Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation
Anonymous Author(s)
AfﬁliationAddress email
Abstract
Many methods for fair, robust, or disparity-minimizing machine learning havebeen proposed across the machine learning community, but thorough empiricalevaluation of their subgroup robustness is lacking.
In this work, we address thisgap in the context of tabular data, where sensitive subgroups are clearly-deﬁned,real-world fairness problems abound, and prior works often fail to compare tostate-of-the-art tree-based tabular data models.
We conduct an empirical studyof several previously-proposed methods for fair and robust learning alongsidestate-of-the-art tree-based methods for tabular data and other baseline methods.
Over experiments with more than 300 , 000 model conﬁgurations on eight datasets,we show that tree-based methods have surprisingly strong subgroup robustnessproperties even when compared to robustness- and fairness-enhancing methods.
We show that three families of metrics – those derived from accuracy, robust losses,and fairness metrics – show strong empirical agreement within their family, butdisplay little or no correlation across these families for non-tree models.
As aresult, the best tree-based models tend to show good performance over a range ofmetrics, while robust or group-fair models can show brittleness, with signiﬁcantperformance differences across different metrics for a ﬁxed model.
Our worksuggests that tree-based ensemble models make an effective baseline for tabulardata, and are a sensible default when subgroup robustness is desired.
Introduction
Over the past decade, the ﬁeld of machine learning (ML) has seen a dramatic expansion along tworelated lines.
On one hand, concerns about the fairness of ML models and more broadly theirperformance on data outside the training distribution, have grown [43].
These concerns have beenraised in both theoretical and empirical works demonstrating the vulnerability of models to learnbiases from data or suffer performance drops under distribution shifts [37, 59, 28].
On the other hand,an abundance of methods have been proposed to address these limitations.
These include fairnessmethods used to equalize metrics across groups, as well as distributional robustness methods which optimize for some 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 share the (sometimes implicit) criteria that models should have low disparity (variation in performance over all subgroups should be minimized; cf.
[68, 15, 27, 36]) and good worst-group performance (the lowest accuracy over all subgroups should be maximized; cf.[67, 55]) – that is, both fairness and robustness typically entail improving subgroup robustness
Our work evaluates 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 importantfairness impacts such as medicine, ﬁnance, and recommender systems [31, 57].
Second, tabular dataoften 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 thedataset.
Finally, tabular data is challenging to model.
It is often heterogeneous, containing mixeddata types; it lacks the spatial, linguistic, or temporal structures common to other data (image, text,audio) where machine learning has historically excelled; and it can be relatively small, containingpersonal information which cannot be scraped at Internet scale.
In this work, we conduct a series of experiments to jointly compare methods from the fairness androbustness literature.
Despite the fact that many works often use similar metrics and datasets, thereis a lack of large-scale empirical studies comparing relevant methods to each other, and to strongbaselines.
The latter, our analysis shows, is especially important, as strong baselines can outperformeven well-tuned state-of-the-art disparity-mitigation methods with a fraction of the computational cost.
Our analysis includes a set of tree-based models which achieve strong performance on tabular databut are absent from most works on robustness, which largely only compare to deep learning-basedapproaches despite their tendency to perform poorly on tabular data [31].
This lack of effectivebaselines is particularly concerning in light of recent works across several other areas of machinelearning which have shown that simple baselines can perform surprisingly well against state-of-the-arttechniques [40].
In our experiments, we endeavor to tune both the “fair” or “robust” models and arepresentative suite of baseline methods for tabular data to obtain estimates of performance “frontiers”for each technique.
To this end, we explore a wide space of architectures, regularization schemes,and training hyperparameters, across ﬁve tabular datasets and 16 model classes.
Our work is anempirical contribution concerned not with proposing new methods, but with conducting a novel andrigorous evaluation of existing methods for learning subgroup-robust models from tabular data.
