,928
Y X
14
ACS Pab
Spatial
18
Public Ins. Coverage
Indiana
24,330
50
Y XIX 11/13
Accident
Sputial
Severity Accident
26,664
Y
16
US Accident
Spatial
Severity of Accident
Califomii
64,909
13
22/31
17 US Accident
Spatial
47
Severity of Accident
Florida
32,278
13
X: S77
Accident
Spatial
Severity of Accident
Minnesota
8,927
19
ACS Pob. Cav
Temporal
18
Public Ins. Coverage
Year 2010 (NY)
73,208
X 22
Pub. Cov
Temporal
Public Ins. Coverage
Year (CA)
149,441
2/2
21
ACS Income
Synthetic
nicome-500
Younger People (80%)
20,000
X 1/1
22
ACS Income
Synthetic
Income250K. 50k
Younger People (90%)
20,000
1/1
D.1 Datasets & Settings
Here we introduce 5 real-world tabular datasets in detail. ACS Income, ACS Mobility, ACS Public Coverage are based on American Community Survey (ACS) Public Use Microdata Sample (PUMS) (25). And here use the same data filtering as (25).
26

---

ACS Income The task is to predict whether an individual's income is above $50,000. We filter the dataset to only include individuals above the age of 16, usual working hours of at least hour per week in the past year, and an income of at least $100.
In our Setting 1 1~4, we use data from 2018 and the source/target domain refers to Amer- ican states, which contain natural spatial distribution shifts. We train methods on data from California, Connecticut, Massachusetts, and South Dakota respectively, and test the generalization performance on the other 50 American states.
In our Setting 21~22, we sub-sample the dataset according to age to introduce covariate shift, where we focus on individuals from California and form two groups according to whether their age is 2 25. In Setting 21, the source data over-samples the low age group where 80% is drawn from the age 2 25 group, and the proportions are reversed the target data (20% from age 2 25 group). In Setting 22, the source data over-samples the low age group where 90% drawn from the age 2 25 group, and the proportions are reversed in the target data (10% from age > 25 group).
ACS Mobility The task is to predict whether an individual had the same residential address one year ago. We filter the dataset to only include individuals between the ages of 18 and 35, which increases the difficulty of the prediction task.
In our Setting 5-8, we use data from 2018 and the source/target domain refers to American states, which contain natural spatial distribution shifts. We train methods on data from Mississippi, New York, California, and Pennsylvania respectively, and test the generalization performance on the other 50 American states.
ACS Public Coverage focus on low-income individuals who are not eligible for Medicare by filtering the dataset to only include individuals under the age of 65 and with an income of less than $30,000.
The task is to predict whether an individual has public health insurance. We
In our Setting 11~14, we use data from 2018 and the source/target domain refers to American states, which contain natural spatial distribution shifts. We train methods on data from Nebraska, Florida, Texas, and Indiana respectively, and test the generalization performance the other 50 American states.
In our Setting 19~20,, we consider the temporal shifts. We use data from 2010 in training and data from 2014, 2017, and 2021 in testing (3 test domains). Setting 19, the training data come from New York, and in Setting 20, the training data come from California.
US Accident
The task to predict whether an accident severe (long delay) or not (short delay) based on weather features and Road conditions features.
In our Setting 15,188 the source/target domain refers to American states, which contain natural spatial distribution shifts. We train methods on data from California, Florida, Texas, and Minnesota respectively, and test the generalization performance on other 13 American states. Here we only involve 13 test domains because the sample sizes in the other states are quite small.
Taxi The task is to predict whether the total ride duration time exceeds 30 minutes, based on location and temporal features. We filter the data in 2017 and remove some extremely large or small features (e.g. samples with too long distances which can be easily classified).
In our Setting 9~,0, we use data from 2016 and the source/target domain refers to different cities. We train methods on data from Bogota and New York City and test the generalization performance in the other cities.
D.2 Algorithms & Implementations
In our benchmark, we evaluate 22 algorithms that span wide range of learning strategies on tabular data and compare their performances under different patterns of distribution shifts we construct. Concretely, these algorithms include:
27

---

Base Methods We include some typical supervised learning methods for tabular data: Logistic Regression (LR), SVM, and fully-connected neural networks (MLP) with standard ERM optimization. For L.R and SVM, we use the standard implementation in scikit-learn CPUs. For MI.,, we implement it via PyTorch 77] and train it on GPUs.
71 and train them on Tree Ensemble Models
As shown by Gardner et al. [31] several tree-based methods achieve good performances on tabular datasets. And gradient-boosted trees (e.g., XGBoost, LightGBMM are widely considered as the state-of-the-art methods on tabular data. Therefore, we evaluate XGBoost and LightGBM in our benchmark. Also, we evaluate Random Forest (RF) incorporate the performance of tree bagging methods.
DRO Methods Distributionally Robust Optimization (DRO) methods are proposed to address the distribution shifts, which is the form of:
min sup EQ (ol((fe(XX,)) EE QEP(P(.)
(D.1)
where P(Ptr) denotes the uncertainty around the training distribution Ptr- Following Gardner al. [1]. we implement two typical variants of DRO, namely CVaR-DRO and X2-DRO. CVaR-DRO is equivalent Conditional Value at Risk (CVaR), and -DRO uses x² divergeence
regulate the uncertainty set. We use the fast implementation [53] in PyTorch [70]. We also consider the DORO [055, which discards proportion e of the largest error points in each iteration mitigate the outliers in DRO with two variants, CVaR-DORO and x²-DORO. We also evaluate the Group DRO [79], which is proposed to minimize the gorst-group loss and shows good generalization performances on many vision tasks. This method needs the group label and we define groups according to the "SEX" feature on ACS datasets. For Accident and Taxi, we do not run Group DRO, since the current Group DRO model in the codebase only accepts the input with few groups while is hard to define such group here. For DRO methods, we use the MLP as the backbone model. We do not choose tree ensemble methods since tree ensemble methods are difficult to adapt to the distributionally robust case. Therefore, we leave their method developments and implementations as our future work.
Imbalanced Learning Methods Recently, some simple data balancing methods [42 have shown good worst-group performances under distribution shifts. In our benchmark, we implement typical balancing methods, namely Sub-Sampling Y (SUBY), Reweighting Y (RWY), Sub-Sampling Group (SUBG), and Reweighting Group (RWG). Besides, "Just Train Twice" (JTT (57)) exhibits good performances in many vision tasks, and therefore we also evaluate in our tabular settings. Furthermore, stable learning methods [51] (44] propose to de-correlate sample covariates for an accurate estimation of causal relationships via global balancing, which could mitigate distribution shifts. In our benchmark, we implement one typical method named DWR (5T). For these imbalanced learning methods, we use XGBoost as the backbone model due its superiority on tabular data and adjust sample weight or training procedure accordingly for each of the methods.
Fairness-enhancing Methods Following Ding et al. 125 and Gardner et al. BII. fairness- enhancing methods have the potential to mitigate the performance degradation under distribution shifts. In our benchmark, we evaluate the in-processing and proceesscssnng intervention methods. The in nn-proeessing method 4 minimizes the prediction error subject to some fairness constraints, and in our benchmark, we choose three typical fairness constraints, including demographic parity (DP), equal opportunity (EO), error parity (EP). And the post-processing method (37 randomizes the pre- dictions of fixed classifier satisfy equalized odds criterion, and we use exponential and threshold controls in our benchmark. We use the implementations of aif360 11 and fairlearn
[12
D.3 Parameter Search Space
We provide the hyperparameter grids in Table 4 We mainly use the hyperparameter grids proposed in [3I], and we restrict the grid size of each method in each setting to 200 in consideration of computational costs. For each setting, we randomly pick 200 configurations for each algorithm for a fair comparison. For methods incorporating backbone models (e.g.. MLP/XGBoost), we choose the top 10 best configurations for that backbone model to reduce the search space, making the searched best configuration represent its best performance more accurately. Moreover, to accelerate the grid search process, we utilize Ray (55) to run experiments in parallel.
28

