Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation
Authors: Joshua P Gardner
Zoran Popovi
Ludwig Schmidt
Venue: NeurIPS 2022 Accept (2022)
Keywords: robustness
fairness
tabular data
gradient boosting

Abstract: Researchers have proposed many methods for fair and robust machine learning, but comprehensive empirical evaluation of their subgroup robustness is lacking. In this work, we address this gap in the context of tabular data, where sensitive subgroups are clearly-defined, real-world fairness problems abound, and prior works often do not compare to state-of-the-art tree-based models as baselines. We conduct an empirical comparison of several previously-proposed methods for fair and robust learning  alongside state-of-the-art tree-based methods  and other baselines. Via experiments with more than $340{,}000$ model configurations on eight datasets, we show that tree-based methods have strong subgroup robustness, even when compared to robustness- and fairness-enhancing methods. Moreover, the best tree-based models tend to show good performance over a range of metrics, while robust or group-fair models can show brittleness, with significant performance differences across different metrics for a fixed model. We also demonstrate that tree-based models show less sensitivity to hyperparameter configurations, and are less costly to train. Our work suggests that tree-based ensemble models make an effective baseline for tabular data, and are a sensible default when subgroup robustness is desired. See https://github.com/jpgard/subgroup-robustness-grows-on-trees for code to reproduce our experiments and detailed experimental results.

Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation
Josh Gardner!
Zoran Popović
Ludwig Schmidt 1.2
University of Washington 2 Allen Institute for Al
{jgarrd zoran, schmidt) @cs. washington. edu
Abstract
Researchers have proposed many methods for fair and robust machine learning, but comprehensive empirical evaluation of their subgroup robustness is lacking. this work, we address this gap in the context of tabular data, where sensitive subgroups are clearly-defined, real-world fairness problems abound, and prior works often not compare to state-of-the-an tree-based models as baselines. We conduct empirical comparison of several previously-prope pprooosed methods for fair and robust learning alongside state-of-the-an tree-based methods and other baselines. Via experiments with more than 340,000 model configurations on eight datasets, we show that tree-based methods have strong subgroup robustness, even when compared to robustness- and fairness-ent hiimess-enhancing methods. Moreover, the best tree- based models tend to show good performance over a range of metrics, while robust group-fitt soiu--fair models can show brittleness, with significant performance differences across different metrics for fixed model. We also demonstrate that tree-based models show less sensitivity hyperparameter configurations, and are less costly to train. Our work suggests that tree-based ensemble models make effective baseline for tabular data, and are sensible default when subgroup robustness is desired."
Introduction
Over the past decade, the field of machine learning (ML) has seen a dramatic expansion along two related lines. On one hand, concerns about the fairness of ML models, and more broadly their performance on data outside the training distribution, have grown [50]. Both theoretical and empirical works have raised these concerns, demonstrating the vulnerability of models to learn biases from data or suffer performance drops under distribution shifts [44, 66, 35). On the other hand, an abundance of methods have been proposed to address these limitations. These include fairness methods used to equalize metrics across groups, as well as distributional robustness methods which optimize for a worst-case distribution within a bounded distance of the training distribution.
Our work begins from the observation that, while "fairness" and "robustness" are distinct concepts, methods in both areas often have similar goals. In particular, they share two (sometimes implicit) goals: First, models should have low disparity (variation in performance over all subgroups should be minimized; cf. [75, 17, 25, 43]). Second, models should have good worst-group performance (the lowest accuracy over all subgroups should be maximized; cf. [74, 62)). As a consequence these two criteria, both fairness and robustness typically entail improving subgroup robustness.
'See https://t/tiiii com/ our experiments and detailed experimental results.
robusstnessro wwwee-rrowwwoeoeeeo on- trees for code to reproduce
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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ACS Income
ACS Income
ACS Income
Worst: Grott-rruupp. Accuracy
08
84
Worst Group Accuracy
87
do as 8a
Bi
Prrst-Group
6.2
6-4
0.1
0.2
With Beyt Clu
Accuracy
Accuracy
XGBoost Group DRO
ACS Public Coverage
Public Coverage
ACS Public Coverage
Worst- Grouprrappp Accuracy
Worst-Grn Groupprrupppp Accurary
Worst- Group Accuracy
8.5
04
0.4
82
With Bell Auctmay
Accuracy
Accuracy
60
XGBoost Group DRO
LARC
LARC
LARC
Worst-Ga Group Accuracy
97
Worst-Gris Accuracy
Worst-ca Worst-Group Perr-rroupppp Accuracy
Be
de.
94/20.000
0.3
0.5
633
0.4
HBP
05
0.7
0.4
0.6
0.7
80
XGBoost Group DRO
Accuracy
Accuracy
Majority Baseline
DRO x
Group DRO
Subgroup Maj. Baseline
XGBeast
Zero-D D'sparrity Line
Random Baseline
Figure Results from three datasets in our study. (a) Left: Tree-based methods such as XG- Boost show similar subgroup robustness, with sometimes better overall performance, robustness- enhancing or disparity- methods. (b) Center: Model performance frontiers corresponding to (a) show similar recuracy-robustnes frontiers for XGBoost and DRO/Group DRO. (c) Right: Tree-based methods' worst-group accuracy is robust to model selection metrics.