Ourcontributions are as follows:
Trees Are Subgroup-Robust Learners: We show that modern tree-based methods are surprisinglyrobust to subgroup shift, achieving competitive or better performance against state-of-the-art methodsfor fairness and robustness (Fig. 1a,1b) over a large hyperparameter and model search space.
Tosupport the above analysis, we apply several techniques for the analysis of hyperparameter sweepssuch as model performance frontier curves (Fig.
1b,d), hyperparameter sensitivity analysis (Figs.7,8), and model feasibility regions (Table 3, Figures 18,19).
Trees Show Consistent Performance Across Accuracy and Robustness Metrics: We empiricallyinvestigate the relationship between three types of metrics (accuracy, robustness, fairness).
Weshow 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 modelselection techniques affect tree-based models and “robust” or fairness-enhancing methods differently:tree-based methods show consistent subgroup robustness across metrics (Fig. 1c), while robustand fairness-enhancing methods are “metric-brittle” and tend to display poor subgroup robustnessaccording to other metrics (e.g. worst-group accuracy).
Related Work2.1 Fairness-Enhancing Methods for Supervised Learning
A 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, 16].
Most methods can becharacterized as performing either pre- in-, or post-processing, which attempt to ensure fairnessconsiderations are met in different stages of the modeling lifecycle.
Preprocessing [66, 13] attemptsto modify the input data to meet fairness criteria, while preserving the structure of the inputs and theirrelationship to the prediction target.
Inprocessing uses a modiﬁed training procedure to explicitlyoptimize for a fairness-aware objective during model training.
This includes using constrained orreduction-based optimization [1, 65], or including explicit regularizers designed to encourage fairness[7, 9, 36, 49].
Postprocessing [26, 46] operates on the predictions of a model, modifying them toachieve fairness criteria.
The impact of fairness under subpopulation shift is analyzed in [41], which shows theoretically thatenforcing fairness during training can harm or improve the model, under certain conditions, and[58] conducts a causal analysis of fairness under covariate shift.
Perhaps the work most closelyrelated to the current study is [20], which evaluates a set of pre-, in-, and postprocessing algorithms,demonstrating that many of these techniques show instability (variations in performance over differenttrain-test splits) and that several fairness metrics are empirically correlated.
[20] does not, however,evaluate robust learning techniques, modern tree-based techniques (besides CART), or neural methods,and empirical evaluation of recent methods is needed.
2.2 Distributionally Robust Learning
While efforts to learn models with good performance beyond the training distribution date backdecades, recent works have adapted and extended this to deep learning.
For example, several variantsof distributionally robust optimization (DRO) have been proposed for the training of neural networkswith robustness guarantees [29, 39, 55, 54, 67].
While these approaches are not always explicitlyoriented toward fairness, they are frequently evaluated in terms of their performance beneﬁts forminimizing performance gaps between sensitive subgroups in real-world data [67, 55, 27].
A particular form of shift (and robustness) evaluated by these works is subgroup shift (also calledsubpopulation shift)
[43], where the balance of subgroups in the data shifts between training andtesting.
Evaluating performance on individual subgroups is an extreme version of subgroup shift.
Inthe context of fairness, these subgroups are often deﬁned by one or more discrete sensitive attributes,such as race, gender, or income level, and intersections between these sensitive groups can oftenidentify groups most susceptible to performance disparities [12].
2.3 Models for Tabular Data
Deep learning-based approaches largely have not achieved the transformative performance gains ontabular data that they have with other data modalities such as images, text, and audio [31, 11, 57].
The existing state-of-the-art for learning with tabular data is widely acknowledged to be tree-basedmethods, and in particular gradient-boosted trees [25, 47, 57, 11].
This includes GBM [21, 22],
LightGBM [33], XGBoost [14], and CatBoost [18, 48], which often show only small differencesin performance between them.
Several deep learning-based approaches have recently attempted toﬁll the gap of deep learning-based solutions for tabular data [31, 2, 30, 47, 32].