---

Table 4. Hyperparameter grids used in all experiments. for methods with the total grid size above 200, randomly sample 200 configurations for fair comparisons. For methods incorporating backhone models (e.g., MLP/XGBoost), choose top- hest configurations for that hackhone model to reduce the search space, making the searched best configuration represent its best performance more accurately.
Model
Total Grid Size
Hyperparameter
Value Range
Base Methods
Learning Rate
(0.001, 0.003, 0.0001, 0.005, 0.01) (64, 128, 256]
Butch Size
MLP
270
Hidden Units
116,32.64)
Dropout Ratio
(0,0.1)
Train Epoch
(50, 100, 200)
C
(0.01, 10, 100, 1000) [lincar, RBF)
Keree
SVM
96
Loss
Squared Hinge
(0.1. 0.3, 0.5, 1.0, 1.5, 1.5, 2.0, scale, auto)
(0.001, 0.03, 0.005, 0.007, 0.01, 0.03, 0.05. 1.3, 1.7,5, 10, 50, 100, 5e2, 1e3, 5c3, 1o4)
Logistic Regression
23
La penalty
Tree Ensemble Methods
Num. Estimators
64,,64, 128, 256, (syrt, log2) (2,4,8, 16)
Max l'eatures
Random Forest
640
Min. Samples Split
Min. Samples Leaf
(1,2,4.83
Cost-Compeextt
(0.,0.001, 0.1]
Learning Rate
(0.1. 1.0,
Min. Sphit Loss
(0.0:1,0.5)
Max. Depth
(4,6,8)
XGBoost
19449
Column Subsample Ratio (tree)
(0.7.09.. 1}
Column Subsample Ratio (level)
(0.7, 1)
Max.
[128, 256, 512)
Growth Policy
(Depthwise, Loss Guide)
Learning Rate
(0.01, 0.5, (64, 128, 256, 512)
Num. Estimators
LightGBM
1680
Lg-reg
(0., 0.000,01,100 0.01, 0.1, 1.)
Min. Child Samples
2, 34,
Column Subsample Ratio (trec)
005. 0.8, 1.}
DRO Methods
DRO x²
1890
Uncertainty size
1000,011,02033,44000,000
Backbone Model
MLP
Uncertainty size
110000000.01102003000000000000
DRO CVaR
1890
Backbone Model
MLP
Uncertainty
(0.1. (0.1,022.03.. 001.0.2.03.0440550000
DORO x²
8100
Outlier proportion
(0.001,001,001,02,003333
Backbone Model
MLP
Uncertainty size
0..
DORO CVaR
8100
Outlirr proportion
00.10000.001011102200.33
Group weights stop size Backbone Model
(0.001,
Group DRO
1080
MI.P
Imbalanced Learning Methods
SUBY, RWY, SUBG, RWG
1944
Buckbone Model
XGBoss
Up-weight À
(4,5,6, 6, 20, 50, 100] XGBoost
JTT
11664
Backbone Model
L, penalty À
(1c 3, 2, le 1,0.2,0.3 (1e - 3, 2, le 1.0.2.0.3) XGBoust
DWR
48600
To penalty À
Backbone Model
Fairness Methods
Constraint Type
[DP,EO, Error Parity) XGBorst
In-processing
1944
Backbone Model
Constraint Type
(Exp, Threshold
cost-processing
1944
Backbone Model
XGBonst
29

---

Kenkkpt Doese dea Ci)
crabino
Figure 10: Algorithmic rankings vary across different target states for the fixed source state and task.
D.4 Training Details
In each setting, we randomly sample 20,000 samples from the source domain for training, 20,000 samples from the source domain for validation, and 20,000 samples from the target domain for testing. For US Accident and Taxi datasets, we only randomly sample 8,000 samples for the source/target domain due to fewer samples involved in each setting. For setting where the source domain has fewer samples, we use 80% samples for training and 20% for validation. For results not specified by the validation protocol, we selected the best configuration according to the performance on such validation set (i.i.d with training).
For settings with ACS Income, ACS Public Coverage, ACS Mobility and US Accident datasets, all experiments were run a server using 48 cores from two AMD EPYC 7402 24- Core Processors. For settings with Taxi dataset, all experiments were run on a cluster using 24 cores from Intel Xeon Gold 6126 Processor. Neural-nettorrk-baee were trained on GPU, NVIDIA GeForce RTX 3090, the other methods were trained only on CPUs. Note that all experiments are small-scale and could be run efficiently. Besides, during training, we found that the bi-search in x 2DRO sometimes failed to converge, and therefore we set the maximal iteration num to 2500.
models (MLP, DRO methods)
D.5 Detailed Results of 7 Selected Settings in Main Body
In the main body, due to space limitations, we only visualize the target performances of different methods. Here we provide the detailed results of all algorithms on the 7 selected settings in Table We select the top-10 configurations according to the validation set i.i.d with training data and report the mean accuracy well the standard deviation in Table Also, in Figure 11 visualize the results of 22 algorithms of all configurations in our 7 selected settings.
Table 5. Results of 7 selected settings in the main body, where we run cach method with its best configuration 10 times and report their mean accuracies and standard deviations.
Dataset
ACS Incone
ACS Kobility
US Taxi
ACS Pub. Cor
US Accident YIX nore Ct. .OR
ACS Time
Sub-Sarpling dominitess Young .Odd
Shift Pattern
YJX donisate
VIN deminotes
VI domitates
FJN nore
X mor
Source Target Pair
CA :RR
MS 3ll
NYC :BOG
NE 3LA
2010 1007
and
and
wod
and
4..
and
and
Methods
Base
IR
SVM MLP
50.5
7322
76.9 500
73.6
769 334
169
836533
83.e22
74
73.7
83 2:0
66.311
82 Sena
6M.rra
454e00
35
667734
674433
924400
81.5ano
9.04
68 992s
75.8 500
76.4 =27
84.585
73
815
66.
83 6ans
65.5cc
770
70.533
903
816608
Thee
Random Sorest
8L lasz
80.2
72.0
85.8
734
85 S
63.3
86 2:00
665ra.
78 7855
706
22
81 2ona
Frsemble
1igh
.n5
86.418
72.7
7000.0
19.
718:03
Methods
XGBBoost
81 4:u
71.7
80.0 .04
71.2
36.513.4
73.0
85
35.8
70
86..04
65 45.4
7900
71.6:12
92.600
51 6:00
DRO
73.2
2013
:33
$4.8334
73.0a11
20.
609:17
K3.3ma
50.5
6422sa
12.
DRO
(XAR-DRO
80. 9una
71/2217
76.4 .05
78.
85.
7388
53.5
61.7
84 Lana
64R
635537
92.3g1
81 4:m8
Methods
2 2-DOR0
71.0a11
736
84/6344
73.6
6:04
71 220a
645533
(bese: Pj
CVAR-DORO
78 Setus
72.4s42
75.4 2014
78.6 =11
85.2611
74.3
83.7
6,90
13 4est
63.9011
77
67
70.734
920ea
51 Deno
Group DRO
$0.7.03
71.9.44
75.5 .no
78.5
113
N/A
NIA
30.3
66.8.us
Nit
NiA
74A.11
63.3149
92.3
816
68.7.1.
.no3
135
85.01a3
71.111
68.9...7
729.us
67.71t
91.5
Inbelanced
SUBB
50.5
64.9
760 505
70.5
72.021
152211
68 (8.i
85 Sana
64 4.r.4
73.5
70.3.15
85.7an
88 Sunt
Leatting
RWY
80.91122
63.9
75.9 294
68.5
86.2e15
73.1m1
82.
09.700
86 1s04
65 3es.0
74.7aas
71.3e1
90,6500
78 Se50
Methods
SUBG
79.1 205
2344
85.3
71.4a1a
1205
70.20.1
2edi4
78 288a
21.4
92.4301
81 2066
(beae XGB;
RWG
81 41s4
71.5=11
70.7 =02
=1.
86.3e23
72.8eaa
8535
85
70.s
16 Tana
65 (5.2cst.
7V 70.1
72.1=13
92.900
82 52.
DWR
71.3:us
79.2
69.8
83.5
71.2112
85..,04
698
7.7.0.
65.4..4
7900.uu
72.0.13
92.5p00
$1.2:00
DP
80.8
70.4.us
79.5 .mo
71.3 235
86.3134
72.01a
8522.u
M6....
65.6.r.
790
718
92.7au
816
Primess
FD
$1 Rana
21.2
79.3
11.4
728
8/
864.05
7900aa
718:33
92.7a00
81 S1.5an
Methods
EP
71.4a0
85.7634
7L.714
661-ca
790
718-12
$1.5
(bese: XGB
Exp
9a0a
794 206
85.6a5
71.3a111
853
712205
85 8ans
6855c
190aa
718
92,6a0
81 $1.5000
Throskod
2:00
736634
70.5
69.9
84.le3a
$13694
815eas
68.2
838s0
61.ec.
788502
71.731
91,6300
78.3
Top 3 Classes
Fair Rases
DRO' Tree.
Frrs:Fir::Ih Tee--Tr
Base> Tair
Imh-Pairs: Tre
TreeslmboOther
30

---

100
100
100
Target Ace
Target Ace
Target Ace
60
100
100
100
Source Ace
Source Ace
Source Acc
ACS Income (CA-> PR)
ACS Income (CA SD)
ACB Mobility (MS HI)
100
100
100
Target Acc
Target Ace
Target Ace
60
60
60
20
Source Ace (NYC-, BOG)
Source Ace (e) Pub (NE- L.A)
Source Ace
(f) Accidant (CA-> OR)
Target Acc
20
60
160 580
100
Source Ace
Source Acc
(g) ACS Pub. Cov (2010-22017)
(h) ACS Income (Young-> Old)
Figure 11. Target source accuracies for 22 algorithms and datasets in our benchmark. Each point represents one hyperparameter configuration. (a)-(b): two examples of ACS Income dataset with California (CA) as the source state, and Puerto Rico (PR) and South Dakota (SD) targets. (c)-(g): five examples of ACS Mobility, Taxi, ACS Pub. US Accident datasets. (h): simulated covariate shifts on sub-sampled ACS Income dataset.
Analysis From the numbers of numerical results in that Table, we give more detailed analysis corresponding with our main body.
Different algorithms do not exhibit consistent rankings over different distribution shift patterns. In T boldface the best target performance within each class of methods. And we show the top-3 classes at the bottom. The results show that the algorithmic rankings across different settings and tasks quite different. And even the rankings of algorithms within the same class vary a lot. This further demonstrates the complexity of Y|X shifts. Also, Figure 10 shows that even for the fixed source state, algorithmic rankings vary lot across different target states.
Tree ensemble methods show competitive performances but do not significantly eliminate the generalization error between source and target data, characterized by the difference
31