Our work focuses on subgroup robustness in the context of tabular data, for several reasons. First, tabular data is widely used in practice, being the most common format in areas with important fairness impacts such as medicine, finance, and recommender systems [38, 64). Second, tabular data often directly encodes sensitive attributes with respect to which subgroup robustness is desired (race, gender, income level), and these attributes are often declared by the individuals represented in the dataset. This is an important difference compared to crowdsourced group annotations (e.g., gender or race for image datasets), which can be unreliable [21] or fail reflect the lived experiences of individuals represented [19]. Finally, tabular data is challenging to model. It is often heterogeneous, containing mixed data types; lacks the spatial, linguistic. or temporal structures common to other data (image, text, audio) where machine learning has seen dramatic progress over the past decade; and it can relatively small, containing personal information which cannot be scraped at Internet scale.
In this work, we conduct a series of experiments to jointly compare methods from the fairness and robustness literature. Despite the fact that many works often use similar metrics and datasets, there is a lack large-scale empirical studies comparing relevant methods to each other, and to strong baselines. This lack of effective baselines is particularly concerning in light of recent works across several other areas of machine learning which have shown that simple baselines can perform surprisingly well against state-of-the-art techniques [47].

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Our results show that modern tabular- dablaa-data baselines can outperform even well-tuned ofateoo--hhe-a robustness- or
methods with fraction of the computational cost. Our analysis includes set of tree-based models which achieve strong performance on tabular data but are absent from prior works on robustness, which largely only compare to deep learning-based approaches despite their tendency to perform poorly on tabular data [38]. In our experiments, we endeavor to tune both the "fair" or "robust" models and representative suite of baseline methods for tabular data to obtain estimates of the empirical accuracy-subgrone robustness Pareto frontier for each model. To this end, we explore a wide space of architectures, regularization schemes, and training hyperparameters, across eight tabular datasets and 17 model classes. Our work is empirical contribution concerned not with proposing new methods, but with conducting a novel and rigorous evaluation of existing methods for learning subgroup-robuss models from tabular data. Our contributions
follows:
Trees are subgroup-robust learners: While previous works have shown that modern tree-based ensembles have strong wverage-group performance (see Section 2.3), we show that these models are also surprisingly robust to subgroup shift. Tree-based models achieve this robustness despite lacking any explicit robustness intervention and using only average-case classification losses, achieving competitive or better performance against state-of-the-art methods for fairness and robustness (Figure la, lb) over a large hyperparameter and model search space. To support the above analysis, we apply several techniques for the analysis of hyperparameter sweeps such as model performance frontier curves (Figure lb,3) and hyperparameter sensitivity analysis (Figures 7, 8, 9).
Trees show show consistent performance across accuracy and robustness metries: We empirically investigate the relationship between three types of metrics (accuracy, robustness, fairness). We show that metrics within these groups often agree, but the relationships across metric groups (i.e. robust CVaR risk and accuracy) are inconsistent. One consequence of this finding is that model selection techniques affect tree-based models and "robust" or fairness-enhancing methods differently: tree-based methods show consistent subgroup robustness across metrics (Figure Ic), while robust and fairness-enhancing methods are "metric-britlee and tend to display poor subgroup robustness according to other metrics ge.g. worst-group accuracy).
Trees are less sensitive to hyperparameters and less costly to train: We show that, in addition to their improved robustness when fully tuned, trees also require less tuning and are less costly to train. We demonstrate that trees have decreased sensitivity to hyperparameters even when accounting for hyperparameter settings which were part of our initial grid but performed poorly across all datasets and that these models require considerably less compute and financial cost train when compared to deep learning-based robust learning techniques.
In particular, our results highlight the importance of the underlying model class for subgroup robustness in tabular data. Our results suggest that subgroup robustness interventions based on the loss-based perspective alone may be limited, particularly because existing loss-based methods for robustness are incompatible with nondifferentiable functions such as tree-based ensembles. We provide further discussion in Section 7.
We provide code to reproduce our experiments, along with an interactive tool to ex- plore the best-performing hyperparameter configurations, at https: /ttes:://ttttttttee com wtt.r////////////oc www.rroroooussooooeeeeeerr -wo---rooww----- -rwws-on-tresseeee trees.
2
Related Work
2.1 Bhirness-Enhancing Methods for Supervised Learning
wide variety of works have addressed fairness in the context of machine learning, where "fairness" is often measured by the equalization of some metric over groups [5. 18]. Most methods can be characterized as performing either pre- in-, or post-processing, which attempt ensure fairness considerations are met in different stages of the modeling lifecycle. Preprocessing [73, 15) attempts to modify the input data to meet fairness criteria, while preserving the structure of the inputs and their relationship to the prediction target. Inprocessing uses modified training procedure to explicitly optimize for a fairness-aware objective during model training. This includes using constrained or reduction-based optimization [1, 72), or including explicit regularizers designed to encourage faimess [7, 11, 43, 56]. Postprocessing [32, 53] operates on the predictions of model, modifying them to achieve fairness criteria.