However, empiricalanalyses have shown that the reported performance of these methods does not generalize well toother datasets, and gradient boosting methods still achieve better performance with less tuning anda considerably smaller computational budget.
For example, [57] and [11] both show, in separateanalyses, that gradient boosting consistently outperforms these state-of-the-art tabular deep learningmethods across several datasets, and tree-based methods achieve competitive performance with thedeep learning approaches proposed in [23, 30].
While the overall predictive performance of these tabular methods has been evaluated, their fairnessproperties, subgroup performance, and robustness to subgroup shift have not been carefully investigated or compared with subgroup-robust learning methods.
Additionally, despite the widely-knownstrong performance of these models on tabular data, we are aware of no prior work which comparestree-based methods to “robust” neural network-based learners, despite the fact that the latter arecommonly evaluated on tabular data (e.g. [29, 36, 67, 55]).
Notably, [1] evaluates GBM in conjunction with their proposed inprocessing method, but does not evaluate subpopulation robustness; [17]evaluates GBM with fairness methods but does not compare to robust methods and does not tune the
GBM with fairness methods.
Setup
Our work is primarily concerned with empirically evaluating the sensitivity of various supervisedlearning methods to subpopulation shift.
Below, we introduce our formal model, and then describe themain axes of variation in our experiments.
This includes a large set of models, many of which havenot been directly compared in previous works; a set of metrics used across the disparate literature onrobustness, subpopulation shift, and fairness in machine learning; the hyperparameters used for each;and a suite of eight real-world fairness datasets.
3.1 Preliminaries
Our work evaluates the task of learning a model f ✓ 2 F , a function from model class F parameterizedby ✓ .
The parameters are learned from a dataset D :=
( x i , y i ) ni =1 ⇠ P where P is the data-generatingdistribution.
This matches the case, most common in practice, where a single model is learned byestimating min ✓ E ( L ( y, f ✓ ( x ))) and deployed for all users.
We evaluate the binary classiﬁcationcontext, where
y 2 { 0 , 1 } and f ✓ ( x ) = ˆ y 2 [0 , 1] is the predicted probability that y i
= 1 .
Eachx i
R d can be partitioned into x i =
( x i, 1 , . . .
, x i,d  1 , a ) where a is a sensitive attribute.
Fornotational convenience, we represent a as a single feature here, but in our data, a is typically deﬁnedas the concatenation of multiple binary sensitive attributes (e.g. gender = female, race = white).
Let
D a :=
{ ( x i , y i )
⇠ P| a i = a } denote the subgroup of the dataset with a given sensitive identity.
Following many of the previous works in both fairness [16] and robustness [67, 36], our analysisfocuses on the performance of f ✓ on each D a 8 a 2 A .
We are particularly interested in the worst-groupperformance and the loss disparity, respectively deﬁned as
[Equation]
and
[Equation]
These metrics can be thought of as assessing the sensitivity of f ✓ to subgroup shift, evaluating theworst-group shift from D to D a (note that subgroup shift is itself a form of covariate shift [43])
3.2 Models
Our goal is to conduct a thorough empirical comparison of the subgroup robustness of a suite ofmethods for tabular data.
We provide a more detailed description of all models used in Section B.
Fairness-Enhancing Models :
We evaluate the LFR preprocessing method of [66]; the inprocessingmethod of[1], and the postprocessing method of [26].
As in [1, 17], we use GBM as the base learnerfor each model; however, unlike [17], we also tune the base learner parameters.
Robust Models: We evaluate both the CVaR and  2 constraint forms of DRO via [39]; the CVaR and 2 constraint forms of DORO [67]; Group DRO [55]; and Maximum Weighted Loss Discrepancy[36].
Each robust optimization method is used with a fully-connected multilayer perceptron (MLP),as in most previous works when using tabular data [67].
Tree-Based Models: We evaluate GBM, LightGBM [33], XGBoost [14], and Random Forest models.