---

between o.o.d. and i..dd. model performance. From the bottom, we could see that tree ensemble methods achieve top-3 performances in most of the selected settings (6 out of 7), exhibiting their superiority on tabular data. However, the performance degradation between source and target is still large.
Imbalance methods and fairnsss methods show similar performance with the base learner (XGBoost). We find these methods do not have significant improvement over the base learner (XGBoost). This may be due to that they are not designed to incorporate tree ensemble methods.
D.6 Full Results of 22 Settings
In this section, we provide the full results of our 22 settings in Table
D.6.1 Average Accuracy
In Table Table and T we report the source accuracy and the target accuracy of all algorithms. Since in these settings, we have multiple target domains, as for the target accuracy of each algorithm, we report the average accuracy well as the standard deviation calculated on all target domains. generalization performances
Here the standard deviation reflects the stability of aut-of-distribun across different target domains different instead of random seeds.
From the average result over, Table 6 Table 7 and Table g can still obtain similar findings compared to that from the 7 selected settings in the main body. Especially, while tree ensemble methods serve strong in-sample benchmark illustrated by their competitive i.i.d. performance, these methods do not yield better performance than other methods in the target distribution uniformly. And when we average across different target domains, DRO methods do not perform better than their empirical counterpart, indicating that the worst-case optimization from the uncertainty sets constructed by existing DRO methods can rarely occur in practical setups and does not help much compared with standard ERM cases. This tricky part of worst-case intervention also holds when we compare imbalanced learning and fairness methods with the XGB base learner. These methods can lead to better o.o.d. results than the base learner sometimes indeed, while this may not hold true when we average over different target domains. general, existing methods cannot generalize well averaging over different target domains, and it would be interesting to develop methods to close that gap.
D.7 Worst-Domain Accuracy
Another widely-used metric in evaluating generalization performance is worst-case accuracy. In settings built on ACS Income, ACS Pub. Cov, ACS Mobility, and US Accident, for the target accuracy of each algorithm, we report the worst target domain accuracy in Table 9 and Table I0] For other settings, we do not report the worst-case accuracy because there are not many target domains, and the average& standard deviation results could reflect the population generalization performance well. In terms of the worst target accuracy for each setting, performance degradation (usually over a 10 percent performance drop) in all of the existing methods. And algorithms do not show consistent and stable ranking performance in the o.o.d. performance. DRO/ / Imbalanced learning methods can perform quite well in one o.o.d. setup but are dominated by other methods in some other cases. This demonstrates need carefully understand the difference between different domains first and develop corresponding methods then.
usually observe large
D.8 Average Macro-F1 Score
In consideration of the label imbalance in real-world tabular datasets, we also calculate the Macro-FI Score for all algorithms under our settings. In this section, we report the average results in Table [T Table [2] and Table [3] Here the standard deviation reflects the stability of out-of-distribution generalization performances (not the randomness).
D.9 Worst-Domain Macro-F1 Score
In settings built on ACS Income, ACS Pub. Cov, ACS Mobility, and US Accident, for the target accuracy of each algorithm, report the worst target domain Macro-Fl score in Table [4 and
32

---

Table 6. Average target domain accuracy of all algorithms on the ACS Income and ACS Pub.Cor datasets. In each setting, we test all algorithms on the 50 American states and report the mean and standard deviation across all 50 target states. The standard deviation here reflects the stability performances across different target states.
Dataset
ACS INCINE
ACS PUB.CO
Source State
XA
Ed.
a.aud
1.1.
wad
Ed..
and
v.d.
a.0.d
1.l.
a.oud
id..
0.oul
f.d.
sudd
idd.
outul
Methods
Base
LR
SVM
$1.1
79.4
77.3
74.8 =10
#19
80.7
78.6
76.2.s25 128
72.4
90.1
80.9
=3.0=21
768 =23
79.3
50.1
75.3
15.8
:0.
81.3
80.5
7444
73.3
57.5
B4L1
74.1
13.9 e1:2
$4.5
75.0 #1.7
73.8 #6.5
78.6
73.1
75.8
14.3
=51
MLP
$1.8
76.4 ssa
81.4
76.5
525
81.7
17.4=22
80.5
76.8
+20
83.3
76.5
11.4
63.4
76.6 aus
$4.5
75.3 st.5
76.5
76.2
Tiee
Kandom Forest
$1.7
77.9 =1.
81.2
77.1 82.
81.5
124
80.2
75.5 =30
84.5
77.3 #1.7
56.8
17.0 =4u
762 #6.7
81.2
71.7
:3.
Exsemble
LighGBM
$18
77.3 esu
82.1
76.7
62.3
77.4
50.2
76.1
84.6
77.3
66.9
17.4
86.9
76.6 14:3
81.2
78.0
1533
Methods
XGBoort
$2.0
72.5 Lmv4
81.9
76.6 1.44
K2.2
$0.5
76.9
84.6
1577
66.7
17.2
267
87.3
76.3
81.2
77.9
A-DRO
$1.8
77.0
81.2
76.7 #24
81.6
-6.0=2
50.2
76.3 =3.0
81.9
75.9
15.4
=n.2
85.4
74.7
+0.0
78.4
75.5 246
DRO
CVRR-DRO
$1.4
77.7 an.
81.2
76.3 2.44
K2.0
76.7 2041
79.7
75.5 53.5
82.6
75.3 670
65.2
75.8
263
83.5
73.4
24.5
71.8
75.0
Methods
x ADORD
61.1
77.8 2017
80.4
75.0
1299
81.2
15.7
78.8
75.9
75.6
7000
143
62.1
69.9
822
70.0
14.1
72.4
70:2
CVSR-DORD
50.9
76.
80.5
75.6
81.1
79.6
75%
80.7
73.0
84.3
75.4
$1.9
69.9
76.4
74.2.55 158
Group DRO
$1.9
77.7
=5.0
81.3
77.0
#2.
81.7
76.8
=0.4
79.8
75.7
#3.
83.3
76.1
66.7
65.4
76.6
$3.5
72.8 #6.0
72.2
70.2
SUBY
$1.0
81.5
76.0 8888
62.0
=0.
74.8
75.7 213
79.5
72.8 4644
71.5
#2.4
77.8
74.9 :11
Inbalatced
KWY
$1.5
15.7 =5.0
81.8
75.9
#2.
62.1
76.5
=277
97.7
76.2
80.7
75.2
12.5
12.2
85.7
14.3 e4.
78.7
75.6
:1.
Lesming
SUBG
=s.
81.6
76.8 2.:4
62.0
76.9 =035
60.2
76.0
84.3
77.
77.1
1677
+5.8
90.8
77.8 150
Methods
KWG
$2.0
27.4
81.9
76.7 +2.4
62.2
77.2
80.2
76.8
84.5
77.5
56.8
17.4
86.7
76.4 =E.0
81.0
78.0
:5.4
JIT
78.3
74.1 ss.5
75.1
75.3 6:.3
79.1
75.8 =1.5
37.9
74.7 ss3
80.6
74.9
13.1
13.1
75.6
$4.7
75.4 =t.77
77.6
74.22 246
DWR
$1.9
77.5
81.6
76.8
62.1
-7.0.25
50.1
76.3
84.3
77.5
66.8
17.3
85.9
76.4
8006
75.0 1533
DP
$1.3
763 :s.4
81.0
75.4 k26
81.8
76.7 :2.1
79.3
75.5 :::3
84.3
77.4 11.4
96.6
17.2 267
$6.4
76.3 at.6
80.6
77.8 1..2
Fairness Methods
133
76.5 1.4
K0.1
-7.2.24
$0.0
76.7
77.2
1177
17.1 164
11-3
73.7 111
EP
$1.8
77.2
81.9
76.5 125
K2.1
17.5
:23
$0.3
76.2
::3
84.4
71.1
66.8
17.3
:64
$6.4
76.5 11:2
8099
77.6 145
Exp
LSa
75.3 136
81.8
26.5
79.1
75.5
84.5
77.5
17.1
263
1x3
76.1 153
Threshold
77.9
21.0
77.0
74.1
816
77.5
144
78.0
31.7
84.3
71.2
86.2
76.7
263
85.8
26.0
80.0
77.0 553
Table 7. Average target domain accuracy of all algorithms on the ACS Mobility and US Accident datasets. In ACS Mobility, we test all algorithms on the 50 American states and report the mean and standard deviation across all 50 target states. And in US Accident, we choose 13 American states with relatively high sample sizes in testing. The standard deviation here reflects the stability of performances across different target states.
Dataset
ACB MOBILITY
US ROCIDENT
Source State
HY
CA
KS
PA
CA
FL
TI
.d..
a.d
id.
a.d.i
Ld.
0.0.
1.4.
0.0.
id.
0.0.d
1.6.
o.dd
1.l.
6.d
auou
78.6
72.7
=33
71.1
727
77.3
72.7 637
15.4
72.7 =8.4
132
#154
90.3
31.7
4333
74.5 =033
56.4
72.2 122-11.8
SVM
79.8
72.7
71.3
12.9 ss.1
79.4
73.9
554
77.1
72.7
:36
K3.2
69.4
1:2/
85.7
71.9 :su
93.7
70.7 2911
$8.6
69.7 183
Mehhods
78.7
72.7
77.1
13.7
72.4
133
:311
1/07
92.7
78.2 2K2
73.0 u933
Thee
Random Forest
50.4
74.0
79:0
14.1
$0.6
73.5 134
78.6
74.3
66.6
17.9
90.5
84.4
95.2
84.4
91.6
82.0
Easembble
Ly51GBM
$0.6
74.6
224
75.7
74.1
23.6
80.0
71.9
#2.
75.5
74.7
=2.
67.1
79.1 29
93.3
843
=0u4
95.4
64.3
=330
92.2
80.9 11.4
Methods
XGBoss
50.4
74.6
0.79
14.5
60.9
73.5
130
79.0
74.3.34
67.1
79.8
94.6
K2.6
95.3
64.4 293
92.5
79.6
-DRO
78.5
72.7 s9.
71.5
768
72.7 535
76.0
73.1 =3a
84.4
17,3 6n1
92.6
13.4 212.
95.0
74.6 snt
$9.0
72.3 =104
Methods
DWO
CVaR-D8O
-DORO
78.6
78.6
235
22.6
71.8
71.2
12.8 e8.5
12.8
77.1
11.7
72.6
73.7
537
75.3
15.7
22.7
13.3
=02
84.7
84.7
72.9
74.5
#11.5
+00.3
92.7
92.3
14.4
77.6
#11.4
94.3
95.0
74.3
74.9 esu4
39.5
$7.6
73.4
77.77
CVaR DORO
78.7
72.7
75.0
73.6
u3.1
77.4
72.7
137
75.3
72.7
L33
BA9
74.1
1103
90.8
74.
111.2
94.9
74.7 5945
49.1
74.1 19.3
Grosp DRO
78.6
72.5
77.1
a2.7
76.0
72.7
637
76:0
72.8
NIA
NIA
NIA
NIA
NIA
N/A
SUBY
78.2
72.7 1335
76.3
12.5
76.6
70.0
74.7
69.5
M6.5
65.4
93.7
$4.5.000
95.2
84.4 soa
91.8
81.8
Imbilaned
RWY
78.5
72.7
76.7
22.7
7655
72.2
A34
74.5
72.6
23.
52.2 e71
93.4
84.5
95.3
643
92.5
81.1
Learingg
SUBG
60.2
74.3
=2.0
79.2
64.2
19.5
72.5
52.
78.6
74.
86.3
$1.0 ams
93.0
838
95.1
91.1
80.1 55.5
Mehoods
KWG
$0.3
74.6
79.1
74L4
23.6
80.1
73.3
12.9
75.7
74.2
:03
67.5
79.7 s3.b
93.4
838
=544
95.2
84.4
92.4
79.3 13.3
JTT
18.3
72.7
75.5
12.4
77.6
71.5
62.6
75.1
70.7
=54
86.5
19.0 21.5
92.7
83.6
94.9
84.3 203
91.8
78.2 36.6
DWR
79.7
74.2
75.3
73.9
13.5
79.1
72.9
12.9
73.5
74.0=20
::3
67.2
79.8 s3:7
93.4
K3.7 L200
95.3
84.4 ss4
92.3
78.5 3..9
50.5
74.2
75.8
50.0
73.8
:2:
19.7
81.3 =s0
$5.9
Faimess
BO
40.3
74.7 :23
75.9
74.1
79%
73.4
75.5
73.
:37
66.6
19.5
93.2
84.4 :944
95.2
$4.4 54.42111
92.2
79.6
Mechods
50.3
74.7
20.
75.8
74.1 130
30.1
14.0
333
18.4
237
50.3
93.3
842
:50
544
91.9
15.7
Exp
50.5
74.8
=20
75.9
14.1 45.
81.0
73.9
423
78.4
74.326
85.9
68.6
90.1
82.3
93.1
81.6
96.3
80:4 66.
Threshold
$0.5
74.5
2033
75.6
74.3
298
78.2
23.
78.5
236
17.8
88.1
799
91.2
79.9 2933
$2.0
75.7 408
33