3

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The impact of fairness under subpopulation shift is analyzed in [48], which shows theoretically that enforcing fairness during training can harm or improve the model, under certain conditions, and [65] conducts a causal analysis of fairness under covariate shift. Perhaps the work most closely related to the current study Friedler et al. [26], which evaluates set of pre-, in-, and postprocessing algorithms, demonstrating that many of these techniques show instability (variations in performance over different train-test splits) and that several fairness metrics are empirically correlated. Friedler et al. [26] do not, however, evaluate robust learning techniques, modern tree-based techniques (besides CART), or neural methods. Empirical evaluation recent methods is needed.
2.2 Distributionally Robust Learning
While efforts in robust optimization date back several decades [10], recent works have adapted and extended robust learning approaches to deep learning. For example, several variants of distributionally robust optimization (DRO) have been proposed for the training of neural networks with robustness guarantees [36, 46, 62, 61, 74, 25]. While these approaches toward fairness, they are frequently evaluated in terms of their performance benefits for minimizing performance gaps between sensitive subgroups in real-world data [74, 62, 33).
not always explicitly oriented
A particular form of shift (and robustness) evaluated by these works is subgroup shift (also called subpopulation shift) [50], where the balance of subgroups in the data shifts between training and testing. Evaluating performance on individual subgroups is an extreme version of subgroup shift. In the context of faireess, these subgroups often defined by one more discrete sensitive attributes, such as race, gender, or income level, and intersections between these sensitive groups can often identify groups most susceptible to performance disparities [14].
2.3 Models for Tabular Data
Deep learning-based approaches largely have not achieved the transformative performance gains on tabular data that they have with other data modalities such as images, text, and audio [38, 13, 64). The existing state-of-the-art for learning with tabular data is widely acknowledged to be tree-based methods, and in particular gradient-hoosted trees [31, 54, 64, 13]. This includes GBM [27, 28), LightGBM [40], XGBoost [16], and CatBoost [22, 55J, which often show only small differences in performance between them. Several deep lcarning-based approaches have recently attempted to close the gap of deep learning-based solutions for tabular data [38, 2, 37, 54, 39]. However, empirical analyses have shown that the reported performance of these methods does not generalize well to other datasets, and gradient boosting methods still achieve better performance with less tuning and a considerably smaller computational budget. For example, [64] and [13] both show, in separate analyses, that gradient boosting consistently outperforms these state-of-the-arr tabular deep learning methods across several datasets, and tree-based methods achieve competitive performance with the deep learning approaches proposed in [29.3]]-
The overall predictive performance of these tabular methods is evaluated in e.g. [13, 29, 38, 54, 64]. However, the existing literature does not investigate the fairness properties, subgroup performance, or robustness to subgroup shift of tabular data models; nor does it compare to subgroup-robust learning methods. Additionally, despite the widely-know known strong performance of these models on tabular data, we are aware of no prior work which compares tree-based methods to robust neural network- based learners, despite the fact that the latter are commonly evaluated on tabular data (e.g. [36, 43, 74, 621). Notably, [1] evaluates GBM in conjunction with their proposed inprocessing method, but does not evaluate subpopulation robustness; [20] evaluates GBM with faimess methods but does not compare to robust methods and does not tune the GBM with fairness methods.
3 Setup
Our work is primarily concerned with empirically evaluating the sensitivity of various supervised learning methods to subpopulation shift. Below, we introduce our formal model, and then describe the main axes of variation in our experiments. This includes
(i) large set of models, many of which have not been directly compared in previous works; (ii) the hyperparameters used for each model;
(iii) suite of eight real-world fairness datasets; and (iv) a set of evaluation metrics used across the disparate literature on robustness, subpopulation shift, and fairness in machine learning.

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3.1 Preliminaries
Our work evaluates the task of learning a model fa E F, function from model class parameterized by 0. The parameters are learned from dataset D == (Ia, Vi)i=1 P where P is the data-generating distribution. This matches the case, most common practice, where single model is learned by estimating ming E (CC (e(x)) fo())) and deployed for all users. We evaluate the binary classification context, where y E {0, } and fa( = 2 E [0, 1] the score assigned by f to the outcome y/4 = 1. Each 2; R2 can be partitioned into I; (II,1..... -i, a) where
a sensitive attribute. For notational convenience, we represent a as a single feature here, but in our data, is typically defined as the concatenation of multiple binary sensitive attributes (e.g. gender female, race white). Let Da = ((1; vi) Pla, a} denote the subgroup of the dataset with given sensitive identity.
Following many of the previous works in both faireess [18] and robustness [74, 43], our analysis focuses on the performance of fe on each D. for all E A. We are particularly interested in the worst-group performance and the loss disparity, respectively defined
(I) These metrics can be thought of as assessing the sensitivity of fo to subgroup shift, evaluating the worst-group shift from D to Da (note that subgroup shift is itself form of covariate shift [50]).
WoestGrroup = max ED-P (Ca(oo] and DISP == max EDNP [FCa Ca (fo)l a,a' E.A
acA
3.2 Models
Our goal is to conduct a thorough empirical comparison of the subgroup robustness of a suite of methods for tabular data. We provide more detailed description of all models used in Section B.
Fairness-enhancing models: We evaluate the LFR preprocessing method of [73]; the inprocessing method ]] and the postprocessing method of [32]. As in [1, 20), we use GBM the base learner for each model; however, unlike [20], we also tune the base learner parameters.