Baseline Models: As baselines, we include L 2 -regularized logistic regression, Support Vector
Machines, and fully-connected neural networks (MLP) with standard (non-DRO) ERM optimization.
Hyperparameter Sweeps: For each model, we conduct a grid search over a large set of hyperparameters.
We give the complete set of hyperparameters tuned for each model in Section F. Ourhyperparameter search for each model is extensive by design in order to ensure a reliable comparisonof the best-performing models from each class.
We expand the initial grid for continuous hyperparameters when a model on the Pareto frontier is at the edge of the grid.
When one method includesanother as a “base” learner (e.g. LFR preprocessing with GBM, or DRO with MLP), we include thefull tuning grid for the base model (i.e. we explore the cross-product of all MLP hyperparameterswith all DRO hyperparameters).
We note that previous works tend to either compare against a ﬁxedbaseline architecture and/or training hyperparameters (e.g. [67, 31]), perform manual tuning ([39]),or do not tune hyperparameters of the base model when using fairness-enhancing techniques ([17]).
3.3 Metrics
One goal of our work is to assess the empirical relationship between the model evaluation metricsused in the robustness, fairness, and classiﬁcation literatures.
This relationship is not explored inexisting work, and these models optimize for a wide variety of different objectives during training.
Additionally, there have been several metrics used across prior works to compare the performance ofmodels, evaluate their fairness with respect to subgroups, and to measure their robustness to variousshifts or outliers.
We draw several metrics, from prior works and report them for our experiments.
For each metric L (e.g. loss, accuracy, Equalized Odds), we can not only measure the overall empiricalperformance of a model, but we can measure the worst-group loss and disparity over subgroups of thedata, as deﬁned in Equation (1).
Worst-group and disparity measures, for various formulations of theloss functions above, are a widely-used measure of fairness and robustness [10, 67, 55, 54, 27, 37].
In particular, we use the L DISP and L WorstGroup with binary accuracy as the loss function.
Accuracy iswidely used in practice; directly interpretable; and invariant to rescaling of the model’s predictions.
We also use the CVaR risk metric from the robustness literature.
CVaR risk is measured over a setof inputs D
=
( x i , y i )
Ni =1 ⇠ P and measures the worst-case weighted loss, according to some lossfunction ` , at level ↵ over the inputs in D :
[Equation]
(2) is the risk function optimized by the DRO CVaR model [39], but it is also used more widely as ameasure of the tail risk of a classiﬁer (cf.
Additional fairness and robustness metrics are reported in Section G and deﬁned in Section C.
[Table]
3.4 Datasets
We evaluate the 16 models over a set of eight datasets covering a variety of prediction tasks anddomains.
We use a set of two binary sensitive attributes from each dataset, for a total of fournonoverlapping subgroups in each dataset.
A summary of the datasets used in this work is givenin Table 1.
We provide additional details on each dataset, along with critical framing and contextregarding these prediction tasks and their representations of individuals, in Section A.
Results: Tree Models are Subgroup-Robust Learners
Our main ﬁnding is that tree-based models are subgroup-robust learners; indeed, tree-based modelsmatch or exceed the performance of distributionally robust and fairness-enhancing models in termsof best overall accuracy, worst-group accuracy, and accuracy disparity on all datasets evaluated.
A summary of our results is shown in Figures 2, 3, and 4.
Following previous works, our mainevaluation metrics 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 characteristicson par with, or better than, the set of robust or fairness-enhancing models evaluated.
We note that thisis particularly surprising because none of the tree-based models explicitly optimize for robustness,fairness, or subgroup performance in any way; in contrast, the distributionally robust learners andfairness-enhancing techniques explicitly optimize for such criteria and in some cases (DORO, DRO,
Group DRO) provide explicit guarantees of various forms of robustness.
A similar analysis showingaccuracy disparity is shown in Supplemental Figure 14, and a complete set of model performanceobservations from each algorithm and dataset, are in Supplementary Section G.
Tree-based models achieve comparable and sometimes improved frontiers with the highest-performing robustness methods.