---

Table 8. Average target domain accuracy of all algorithms the Taxi, ACS Pub. Cov (Temporal) and ACS Income (Synthetic) datascts. In Taxi and ACS Pub. Cov (Temporal), we test all algorithms the 3 target domains and report the mean and standard deviation across all 3 target domains. The standard deviation here reflects the stability of performances across different target states. In ACS Income (Synthetic), we simulate strong covariate shifts according to the "Age" feature, where 10% and 20% means the minor group ratio in training, respectively.
Dataset
Taxi
ACS Ctv (Temporal)
ACS Income (Synthetic) 20X
Sourve
30G
NYC
E.d.
0.0.d
t.d.
o.0.d
0.0.a
1.d.
0.0.d
t.d.
6.ddd
1.d.
0.0.a
Methods
Base
LR
SVM
75.6
71.2
+23
1S..
83.6
83.4
74.2
412
11.4
76.3
77.4
68.5 #23
220
50.8
50.3
68.2
#4.3
18.1
92.0
92.2
81.6
96.1
94.0
79.5
79.3
MLP
77.3
70.0
84.5
73.7
16/6
78.0
70.6 224
82.5
70.3
15.
92.5
82.1
94.3
79.5
Tree
Random Forest
76.1
77.5
#4.7
85.7
71.6 #0.0
79.1
=25
$3.4
70.4
#42
92.7
81.7
94.4
78.5
Ensemble
LightGiBM
86.3
13.2
64.1
87.0
72.0
79.7
72.1
#24
BA10
70.7
92.6
83.0
94.2
50.4
Methods
XGBoest
$5.0
71.5
86.7
72.5
1300
79.3
71.9
226
$3.6
71.1
1537
92.7
82.2
90.4
79.7
>DDRO
72.2
84.6
75.0 28.8
77.3
220
$1.9
70.0 23.9
92.5
94.2
79.7
DRO
CVRR-DRO
77.0
13.4 +0.5
85.9
72.8 +6.0
766.6
09.1 =24
82.2
69.1
64.5
92.5
81.2
94.3
79.0
Mathods
+DOOO
75.8
73.3 62.
84.9
73.9
16.6
71.7
61.2
#15
79.7
64.8
92.3
81.4
95.8
77.4
CVaR DORD
75.6
74.3
85.1
738
76,0
67.9
79.5
64.9
92.5
81.4
95.9
76.7
Grop DRO
NFA
N/A
N/A
NIA
76.8
70.5
2:11
$1.9
70.0
92.5
81
94.2
79.8
SUBY
11.5
18.5
73.9
68.8 21.5
13.4
87.00
Inbolancel
RWY
$1.2
73.0 =1.4
86.7
72.4
75.1
70.9 #1.6
79.4
65.8 #4.
90.3
78.6
92.1
76,3
Learning
SUBG
14.1
85.6
18.9
79.4
71.8
233
18.
92.6
94.4
79.5
Methods
RWG
$1.1
69.1
59.5
86.5
71.3 46.0
79.4
=2.
83.8
70,8
92.6
82.7
94.5
50.1
JTT
$4.6
69.5
20.3
85.4
71.2 #8.8
73.8
66.7 =2.5
79.5
67.4
91.5
78.9
93.5
76.5
DWR
$2.9
68.2
51.1
83.7
70.7
79.2
72.
53.8
70.77
s5.1
92.5
82.6
94.2
50.3
DP
$4.1
10.2
54.3
86.3
72.0 #4.8
79.6
72.7=22
83.7
71.1 18.1
92.5
82.7
94.2
80.2
Faineas
EO
71.9
87.1
#5.8
79.5
72.3
83.4
#4.
92.6
94.3
79.5
Mathods
EP
19.7
71.6 +1.7
85.7
70.9
24.0
79.6
12.5 #2.1
$3.6
71.0 s8.1
92.4
82.6
96.2
80.0
Esp
1m44
19.6
79.3
14.2
92.6
96.3
79.4
Threshold
$0.8
69.8
84.3
59.7
13.
79.2
71.9
83.4
70.4
91.8
78.3
93.5
74.0
Table 9. Worst target domain accuracy of all algorithms the ACS Income and ACS Pub.Co Cov datasets. In each setting, test all algorithms on the 50 American states and report the worst accuracy among all 50 target states.
Dataset
ACS
INCONE
ACS TX
PUB. CDV NE
Source State
CA
CT
MA
SD
FL
IN
i.d.
ood
i.d.
o.0.d
i.d.
0.o.d
s.d.
0.0.d
i.l.
0.3.d
i.d.
0.o.d
i.d.
aod
i.d.
0.0.d
LR
81.1
72.3
80.7
70.5
80.9
71.1
80.1
69.4
81.3
49.6
84.1
49.0
84,3
0.52
78.5
54.7
Base
SVM
79.4
67.1
78.6
61.6
80.1
62.2
79.3
64.6
80.5
$3.0
84,2
50,3
84.8
50.4
77.1
57.4
Methods
MLP
81.8
68.3
81.4
70.8
81.7
71.3
80.5
70.5
83.3
54,3
85.4
53.9
84.5
52.9
78.8
56.7
Tree
Random Forest
81.7
72.6
81.2
71.6
81.5
71.2
80.2
68.3
84.6
$4.2
86.8
52.8
86.7
52.9
81.2
59.0
Ensembic
LightGBM
81.8
71.1
82.1
69.5
82.3
70.1
80.2
69.6
84.6
56.9
86.9
53.9
86.9
52.3
81.2
60.4
Methods
XGBoost
82.0
72.2
$1.9
70.1
82.2
70.9
80.5
70.5
84.6
54.8
86.7
53.7
87.3
55.4
81.2
59.6
-DRO
81.8
69.7
81.2
69.7
81.6
67.9
80.2
70.3
82.9
$2.5
85.4
50.5
83.4
52.9
78.4
62.4
CVaR-DRO
81.4
72.1
81.2
70.7
82.0
70.0
79.7
68.4
82.6
52.2
85.2
51.7
83.3
52.3
77.8
53.9
DRO Methods
-DORO
81.1
70.3
80.4
62.6
81.2
63.8
78.8
69.5
78.8
43.6
82,1
43.6
82.2
43.6
72.4
49.9
CVAR-DORO
80.9
68.7
$0.5
64,9
81.1
64.3
79.6
69.
80.7
49.5
84.3
52.4
81.9
43.6
76.4
56.2
Group DRO
81.9
72.6
81.3
71.8
81.7
69.2
79.8
0.68
83.33
53.2
85.4
53.2
83.5
51.3
72.2
43.6
SUBY
81.0
65.2
$1.5
68.0
82.0
66.3
74.8
72.5
79.8
51.3
82.3
45.4
77.8
64.5
77.8
68.3
Imbalanced
RWY
81.5
65.2
$1.8
68.3
82.1
67.6
77.7
73.2
80.7
53.3
82.5
45.6
83.7
57.1
78.7
65.8
SUBG
81.9
71.4
$1.6
82.0
68.4
70.3
84.3
$6.1
86.7
$3.0
86.3
80.8
60.2
Learning
RWG
82.0
71.3
81.9
70.6
82.2
70.3
80.2
70.6
84.5
$6.8
86.8
52.1
86.7
55.1
81.0
57.2
Methods
JTT
78.3
68.4
78.1
71.2
79.1
71.6
77.9
68.6
80.6
59.4
83.1
56.2
84.7
55.4
77.6
56.7
DWR
81.9
71.2
81.6
71.0
82.1
69.0
80.1
72.0
84.3
5R.1
86.8
54.2
85.9
52.8
80.6
59.4
DP
81.3
70.3
$1.0
68.8
81.8
70.7
79.3
68.4
84.3
57.4
86.6
53.7
86.4
52.9
80.6
57.8
Faimess
EO
81.8
70.6
81.8
70.5
82,1
70.8
80.0
70.6
84.4
55.4
86.8
53.6
86.4
53.6
80.8
61.6
EP
81.8
70.7
81.9
69.8
82,1
70.9
80.3
69.2
84.4
55,5
86.8
54,4
86.4
53.6
80.9
60.1
Methods
Exp
81.4
70.6
81.0
69.4
81.8
70.4
79.1
68.8
84.5
55.4
86.8
52.8
86.4
52.5
80.9
61.5
Thresbold
77.9
71.8
77.0
69.8
77.5
70.9
78.0
62.8
84.3
57.3
86.2
52.4
85.8
52.9
80.0
59.9
34