We evaluate both the CVaR and x2 constraint forms of DRO via [46]; the CVaR and x² constraint forms of DORO [74]; Group DRO [62]; Marginal DRO [24]; and Maximum Weighted Loss Discrepancy [43]. Each robust optimization method is used with multilayer perceptron (MLP), as most previous works when using tabular data, e-g. [43, 46, 62, 74]. We note that the use of these losses requires performing optimization over a continuous function (such neural network), which makes these loss-based robustness interventions incompatible with existing training procedures for e.g. tree-based models.
Robust models:
Tree-based models: We evaluate GBM, LightGBM [40], XGBoost [16], and Random Forest models.
Baseline models: As baselines, we include Izgrreularized logistic regression, Support Vector Machines, and fully-connected neural networks (MLP) with standard (non-DRO) ERM optimization.
3.3 Hyperparameter Sweeps
For each model, conduct a grid search over large set of hyperparameters. We give the complete set of hyperparameters tuned for each model in Section F.
Our hyperparameter search for each model is extensive by design, in order to ensure reliable comparison of the best-performing models from each class. We expand the initial grid for continuous hyprraarameters when model on the Pareto frontier is at the edge of the grid. When one method includes another as a "base" learner (e.g. LFR preprocessing with GBM, or DRO with MLP), we include the full tuning grid for the base model (i.e. we explore the cross-product of all MLP hyperparameters with all DRO hyperparameters).
We note that previous works tend to either compare against fixed baseline architecture and training hyperparameters (e.g. [74, 38)), perform manual tuning ([46)), or do not tune hyperparameters the base model when using fairness- chihnncng techniques ([20]).
5

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3,4 Metrics
One goal our work to assess the empirical relationship between the model evaluation metrics used in the robustness, fairness, and classification literatures. Differences in the training objectives used across the various fair and robust models in prior work make such a comparison particularly usefull The relationship between these diverse evaluation metrics is not explored in existing work, where several different metrics have been used to compare the performance models, evaluate their fairness with respect subgroups, and measure their robustness to various shifts or outliers. We draw several metrics from prior works and report them for our experiments. We also explore the empirical relationships between different metries.
For each metric (e.g. loss, accuracy, Equalized Odds), we can not only measure the overall empirical performance of model, but can measure the worst-group loss and disparity over subgroups of the data, as defined in Equation (1). Worst-group and disparity measures, for various formulations loss functions above, In particular, we use the D and WorstGroup with accuracy as the loss function. Accuracy is widely used in practice, directly interpretable, and invariant rescaling of the model's predictions.
the
widely-used measure of fairness and robustness [12, 74, 62, 61, 33, 44].
We also use the CVaR risk metric from the robustness literature. CVaR risk is measured over set of inputs D = (mz, = ~ P and measures the worst-case weighted loss, according to some loss function e, at level a over the inputs in D:
N Σ [e((oox)) s.t. 1|allo S aN TEAN
LevaR DovaR(D,P)r = sup
(2)
(2) is the risk function optimized by the DRO CVaR model [46]. but it is also used more widely as measure of the tail risk of a classifier (ef. [74]).
Additional fairness and robustness metrics are reported in Section G and defined in Section C.
Dataset
1
d
Target
Sensitive Attributes
ACS Income
499,350
20
Income 2 56k
Race, Sex
ACS Public Coverage
341,487
19
Public Ins. Coverage
Race, Sex
Adult
48,845
14
Income 2 56k
Race, Sex
Behavioral Risk
Factors
175,745
28
Diabetes
Race, Sex
Surveillance System (BRFSS)
Communities & Crime
1994
113
High Crime
Income Level, Race
COMPAS
7,215
10
Recidivism
Race, Sex
German Credit
1,000
22
Credit Risk
Age, Sex
Learning Analytics Architec-
169,032
26
At-Risk (Grade)
URM Status, Sex
ture (LARC)
Table Overview of datasets used.
3.5 Datasets
We evaluate the models over eight datasets covering variety of prediction tasks and domains. We two binary sensitive attributes from each dataset, for total of four nonoverlapping subgroups in each dataset. A summary of the datasets used in this work is given in Table I. We provide additional details each dataset, along with critical framing and context regarding these prediction tasks and their representations of individuals, in Section A.
4 Results: Tree Models are Subgroup-Robust Learners
Our main finding is that tree-based models are subgroup-robust learners. Tree-based models match or exceed the performance of distributionally robust and fairness-enhancing models in terms of best overall accuracy, worst-group accuracy, and accuracy disparity all datasets evaluated.

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ACS Income
ACS Public Coverage
Adult
BRFSS
675
Worst- Worst-Srroup Sroo-rrruuppp Accuracy
676
0.44
0.25
0.78
0.83
0.77
0.14
0.10
0.3
0.00
0.11
6.75
0.76
0.70
0.70
0.81
0.05
0.67
0.50
0.50
Communities and Crime
COMPAS
German Credit
LARC
6.73
Wirsst Grropt Accuracy
0.00
6.72
0.73
0.73
6.71
0.75
0.72
0.73
0.70
810
0.02
0.75
0.53
025
0.00 0/1
0.7
0.
3.14
0./0
0:50
0150
0.Y1
0.74 U.d
0.74 Accuracy
Accuracy
Accuracy
Accuracy
Zero-Disparity Line
Tree Methods
Rooust Methods
Falmess Methods
Baseline Methods
Figure 2: Overall Accuracy vs. Worst-Group Accuracy of robust, faimess-cnhancing tree-based, and baseline models over eight tabular datasets. Dashed lines indicate y x, when worst-group accuracy equal to overall accuracy (zero accuracy disparity). See Figures 12-15 for more detailed results by algorithm. Note: "discretization" artifacts are due small test/dataset sizes.
summary of our results is shown Figures 2, 2, 3, and 4. Following previous works, our main evaluation metries are accuracy-based: overall accuracy, worst-group accuracy, and accuracy disparity. Over the wide sweep of datasets and model configurations evaluated, modern tree-based models- GBM, LightGBM, Random Forest and XGBoost all achieve subgroup performance characteristics on par with, or better than, the set of robust or fairness-ent eernesssenhaacingg models evaluated. For example, on three of the four largest datasets our study (ACS Income, ACS Public Coverage, LARC),
Adult
BRFSS
Comm. and Crime
Worst-Groi Group Accuracy
0.9
0.5
0.0
dac
0n
0.C
8.50
0.85 685
0,8s
21
00
COMPAS
German Credit
Worst- Grosp Accuracy
Majority Baseline
Subgroup-Ma,
27.
Random Raseline
DRO y
09613-
0.00
XGBoost
Group DRO
DORO CVaR
hproc.
12
Zero Disperity Line
02
04
Accuracy
Accuracy
Figure 3: Model performance frontiers, formed by tracing the convex envelope of model performance. Tree-based models achieve comparable and sometimes improved frontiers with the highest-performing robustness methods. (See also Figure 1 for the remaining three datasets.)
7

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ACS Income
ACS Public Coverage
Adult
BRFSS
Accuracy Disparity
6.00
3.5
042
000
6:00
060
380
Comm. and Crime
COMPAS
Credit
LARC
Accuracy Disparity
322
023
0.13
0.5
6.0
Accuracy
Accuracy
Accuracy
Accuracy
Majority Baseline
DRO x²
Group DRO
Improc.
SubgrouppMaj. Baseline
XGBoost
DORO CVa
Zero-Disparity Line
Random Baseline
Figure Model disparity frontiers, formed by tracing the convex envelope of model disparity. Tree-based models achieve comparable and sometimes improved frontiers compared to the highest- performing robustness methods, particularly high-accuracy regions.
XGBoost achieves significantly better & and L.ngg than DRO-based methods (Group DRO, x² DRO), as indicated by nonoverlapping Clopper-Pearson confidence intervals (a- = 0.05).
The only cases where another algorithm achieves better maximum overall robustness (as measured by worst-group accuracy) ) than based methods are DORO CVaR on Adult, and Inprocessing on Communities and Crime (see Figures 4, 4). We note that in both cases, (i) these differences not statistically significant, based on the shown Clopper-Pearee and (fi) these differences occur points below the maximum overall accuracy for each model. In all cases, at the point of maximum overall accuracy, tree-based models achieve equivalent or better worst-group accuracy than all other models evaluated, based Clopper- Pearson CIs at 0.05.
confidence intervals at a = 0.05,
We note that this particularly surprising because none of the tree-based models explicitly optimize for robustness, fairnsss, or subgroup performance in any way; in contrast, the distributionally robust learners and fairness-cnhant
techniques explicitly optimize for such criteria and some cases (DORO, DRO, Group DRO) provide explicit guarantees of various forms of robustness. A similar analysis showing accuracy disparity shown in Figures 16, 17, and a complete set model performance observations from each algorithm and dataset, in Supplementary Section G.
To summarize our results over the large hyperparameter sweeps, we use model performance frontiers to measure the best possible set of tradeoffs between (C and W and (L and CDIS)). Model performance frontiers represent the envelope of the convex hull all observations L(fo) E F. example is shown in Figure 1b and 1d, with the remaining datasets in Figures 3 and 4. The frontiers allow us to compare the best best-possible tradeoff between accuracy and worst-group accuracy (Fig 3; higher is better) or between accuracy and accuracy disparity (Fig 4; lower is better).
5 Results: Robust Models Can Be Metric-Brittle
Our results show that, over all models and datasets, metrics which we refer to as "complementary" those measuring the same event on different subsets, or with different conditioning are strongly correlated with each other: accuracy and worst-grout accuracy; CVaR and CVaR DORO; and Demographic Parity Difference and Equalized Odds Difference all show strong correlation with each model class F; we show these correlations on Adult in Figure 5. The median p values over all datasets and algorithms are 0.87, 0.99, 0.79 for the three pairs of metrics, respectively (we show complete set of correlations for each model and metric in Figure 18). These results show that model selection based on one metric from each pair (Overall Accuracy) is likely to lead to a model with strong performance for the other metric in the pair (e.g. Worst-Group Accuracy).

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Accuracy Vs. Worst-Group Acc.