---

Table 10. Worst target domain accuracy of all algorithms on the ACS Mobility and US Accident datasets. In ACS Mobility, we test all algorithms on the 50 American states and report the worst accuracy among all 50 target states. And in US Accident, we choose 13 American states with relatively high sample sizes in testing.
Dataset
ACS MOBILITY
US ACCIDENT
Source State
BY
MS
PA
FL
XII
i.d.
0.0.d
í.d.
0.a.d
i.d.
a.o.d
v...
o.o.d
i.d.
0.0.d
i.d.
0.o.d
i.d.
o.o.d
i.d.
o.a.d
LR
78.6
64.7
77.1
64.6
77.3
64.8
75.4
66.3
83.2
44.9
90.7
48.3
95.1
57.4
86.4
52.8
Base
SVM
79.8
64.6
77.7
66.8
79.4
65.3
77.1
64.7
83.2
49.2
88.7
58.3
93.7
55.7
88.6
56.1
Methods
MLP
78.7
64.7
77.1
64.8
78.1
66.3
75.9
67.0
84.7
58.4
92.7
61.1
94.9
57.2
88.9
57.1
Tree
Random Forest
80.4
68.0
79.0
68.2
80.6
67.5
78.6
68.7
86.6
66.6
93.5
58.2
95.2
58.5
91.6
68.0
Ensemble
LightGBM
80.6
68.7
78.7
69.0
80.0
67.9
78.6
69.8
87.1
65.3
93.3
59.0
95.4
58.6
92.2
68.1
Methods
XGBoost
80.4
68.6
79.0
69.0
80.9
68.3
69.4
87.1
65.6
94.6
59.0
95.3
58.8
92.5
68.5
DDO
78.5
65.1
77.5
66.6
76.8
65.4
76.0
67.1
84.4
62.9
92.6
53.3
95.0
57.9
89.0
53.5
DRO
CVRR-DRO
78.6
65.0
77.2
65.6
77.7
64.4
75.7
67.6
84.7
57.2
92.7
57.5
95.0
58.4
89.5
56.3
x FDDORO
78.6
64.3
77.8
66.9
77.1
64.7
75.3
64.7
84.7
55.9
92.3
61.1
94.3
57.0
87.6
59.8
Methods
CVaR-DORO
78.7
64.7
78.0
67.4
77.4
64.7
75.3
64.9
84.9
$7.8
92.8
58.1
94.9
57.5
89.1
57.6
Group DRO
78.6
65.5
77.1
65.1
76.0
64.5
76.0
66.8
NIA
N/A
N/A
N/A
NIA
NIA
N/A
N/A
SUBY
78.2
65.0
76.3
64.6
76.6
64.7
74.7
65.0
86.5
64.2
93.7
58.8
95.2
58.5
91.8
65.6
RWY
78.5
64.7
76.7
65.0
76.5
65.6
74.5
64.6
86.9
64.8
93.4
58.3
95.3
58.5
92.5
67.5
Imbalanced
Learning
SUBG
80.2
68.8
79.2
68.9
79.5
67.0
78.6
69.2
86.3
66.4
93.0
58.1
95.1
58.4
91.1
67.4
RWG
80.3
68.4
79.1
69.4
80,1
68.3
788.7
69.4
87.55
65,4
93.4
59.4
95.2
58.4
92.4
68.6
Methods
JTT
78.3
64.7
76.5
64.77
77.6
66.6
75.1
65.6
86.5
65.9
92.7
58.6
94.9
58.6
91.8
68.2
DWR
79.7
67.4
78.3
68.5
79.1
67.4
77.5
69.0
87.2
65.8
93.4
58.1
95.3
58.5
92.3
67.6
DP
80.5
69.2
7R.8
68.4
80.0
68.2
78.3
68.7
86.6
65.2
92.8
59.0
94.8
58.4
91.9
66.5
Faimess
EO
80.3
69.3
78.9
68.9
79.8
0.68
78.5
68.5
86.6
65.6
93.2
58.8
95.2
58.5
92.2
68.1
EP
80.3
68.7
78.9
68.5
80.1
68.1
78.4
68.5
87.0
65.6
93.3
59.0
95.1
58.6
91.9
67.9
Methods
Exp
80.5
69.0
78.9
68.6
81.0
68.8
18.4
69.0
85.9
65.4
90.1
58.7
93.1
56.5
86.3
64.7
Thresbold
80.5
69.0
78.6
69.2
78.2
66.7
78.5
68.7
84.3
64.5
88.1
59.5
91.
55.7
82.0
64.0
Table 11. Average target domain Macro-F1 score of all algorithms the ACS Income and ACS Pub.Cov datasets. each setting, we test all algorithms on the 50 American states and report the mean and standard deviation across all 50 target states. The standard deviation here reflects the stability of performances across different target states.
Dataset
ACS Income
AC3 Pub.Cos
Source State
IN
i.d.
0...!
1.
aud
1..
sund
i.d.
0....
ial.
i.d.
0.5..
1al.
a.uud
Base
LR
0.04
0:751
=002
0.907
(1247
0.829
0.152
0.714
bo82=xu0 =kits
0.522
0.531
=t 160
0.644
0.59) 50412
D665
2,12
=30a
0.593
0:699
04.
Midbods
0.995
0772:
50.00
0.733
0,225
11.04
1686
2611
0,596
MLP
0814
0:750
0.514
01755
40.0
0.815
0.355
50022
0.34
0/25
0,709
0.666
0.113
0.664
50400
D696
0.644
=304
0.716
0.690
00.00
Diee
Randon Foes:
0.08
0.75
6008
0.812
0.755
10.00
0.814
0.55
50834
0.68
1673
20004
0,115
0,599
0.727
0.551
40.06
0.729
2004
0,346
0:611
50:000
Encashle
LighGBBM
0:11
0.53
0.621
(1755
0.833
0.59
0735
(1330)
0.700
0.339
0.655
0.755
0.63
01750
0200
10.001
Medoods
XCBood
0814
0651
1000
0.919
(1751
0.822
0.57
30.35
0.733
0710
M000
01725
06675
030
0.599
30:35
0755
0:67
01747
0.201
: A-DRO
0812
0.754
6300
0.812
(1750
00.00
0.515
0.44
50.099
0750
0/33
2000
0.70-
0669
0 0.67
0.67
0685
0646-3008
0,715
0075
50:00
DRD
CHRR-DRO
0.906
0,912
(1749
10.00
0.830
0.352
0730
01726
0.995
06:99
0.305
0.555
50,00
11668
0659
=002
(2000
01675
50.00
Mccoods
2 DOOLD
0:001
0.755
01914
(1758
0.512
0.744
0.11
0711
0L336
(1511
0.5.5
0.45
0.536
3491
0.516
0.877
C15R/DOR
0
0.746
[0901
((740
0.11
(174)
0720
0.706
0/119
0.65
0.29
(0402
0.599
0541
(1629
00255
Group DRD
0812
0.813
(0754
0.517
0.753
0.741
0.43
5000e
0.706
0.666
0.717
0.660
07000
0635
0.419
0:41
100
SUBY
0200
0.735
aaon
0.115
(1745
0.830
0.75
0719
B/759
0.710
[/PP)
0.710
0.872
0.714
5682
2005
01745
0,710
Michoods
Leaning
Inbukaned
KWG
SUBG
KWY
0614
0812
0811
0.741
0259
0100
2100
0,816
(3919
0,918
(1754
(,247
0625
-4:00
0.822
0.820
0.821
0.157
0.753
0.158
60
0/26
0733
0/26
0/723
00715
0733
5000s
5000
0.725
0.723
0607
0,706
0671
st 15:
24.04
0.331
0.73
0.72
0.661
0.693
0,822 50000
20077
0776
6729
0744
3160
5672
2006
2866=306
=008
0,749
0,746
01242
0.700
06696
0.700
000
050
ITT
0.771
0.28
0.781
01735
-0.00
0.79
0.399
07700
0:700
0.211
0.125
0.991
6.21
3508
0.755
0669
0811
0.75
[1916
(1755
0.831
0.756
0.733
0:719
(1721
0.688
0.331
0.661
0.733
0676
01241
(1997
DP
0800
exus
(1510)
(1240
ss.m
0.617
0.752 soass
0.716
0.708 sx0s
0.227
0.77
0.739
0.559
20:144
0.700
2:66
0,242
01688
Madaads
Faimess
EP
0811
0,11
0.751
0.755
ax0m
(1518
(1319
(1252 00
(1752
0.830
0.831
0.77 your
0.75
0.733
0.718
1L234
0.734
01668
0/688
0.714
0.331
0.661
0.657
0.747
0.737
0.611
2671
0,745
0L345
0,202
01699
10
Exp
0,08
0.750
(U500)
(1757
0.518
your
1L734
06667
0.73
0.666
0.738
3661
(1341
0/99
Thrsheid
0.716
0.706
2x0r
(1768
(1711
0.771
0.766 soms
0666
1666
2000
0,722
0/9P
0.7.7
0.652
50:056
0.714
0:44
2
0,733
01681
35