CVaR vs. CVaR DORO (Complementary)
CVaR vs. Accuracy (Non-Complemt Complementrryy
CVaR vs, Worst-Group Acc.
icomplementary) ry)
(Non-Comp jementrry
Worst-rr Accurecy
P-2.000
Worst Cwo.orouup Rocuracy
0.-
0.7
0.0
ChR CORO
3.3
0.4
0.3
0.3
0.3
0.4
0.6
0.8
0.0
0.5
18
13
2.0
2.5
0.0
0.5
3.8
2.0
2.5
0.0
0.5
-.0
2.0
2.5
Accuracy
CVaR
DRO x²
XCBocst
Group
Figure 5: While "complementary" metrics (those measuring the same event with different condition- ing) are closely correlated for all models, non-complementary metries behave differently by model. Accuracy can vary widely for "robust" models with a fixed robust (CVaR) risk, while for tree models, the best (lowest) CVaR risk is typically associated with the best (highest) accuracy. ACS Income dataset shown; see Supplementary Figure 18 and Section G for additional datasets and metrics.
Adult
BRFSS
Comm. and Crime
COMPAS
German Credit
30
Whrrg Droup
04
PROEE TWFT MOST ADCUYROY Wit Best Chi
D60
X08 Group DRO
DRD
XGBooct Group DRO
DRD
XGBooct Group DRO
DR0 XcBroot Group DRD
DRD
XGBloost Group DRO
Figure Worst-group accuracy for models with best overall accuracy (solid), and best CVaR (shaded). Tree-based models show better performance across con-complementary metrics (as indicated by similar heights of orange bars within each plot), whereas robustness- and fairness-based models do not saatiistcaall--iinifeeeee between best-accuracy and best-CVaR DRO X" and Group DRO models (See also Figure for the remaining three datasets.).
gaps between blue, green bars): worst-group accuracy drops significantly
In contrast, our experiments show that there is a severe lack of correlation across almost all of the non-complementary pairs, shown in the bottom row of Figure 5. In particular, our results show that models which achieve strong "robust" risk - for example, a low CVaR DORO risk, one model selection rule used in [74] can achieve very low accuracies. Indeed, the "robust" learning methods are the most susceptible to this discrepancy over metrics in our experiments, as shown Figure
6. While these results confirm the finding in previous works that fairness metrics correlated [26], our broader comparison shows a brittleness to model selection metrics outside these sets of complementary metrics, and reveal the very strict sense in which robustness guarantees apply only to a limited range of metrics. This discrepancy is of practical significance given that robust models often selected using robust metrics (i.e. DORO CVaR, ef. [74]), while models in practice frequently evaluated using other metrics (i.e. accuracy, fairness metrics).
To illustrate the practical implications of this metric brittleness, we also explore the impact of various strategies for choosing a single S' E F over a set models in each hyperparameter grid. While this problem is implicitly addressed in almost all previous works, the decision is often handled differently. For example, models are tuned and selected by hand [46], chosen based on worst-group performance [74], or based robust risk metrics [62]. The empirical implications of model sclection methods for fairness and robustness are not well-understood.
To address this question, we show the worst-group performance of models over our sweeps, se- lected according to either best accuracy or best CVaR in Figure 6. Figure 6 demonstrates the downstream impact of the lack of correlation between robust risk metrics and worst-group accuracy: models can suffer significant drops in worst-group accuracy, when selected based on robust risk. In contrast, tree-based models show "metric robustness" that is, brsed models which perform best according to the robust risk measure (CVaR) still achieve worst-group accuracy near the highest-accuracy model of the same class (here, XGBoost).
distributionalll--oon

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6 Results: Trees Show Lower Hyperparameter Sensitivity and are Less Costly to Train
For many practical applications, both the time and financial costs of training models are of prime importance. These also affect the amount of expertise required to train a model (with sensitive models requiring greater expertise) and directly impact the carbon footprint of training [34]. We conduct a hyperparameter sensitivity analysis by pruning the hyperparameter search space to eliminate configurations that performed poorly across all datasets, ranking the remaining configurations by performance (i.e. accuracy), and plotting the decline in performance over the ranked models. These results, shown in Figure 7 and Section F.2, demonstrate that tree-based models also show less sensitivity to hyperparameters than the other methods evaluated for both overall performance metrics (e.g., accuracy) and subgroup robustness metrics (e.g., worst-group accuracy).
These results are particularly important in light of the large differences in resources required to achieve similar levels of performance between robust models and the tree-based models: for example, the full hyperparameter grid sweep of size 12k XGBoost on the largest dataset in our study, ACS Income, completed in 1 CPU-day; DRO x² sweep of 3250 training runs completed in 58 GPUU-dys. Due to the differences in hardware required to train various models, we conduct an estimated comparison of the cost of training individual model, and of the full sweep. These results, shown in Figure 19, show that tree-based models are also considerably less expensive to train and tune.
7 Conclusion
Machine learning has made significant progress in the past several years in identifying and addressing various challenges which can contribute to real-world performance disparities. However, our results suggest that another form of progress not widely acknowledged as having implications for fairness or robustness advances in tabular data modeling with tree-based algorithms have similar, if not greater, impact in practice than the state of the art in robust neural network learning fairness- enhancing methods. Our results suggest that tree-based algorithms are a surprisingly strong baseline for subgroup robustness in tabular data, and that future work should compare against, and improve upon, the subgroup robustness of rree- models. Our work suggests that, in practice, tree-based ensembles are an effective default for tasks where subgroup robustness is desired.
Our results also suggest that subgroup robustness on par with existing state the art can be achieved with tree-based classifiers that are easier and computationally cheaper to train and tune than either robust or fairness-enin entenncnnnn models, which tend to scale poorly with dataset size (in both n and d). Our work thus contributes critical baseline, similar to how other recent works have contributed much-needed baselines in areas of machine learning affected by the rapid prolifcration of new methods [59, 67, 47], and provides a strong benchmark for future robust and fair learning methods.
Our findings are limited to the set of hyperparameters and models explored our experiments a superset of those from the works discussed above (e.g. [62, 74]). Our findings do not demonstrate that robust learning methods cannor achieve subgroup robustness on par with e.g. XGBoost, but merely that this is not achieved with the configurations widely used in the literature. We note that the loss-based interventions largely favored by existing robust and fair learning techniques require optimization over a continuous function, typically implemented as an MIP; this also makes it difficult to disentangle whether the functional form, or the training procedure and objective, lead to the improved subgroup robustness of tree-based models observed in this study. Future work should investigate the subgroup robustness of non-MLP models trained using robust techniques.
While our experiments do not identify the cause of trees' subgroup robustness, it is likely that this is a consequence of their strong overall performance on tabular data. These findings can be also viewed as an analogue of the empirical relationship between in-distribution and out-of of-iiitibbutiinn accuracy in computer vision documented
[49] but now demonstrated for the tabular domain. It is possible that these improvements are due to (i) an inductive bias in tree-based models beter suited to modeling differences in subpopulations in tabular data, or (ii) the ensembling used by the tree- based models in this work. We leave an identification of such causal factors to future work.
10

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8 Acknowledgements
This work is in part supported by the NSF AI Institute for Foundations of Machine Learning (IFML, (CF-2001844) Open Philanthropy, Google, and the Allen Institute for AI.
Moreover, our research utilized computational resources and services provided by the Hyak computing cluster at the University of Washington, and by Advanced Research Computing at the University of Michigan, Ann Arbor.
We are also grateful to Hongseok Namkoong, Tatsunori Hashimoto, John Miller, Michael Kim, Shafi Goldwasser, and attendees of the 2022 Institute for Foundations of Data Science Workshop Distributional Robustness for useful feedback and discussions about the work, and to Christopher Brooks for assistance with the Learning Analytics Architecture (LARC) dataset.

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16


Reviews:
[{"review_id": "k568PDnm4Pb", "reviewer": "Reviewer_WCHM", "summary": "Through extensive experiments, the authors demonstrate that tree-based methods are a strong and computationally frugal baseline for tabular prediction, ultimately achieving favorable performance in terms of overall and subgroup performance.\n", "questions": "Race and gender and gender are listed as examples of binary sensitive attributes [line 140]. While these variables may be codified as binary in the dataset, they are not binary in reality [https://arxiv.org/abs/2205.04610, https://dl.acm.org/doi/10.1145/3411764.3445742]. Making this distinction is important, especially in settings where the data collection is beyond our control (e.g. fixed benchmark datasets).\nTypo in line 273: “evaluated basedon”\n", "limitations": "I think the authors could do more to contextualize the specific tabular prediction tasks evaluated. For example the use of tabular methods for risk assessment and neighborhood crime-level prediction could have negative societal impacts, even if they achieve some notion of statistical fairness or subgroup robustness. Cf. https://arxiv.org/abs/2106.05498\n", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n* The authors investigate subgroup robustness properties of tree-based models on tabular prediction, which I haven’t seen before and believe will be interesting to the neurips community (although tree-based methods are known to be a strong baseline for tabular benchmarks in general).\n* Quality of presentation is high. Baseline methods and empirical results are presented in an accessible way.\n* Very nice related works section that would serve as a useful mini-survey for the interested reader.\n\nWeaknesses\n* What seems to be missing is some reasonable hypothesis for *why* tree-based methods tend to find subgroup-robust models. Cynthia Rudin has an extensive body of work arguing that tree-based methods (e.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9122117/)  are very effective modeling tabular data, and may be better equipped to find a good solution than deep learning based approaches. The results presented here are consistent with that hypothesis since we see that the tree-based methods are best at robust metrics precisely because they are best at overall accuracy, and the authors show that aggregate accuracy and subgroup accuracy are very correlated on this data. It makes me think that the main takeaway could be that trees are effective tabular learners, rather than subgroup-robust learners (although these are not mutually exclusive).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "K4f3WRZT8i3", "reviewer": "Reviewer_Uv7V", "summary": "The paper empirically evaluates subgroup robustness methodologies on tabular data with clearly defined subgroups. They posit that state of the art tree-based methods are already robust learners in the subgroup-robust sense, and that they outperform the existing state of the art fairness and robustness methods in these categories. Further, they show that existing subgroup robustness methods can be brittle (i.e., show poor performance under other robustness criteria) ", "questions": "What do the authors see as the main limitation for the standard robustness- and fairness-based methods to work on tree-based architectures?