---

Table 12. Average target domain Macro-F1 score of all algorithms on the ACS Mobility biy and US Accident datasets. In ACS Kobility, we test all algorithms on the 50 American states and report the mean and standard deviation across all 50 target states. And in US Accident, we choose 13 American states with relatively high sample sizes in testing. The standard deviation here reflects the stability of performances across different target states.
Dataset
ACS Kobility
UB Accideat
Source State
CA
Pl
CA
FL
35
Eid.
1d
and
La.
0.32
12l.
a.uu
Ld.
suad
E.d.
e...d
1al.
a.au
Bace
LR
0A51
0A2)
0,62
0:566
20.00
0:678
18.16
0.985
0,303
s0.05
1.556
0.73
0.855
0,215
Mefoods
SWM
0604
0,512
1005
11.92
(1590
0.635
0,512
D623
0.581 1M/
0664
18114
0.811
0.888
0.535
2.65
23400
(U.90)
MLP
0600
0.533
230
0.52
[/00
0.67
0.53
30013
0.588
1000
0,327
01755
1010))
6923
0.769
50.09
0.544
0.720
0.3%
0,715
50.000
Duee
Kankon PeEss
0,510
e005
03587
(L56
11.00
0.541
0.53
0625
0.56
0.596
0.752
0.91
0.832
50.06
0:558
0.554
0,11
0:300
Encashil
LighGGBM
0637
0.58
2004
0.625
01001
0.611
0.550
0660
0:500
01351
(1788
0.929
0.531
20.56
0.90
0533
0,918
0.786
Mafoodss
XGBiee
0677
0:591
1300
0.25
[V065
0.78
0.585
0/64
0:566
0.882
11706
km
0.942
0.112
20.
0.599
0833
0,000
0.771
F-080
061
061
0,99
01579
-4.05
0.540
0,514
6080
0006
0:533
0.754
at 199
0
1.721 #0:211
0955
2.741 =300
0,985
0,704 050
DRD
CISR-WWO
0621
061
2000
0,538
0:96
0.544
0.555
0629
1613
0.525
21.164
0.924
0,731 50.11
0956
3540
0.355
0,716
Michood
7-D0RD
0.505
0:00
4000
0,59
0.59
0.55
60813
0540
0315
0200
0.23
60099
1000
0734
=3008
0.87
0,227
C1GR-DORO
0.53
0:534
1300
0.55
(1778
0.521
0.500
D510
D477
0.755
0.748
0922
0730
1994
0774
0.887
0.759
Grong
0.58
0.67
=3005
0.56
0553
-0.00
0.33
0:55
XIX
N/A
NA
NAA
NAA
M/A
SUBY
016T
0625
=307
0,599
0//66 -4X
0.674
0.61
10115
0678
1629
0.55
0.93
0.34
0958
0533
0,915
0.821
Leaning
Mitbods
Inbakancd
SLBO
KWG
KWY
0635
0:61
0,585
0/21
13007
1622
0.677
(6801
1::0
0.671
0.676
0.675
0.535
0661
0.582
0626
D011
D660
0:592
1.56
b651
0.5%
03355
0.700
(1775
03345
0929
0925
0135 2o0s
0334
0.35 1100
1967
09H0
19988
0551 -4406
0333
11900
0.920
01919
(1788 051
1.79%
0,200
06:
ITI
0639
10516
IL572
0.650
0,599
0639
1:584
01545
(1786
21.14
0921
0323 s0u0
04655
0553 :3406
01912
11766 20000
DAR
0/22
0.81
(1:30
0.655
(1535
0164
0.99
0,355
(1777
0.929
0.824
D.599
0333 :3000
01917
(1759
0630
0.585
1004
(1521
[L540
0.663
0.550
11547
0,922
joars
0.553
0832
01915
0C29
Mihoods
Faimess
FO
0d6!
0.59%
ex007
[1625
0.500
0,986
[VVC
mm
0,671
0.665
0.533
0,581
gnans
s0.1
0/60
D662
0:590
0.597
-00
0,952
(1:46)
0,787
(.771
umim
=m:m
0.925
0.955
0.831 1omt
0.83) 50/044
0.588
0:57
0833 .a:05
0831=x00
0,914
11917
0,775 50.000
(L772
Exp
0633
0:365
0,222
01994
-1.00
0.659
0,535
0663
1:595
0.537
0,700
s1.9%
0.833
0.803
souss
0.000
0500
0.854
0,78-
24
Threboid
0/29
0:58
ex003
0.530
0,3%
00.0
0.651
0331
5001
0668
0:90
P000
0.330
0,755
=0.09
0.73
0.782
501
0685
0.787
=3/66
0.819
0,730 00:44
Table 13. Average target domain Macro-F1 score of all algorithms on the Taxi, ACS Pub. Cov (Temporal) and ACS Income (Synthetic) datasets. In Taxi and ACS Pub. Cov (Temporal), we test all algorithms on the 3 target domains and report the mean and standard deviation across all target domains. The standard deviation here reflects the stability of performances across different target states. ACS Income (Synthetic), we simulate strong covariate shifts according to the "Age" feature, where 10% and 20% means the minor group ratio in training, respectively.
Dataset
Taxi
ACS Pub. Cov (Temporal) 1T
ACS Incone (Synthetic) 20%
Source
EDG
XTC
CA
102
id.
0.0d
id.
6.0d
12.
0.0d
idd
0nd
i.d.
0.o.d
0.0.1
Base
I.R
0.754
01665
0,802
0.731
10/14
0.641
0.599
0.586
0.528
20.04
0.797
0.799
0.766
0.780
Methods
SVM
0.757
0,761
0.809
0.738
10,19
0.663
0.613
20:03
0.612
0.556
20.006
0,795
0,764
NIA
NIA
MLP
01757
0.684
08233
0.719
10035
0.692
0.652
20012
0.674
0.587
20.00
0.817
0.796
0.792
0.762
Tree
Random Furest
0.760
0.762
1oar
0.800
0.18 1oms
0.692
01643
0.663
0.571
10:03
0.810
0.797
0.782
0.777
Ensemble
LightBBM
0.866
0.717
0.84]
0.701
1001
0.711
0.668
20855
0.683
0.595
0.817
0.813
0.787
0.788
Methods
XGBoost
0.839
0.625
#00l5
0.845
0.723 20017
0.715
0.679
20.844
0.689
0.591
0.815
0,50]
0.787
0.788
x DRR
0.776
0.693
stvaus
0.830
0.736
10:00
0.675
0.683
0.663
0.580
0.820
0.788
0.790
0.783
DRO
CVaR-DRO
0.767
0.744
500322
0.335
0.732 20:000
0,668
0.625
20004
0.634
0.586
20.055
0.820
0.799
0.791
0.763
Mechuds
2DDORO
0.750
0.752
0.816
0.750
1000
0.568
0,400
20
0,531
0.501
20.000
0,810
0.796
0.778
0.766
CVaR-DORO
0.756
0.724
0.829
0.730
0.652
0.610
20.77
0,618
0.556
0.812
0.776
0.763
Group DRO
N/A
NIA
N/A
NIA
0.682
0.655
0.667
0.605
20.100
0.814
0.798
0.795
0.763
SUBY
0.59
0.699
200014
0.835
0.708
40:14
0.706
0.690
=0.003
0.678
0,660
0.774
0,699
0.716
0.562
Imbolanced
RWY
0311
0.737
20033
0.400
0.713 100r7
0,716
0.703
20.003
0,603
0.656
20.009
0.795
0.780
0.768
0.766
Learnnng
SUBG
0.888
0,712
400m2
0.857
0.701 40003
0.707
0.692
20.033
0.687
0.588
0,816
0,502
0.78%
0.783
Melhoda
RWG
0802
0.731
0.340
0L720 1001s
0.713
0.654
20083
0.686
0.601
0,816
0.510
0.798
(.791
JTT
0882
0.686
1oom
0,830
(.704
0.677
[1654
0.676
0.641
10:014
0.801
0.780
0.772
(1750
DWR
0.455
0.671
sooto
0.813
0.673
20:115
0.713
0.675
20877
0.685
c0
0.817
0,812
0.785
0.765
DP
0.842
(.696
20030
0.843
0,702
20:114
0.712
0.671
L0:05
0.689
0.600
20.031
0.815
0.813
0.785
0.795
Faimess
1003
0.345
(1706
100115
0.713
01670
200:
0.686
0.814
0.79K
0.782
01788
Methods
EP
0.501
0.723
0.835
0,710
10.114
0,712
0.671
20035
0.687
0.597
0,814
0.815
0.786
0.786
Exp
0.797
0.724
40034
0.838
0.700
10.115
0.712
0.643
20.03
0.685
0.597
0.814
0.796
0.781
0.783
Threshold
0.806
0.650
0.812
0.536
0.711
0.670
0
0.605
0,785
0.785
0.752
0.761
36

---

Table 14. Worst target domain Macro-F1 Score of all algorithms on the ACS Income and ACS Pub. Cov datasets. In each setting, we test all algorithms on the 50 American states and report the worst Macro-FI Fl Score among all 50 target states.
Dutaset
ACS INCINE
ACS
PUB.CIV
Source State
CT
KA
5D
FL
TX
ME
IN
i.d.
0.0.d
id.
0.0.4
idA.
o...d
i.d.
0.0.d
1.d.
0.0.d
6.d.
0.0.d
i.d.
0.0.d
i.d.
0.0.d
Base
LR
0.804
0.610
0.807
0.597
0.509
0,599
0.714
0.644
0.652
0.478
0.644
0.430
0.655
0.468
0.698
0,514
Methods
SVM
0.795
0.539
0.790
0.505
0.793
0.521
0,898
0.599
0.663
0.493
0.665
0,475
0.698
0:457
0.996
0.559
MLP
0.814
0,574
0.814
0.591
0.816
0,578
0,734
0.669
0.709
0.527
0.713
0,518
0.698
0.496
0,716
0.369
Tree
Random Forest
0,809
0,608
0812
0.599
0,814
0.595
0.687
0.600
0.715
0,503
0.727
0,484
0,779
0.492
0,746
0:573
Ensemble
LightGBM
0.811
0.595
0.211
0.584
0.823
0.586
0.732
0.644
0.750
0,545
0.739
0.501
0.745
0.474
0,750
0.601
Methods
XGBoost
0.814
0.602
0,588
0.522
0.591
0.723
0.723
0.547
0.130
0.489
0.755
0.525
0.747
0.580
X-DRO
0.813
0,583
0.12
0.584
0,816
0:570
0.732
0.669
0.704
0.536
0.697
0.514
0,685
0.544
0,715
0.588
CVRR DRO
0.808
0.583
0.812
0.591
0.520
0.584
0.730
0.643
0.693
0.517
0.706
0.508
0.668
0.603
0,700
0.549
DRD
Methods
--DORO
0.801
0,588
0.535
0,812
0:41
0.717
0.662
0.526
0,476
0:18
0,431
0,499
0,516
0.419
CVaRtDDORS
0.802
0.560
0.804
0.543
01811
0.539
0.720
0.655
0.660
0.481
0.675
0,474
0.559
0.464
0.549
0.562
Group DRO
0.605
0.596
0.817
0.580
0.741
0.677
0.706
0.511
0.717
0.513
0.700
0.504
0.419
0.304
SUBY
0.807
0.562
0:155
0.574
0.820
0.599
0.719
0 0.606
0.710
0,642
0,710
0,600
0,704
0.616
0,748
0.660
Inbalanced
SUBG
RWY
0.813
0.812
0.603
0.553
0.11
0.818
0.588
0.576
11:20
0.221
0.584
11569-000
0.726
0.733
0.637
0.645
0.719
0.725
0.646
11566
0.729
0.331
0.552
0.610
0.739
0.736
0:517
0.555
0.742
0.749
0.542
0.654
Methods
Leaminng
RWG
0.814
0.557
0.819
0.583
11822
0.588
0.726
0.659
0.723
0.542
0,733
0.485
0.748
0.915
0.746
0.591
JT
0.777
0.576
0.781
0.601
1,,50
0,6022
0.710
0.649
0.711
0618
0.326
0,574
0.727
0.525
0.718
0.548
DWR
0.812
0.545
0.816
0.597
0.221
0.579
0.733
0.658
0,721
0.540
0.731
0.492
0.732
0.562
0.741
0,608
DP
0.585
0.582
0.87
0.593
0.716
0.688
0.727
0,569
0.729
0.507
0.750
0.488
0.742
0.587
Faimess
EO
0.813
0.599
0:18
0.590
0.820
0.591
0.721
0.32
0.724
0,544
0.734
0,516
0.737
0,514
0,748
0.601
Methods
EP
0.811
0.596
0.819
0,588
0,201
0,580
0.723
0.646
0.724
0,561
0.731
0.457
0.747
0.599
0.748
0.589
Exp
0,806
0.586
0.810
0.579
0818
0.585
0.706
0.26
0.724
0,551
0.729
0.484
0.738
0.476
0,741
0611
Threshold
0,766
0.548
0.768
0,570
0.771
0.590
0.665
0.611
0.722
0.548
0,317
0.493
0.714
0.504
0.728
0.568
Table 15. Worst target domain Macro-Fl Score of all algorithms on the ACS Mobility and US Accident datasets. In ACS Mobility: tiy we test all algorithms on the 50 American states and report the worst Macro-FI Score among all 50 target states. And in US Accident, we choose 13 American states with relatively high sample sizes in testing.
Dataset
ACS Nobility
US Accident
Source State
NY
CA
PA
CA.
FL
IX
ND
a.ndd
i.d.
0.3d
i.d.
0.9d
5.d.
6.0.d
i.d.
auoud
LR
0.451
0.397
0.462
0.399
0.531
0.450
0,527
0.449
0.800
0.437
0.898
0.489
0.936
0.573
0.855
0.528
Base
Methods
SVM
0.604
0.544
0.592
0.527
0.635
0.489
0.623
0.539
0,793
0.505
0.891
0.568
0.928
0.542
0,550
0.540
MLP
0.600
0.530
0.622
0.560
0.607
0.551
0,608
0.535
0.827
0.592
0.925
0,595
0.934
0.567
0.856
0.548
Tree
Randen Furest
0,570
0.482
0.587
0.514
0.641
0.492
0.635
0.510
0,846
0.613
0.932
0.579
0.938
0.584
0,911
0.642
Ensemble
LightGBM
0.637
0.554
0.545
0.61
0.660
0.851
0.67
0.929
0.582
0.584
0
0.639
Methods
XGBoost
0.637
0.557
0.625
0,566
0.678
0.521
0.664
0.560
0,852
0.600
0.922
0,582
0.929
0.585
0.920
0.636
x >DR
0.613
0.571
0.599
0.539
11540
0.374
0.606
0.539
0.824
0.596
0,922
0.514
0.933
0.573
0.883
0.534
DRO
CVaR-DRO
0.621
0.551
0.628
0.557
0,574
0312
0,639
0.188
0.825
0.591
0.924
0.572
0.936
0.522
0,888
0.561
Methods
x DDRO
0.509
0.464
0.699
0,568
0.530
0.474
0,540
0.481
0,815
0.540
0.920
0.592
0.927
0.569
0.874
0.590
CVaR-DORO
0.533
0.500
0.625
0,531
0,501
0.479
0.510
0.443
0.825
0.607
0.922
0.589
0.934
0.575
0,857
0.371
Group DRO
0,588
0,516
0.366
0,480
0.564
0:491
0.595
0.508
N/A
N/A
N/A
NAA
N/A
N/A
N/A
NIA
SUBY
0.657
0.590
0.669
0.548
11674
0.565
0.67%
0.568
0.854
0.633
0.335
0.585
0.938
0.582
0.915
1.635
Imbolanced
RWY
0.657
0.574
06647
0.573
01678
0.557
0.677
0.576
0.8%6
0818
09900
0.581
0144
0.82
0.920
D.67
Leaming
SUBG
0.635
0.546
0.624
0.542
0,672
0.525
0.658
0.552
0.847
0.627
0.255
0.578
0.937
0.582
0,906
0.635
Medhods
RWG
0.637
0.542
0.553
0.676
0:521
0.663
0.855
0.614
0.929
0.588
0.833
0.635
JTT
0.639
0.555
0.66
0.546
0.660
0.36
0.639
0.528
0.843
0.611
0.922
0,581
0.935
0.583
0,912
0.635
DWR
0.622
0.553
0.550
0.656
0313
0.647
0.361
0.853
0.623
0.929
0.576
0.583
0.917
0.627
DP
0.630
0.555
0621
0.556
0.663
0.366
0.668
0.557
0.847
0.618
0.922
0,590
0.933
0.582
0.915
0.630
Methods
Faimess
EP
EO
0.63
0.632
0.550
0.552
0620
0.655
0.547
0.552
18811
0.66
0.39
0.59
0.662
0.660
0166220000
0.563
0.543
0.852
0.614
0928
03587
0.594
0933
0.988
0.583
0.583
0.914
0,917
11636
0.634
Exp
0.633
0.544
0.22
0.591
0.69
0.311
0.663
0.544
0.837
0.613
0.893
0.590
0.099
0.564
0.854
0.619
Tareshold
0.629
0.551
0620
0.550
0.661
0.528
0.658
0.551
0.830
0.605
0.570
0,583
0.385
0.560
0.809
06601
Table 15
For other settings, we do not report the worst-case results because there are not many target domains there and the mean/standard deviation results could reflect the generalization performance well.
For the results of Macro-f1 Score reported in Tables 11 patterns to the accuracy score, while we usually witness wider gap between o.o.d. and i.idd. model performance.
12
13 14
and
15
we find similar conclusion
37