\n\nDo the authors believe that tree-based methods cannot be further improved by the use of robust learning?", "limitations": "No dedicated section was provided, the work itself highlights potential areas for improvement in the area, which by itself is a net positive impact.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\nThe paper is clear in its goals and methodology, and the experiments show that worst group loss and worst disparity between subgroups are very well addressed by existing tree-based methods on tabular data, even outperforming many existing subgroup fairness and robustness approaches.\n\nWeaknesses:\n\nThe vast majority of subgroup robustness and fairness algorithms are evaluated on MLP-based architectures. Though this is a limitation of current fairness and robustness work, it is hard to draw conclusions on the field at large other than the need for a greater focus on methods that work on tree-based architectures, or on better base architectures for tabular data specifically.\n\nIt is not clear to me whether these results are surprising, since a sufficiently large improvement in overall model accuracy is warranted to also improve worst-group accuracy.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "B6dfI8BUTq1", "reviewer": "Reviewer_kdGJ", "summary": "\nThis paper provides an extensive empirical analysis of the subgroup robustness of tree-based models (like XGBoost), distributionally robust models (like DRO), and fairness-promoting methods (like fairlearn) on five commonly used datasets for fairness-aware machine learning: ACS Income, Adult, Communities and Crime, COMPAS, and German Credit. For each model type, they train many models over a grid of hyperparameter values, and they report the worst-group accuracy, accuracy, max disparity between groups, and cVaR (a measure of accuracy in the tail). They find evidence that tree-based models show good subgroup-robustness properties, often on par with distributionally robust methods and with fairness-aware methods. ", "questions": "- Can you provide any discussion on why grid search over tree hyper parameters seems to trace out the fairness-accuracy Pareto front?\n- Similarly, can you provide motivation for why trees might have subgroup robustness?\n- Is it possible to update the main text to include some details on the hyperparameter sweeps and other important experimental details?", "limitations": "There is no proper discussion of the limitations of this analysis. I would recommend that the authors add this. For instance, what are the limitations in extrapolating these findings to other datasets, other domains? ", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Originality\n\nThis empirical investigation is original and needed. Prior work (discussed in the paper) had conducted an empirical comparison of fairness methods early in the literature, but the modern update to include distributionally robust methods is original. \n\nHowever, some of the claims of contributions in the paper are not well supported. The paper claims to “introduce techniques for the analysis of hyperparameter sweets such as model performance frontier curves” (line 62-63), but it is not clear how this is different from commonly reported Pareto frontier curves. \n\n# Quality\n\nGiven recent works offering more extensive and more realistic datasets, I am not convinced that it is sufficient to perform this empirical analysis on the five traditional fairness datasets. A comprehensive empirical analysis of the Adult dataset should include analysis on other “folktables” as provided in Ding et al. Additionally, Koh et al. curated a list of datasets that contain “in-the-wild” distribution shifts including subpopulation shift. This seems like an important set of datasets to perform analysis on.\n\nNo uncertainty estimates are provided. In the checklist the authors claim they are “not concerned with point estimates” but most of the metrics reported here are point estimates, right? Relatedly, it may be helpful to present results across datasets—is there a way to graphically summarize the range of results you see across datasets? This might be helpful for readers who want to get a quick overall summary of the results. \n\nDing, Frances, et al. \"Retiring adult: New datasets for fair machine learning.\" Advances in Neural Information Processing Systems 34 (2021): 6478-6490.\n\nKoh, Pang Wei, et al. \"Wilds: A benchmark of in-the-wild distribution shifts.\" International Conference on Machine Learning. PMLR, 2021.\n\n# Clarity\n\nThe paper has a strong introduction with a nice discussion of the relationship between fairness and robustness.\n\nHowever I generally found the remainder of the paper hard to read. For the exposition of the methods, it would be helpful to provide inline text describing the fairness and robust methods you include. It would also be useful to provide more discussion/intuition about why trees seem to have this robustness. It may be relevant to discuss prior work that analyzes when fairness-aware methods can address subpopulation shift: \n\nMaity, Subha, et al. \"Does enforcing fairness mitigate biases caused by subpopulation shift?.\" Advances in Neural Information Processing Systems 34 (2021): 25773-25784.\n\nSingh, Harvineet, et al. \"Fairness violations and mitigation under covariate shift.\" Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency. 2021.\n\n I found the designation of “complementary” metrics (line 245) to be confusing, and it would be helpful to add more details here to explicitly define what makes a metric complementary to another (and perhaps elaborate on an example).\n\nI found it hard to digest many metrics reported over many graphs, and at times hard to make sense of the reported trends. For instance in Figure 1a the XGboost curve seems to track the y=x line, so does this indicate XGBoost had the same accuracy across all groups? Additionally, it was unclear to me what the difference between graph 1a and 1b was. It would be helpful to elaborate in the captions, including describing what the baselines refer to (or at least a pointer to the description in the text).\n\n\n# Significance\n\nThis paper has the potential to be quite significant. Subgroup robustness is desired in many applications and their contribution showing that trees can have subgroup robustness is notable. The significance would be even stronger if the paper offered concrete takeaways/recommendations: e.g., in practice how should one make use of the findings here? 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Author rebuttal:

Decision: Accept