---

D.10 Agreement and Maintenance Plan
Hosting Platform. We will use Github as the hosting platform of our code. We provide detailed preprocessing Python scripts to guide users to replicate and process data from scratch. We also illustrate methodologies to run full experiment results in the code. We also list the license for each dataset and user guidance in the Readme file in that Github
Dependencies. The benchmark built upon Python 3.8+ and depends on PyTorch, aif360, fairleam, xgboost, lightgbm. Besides, it uses numpy, scipy, and pandas for basic data manipulation.
Maintemance Plan. The datasets provided here will be maintained by the authors of the paper, which can be contacted by raising an issue on GitHub or by contacting the first authors directly. Our benchmark and simple open-sourced Python package based on that may be updated the discretion of authors in the future, which includes more refined algorithm implementations, datasets, and framework with improved efficiency.
Author Statements. To the best of our knowledge, the proposed benchmark is based on existing datasets and does violate any existing licenses non contain personally identifiable or privacy- related information. And we claim all the responsibility in case of violation of rights if such violation were to exist.
38


Reviews:
[{"review_id": "hieb2fi6Kd", "reviewer": "Reviewer_np4K", "summary": "", "questions": "", "limitations": "- The authors use the Adult dataset, but some papers argue for retiring this dataset and instead using ACS Income (which the authors also use) [1]. The ACS Income dataset is larger and has more recent data than Adult.\n\n- The authors discuss the limitations of their study in the Appendix (not in Section 5, as indicated by their checklist). The authors should also discuss potential negative implications of their work. (e.g., How may Algorithm 1 be misused, and what would be the implications of this? How can incorrect predictions by Algorithm 1 harm already-vulnerable groups?)\n\n[1] https://arxiv.org/pdf/2108.04884.pdf", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "- The authors motivate studying distribution shifts for tabular data, citing \"missing variables and hidden confounders\" (line 25) (e.g., smoking status, socioeconomic status). The authors also claim that it is unclear which types of distribution shifts existing benchmarks evaluate, which can cause them to have poor external validity across diverse real-world shifts.\n\n- The authors rightly emphasize the need to characterize and understand the source of distribution shifts, towards devising interventions beyond technical solutions; their case study with ACS Income, which includes concrete social groundings of empirical observations, is a nice example of this.\n\n- The authors benchmark an impressive number of distribution shift methods and model configurations (including fairness methods and tree ensembles).\n\n- The authors' findings that: (1) Y | X shifts are most responsible for performance degradation on the tabular datasets (with the exception of temporal shifts), and (2) a small validation set from the target distribution can help with transfer, are interesting.\n\n- Figure 2 clearly shows that across datasets and hyperparameters, even the best XGBoost model experiences considerable degradation in its target accuracy vs. its source accuracy, and there is great variance in the magnitude of degradation.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "q5glq7sVhi", "reviewer": "Reviewer_wGZu", "summary": "", "questions": "", "limitations": "No. The authors not adequately addressed the limitations and potential negative societal impact of their work. Based on this statement, one limitation of this work is that it focuses on exploring distribution shifts in real-world tabular datasets but does not explicitly address potential limitations or challenges associated with generalizing the findings to other types of data or domains. Further investigation and discussion on the transferability and applicability of the proposed algorithmic and data-based interventions across different data modalities would strengthen the overall scope and impact of the research.", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "1. The authors propose a test platform to aid researchers in developing more concise language for distribution shift analysis.\n\n2. The paper discusses various types of distribution changes and their impacts on algorithms and data-driven interventions. This research is highly relevant to the broader field as it delves into the challenges of handling distribution shifts in practical applications.\n\n3. This paper emphasizes the importance of identifying the region of covariates in a table setup where Y|X shifts are most pronounced and proposes a simple yet efficient method to identify data regions with strong Y |X shifts\n", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "K6XJVDXrFL", "reviewer": "Reviewer_Tsg7", "summary": "", "questions": "", "limitations": "The authors themselves point out that gathering supplementary data to the data used in the paper may improve some of the effects of the distribution shifts. Then, they point out that adding supplementary data would be costly and proceed to perform a benchmark that tests distribution shifts across 22 different algorithms- a quite costly endeavor. I had a hard time being convinced that such work would greatly contribute to advancement in the field. ", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "The analysis appears interesting and like there was a lot of effort into the work. ", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "32Dkrcjlww", "reviewer": "Reviewer_AmNg", "summary": "", "questions": "", "limitations": "I see no potential negative societal impact of this work. The work means to develop tools and benchmarks for dealing with a phenomenon which can lead to negative societal impact. \n\nThe authors have a section on limitations, but it only occurs in the appendix. If there is room, it would be better to integrate it into the conclusion.", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "•\teffectively distinguishes Y|X-shift and X shift and motivates qualitatively and empirically why it matters. \n\n•\tShift is an important issue for real world ML deployment and this paper packs in a number of contributions. It provides datasets, compares algorithms on those datasets, complicates some existing results, and introduces and demonstrates non-algorithmic methods for addressing shift .\n\n•\tProvides effective figures illustrating the main points and integrates them well into the text. I particularly like Figure 4 and the accompanying case study.\n\n•\tAlthough presented in a preliminary manner, the tool for identifying target covariate regions where shift may be an issue (section 3.1) could be a useful addition to the body of tools for identifying sources of shift and how to address them. \n\n•\tNo ethical issues\n\n•\tComes with an appendix that provides considerable further detail", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}]

Author rebuttal:

Meta-review: This paper introduces a dataset to benchmark model performance under distribution shifts for tabular data. The reviewers agreed that the ideas in the paper are very relevant and well-motivated, with a rigorous and comprehensive evaluation that covers multiple types of shifts. The writing and presentation were appreciated as well. The reviews contain several suggestions, including a clearer and more comprehensive discussion of limitations and negative implications, along with tips on restructuring the writing, as well as other suggestions. After an active discussion with the authors, it is clear that the paper is ready for publication.
Decision: Accept (Poster)