(See also Fig
Tree-based models achieve comparable and sometimes improved frontiers compared to the highestperforming robustness methods, particularly in high-accuracy regions.
(See also Fig. 1d.)
To summarize over the large hyperparameter sweeps, we propose two techniques.
First, we use modelperformance frontiers to measure the best possible set of tradeoffs between ( L and L WorstGroup ) and ( Land L DISP ).
Model performance frontiers represent the envelope of the convex hull of all observationsof L ( f ✓ ) 2 F .
An example is shown in Figure 1b and 1d, with the remaining four dataset in Figure 3and 4.
The frontiers allow us to compare the best-possible tradeoff between accuracy and worst-groupaccuracy (Fig 3; higher is better) or between accuracy and accuracy disparity (Fig 4; lower is better).
Second, we propose feasible model regions as a measure of the full space of ( L , L WorstGroup ) valuesobserved over f ✓ 2 F .
By comparing the area of the feasible model regions, we can compare thesensitivity of ( L , L WorstGroup ) over the space of possible models f ✓ 2 F .
We provide pseudocodefor computing both the feasible model regions and model performance frontiers in Algorithm 1 of
Section D. We give a more detailed analysis of feasible model regions in the Supplementary Section
D; here we only note that the area encompassed by the FMR for DRO-based methods is consistentlythe largest across all datasets, as shown in Table 3.
These results are particularly important in light of the large differences in resources required toachieve similar levels of performance between robust models and the tree-based models: for example,the full hyperparameter grid sweep of size 12 k XGBoost on the largest dataset in our study, ACS
Income, completed in 1 CPU-day; DRO  2 sweep of 3250 training runs completed in 58 GPU -days.
Results: Relationship Between Fairness, Robustness, Performance Metrics
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 stronglycorrelated with each other: accuracy and worst-group accuracy; CVaR and CVaR DORO; and
Demographic Parity Difference and Equalized Odds Difference all show strong correlation witheach model class F ; we show these correlations on Adult in Fig.
The median ⇢ values over alldatasets and algorithms are 0.87, 0.99, 0.79 for the three pairs of metrics, respectively (we show thecomplete set of correlations for each model and metric in Figure 16).
These results show that modelselection based on one metric from each pair (Overall Accuracy) is likely to lead to a model withstrong performance for the other metric in the pair (e.g. Worst-Group Accuracy).
In contrast, our experiments show that there is a severe lack of correlation across almost all of thenon-complementary pairs, shown in the bottom row of Figure 5.
In particular, our results show thatmodels which achieve a strong “robust” risk – for example, a low CVaR DORO risk, one modelselection rule used in [67] – can achieve very low accuracies.
Indeed, the “robust” learning methodsare the most susceptible to this discrepancy over metrics in our experiments, as shown in Figure6.
While these results conﬁrm the ﬁnding in previous works that fairness metrics are correlated[20], our broader comparison shows a brittleness to model selection metrics outside these sets ofcomplementary metrics, and reveal the very strict sense in which robustness guarantees apply onlyto a limited range of metrics.
This discrepancy is of practical signiﬁcance given that robust modelsare often selected using robust metrics (i.e. DORO CVaR, cf.
[67]), while models in practice arefrequently evaluated using other metrics (i.e. accuracy, fairness metrics).
Results: Robust Models Can Be Metric-Brittle
In this section, we explore the impact of various strategies for choosing a single f ✓ 2 F over a set ofmodels in each hyperparameter grid.
While this problem is implicitly addressed in almost all previousworks, the decision is often handled differently – for example, models are tuned and selected by hand[39], chosen based on worst-group performance [67], or based on robust risk metrics [55] – but theimplications of various model selection methods for fairness and robustness are not well-understood.
Our large-scale empirical study provides valuable data to help address this question.
Figure 6 demonstrates the downstream impact of the lack of correlation between robust risk metricsand worst-group accuracy: distributionally-robust models can suffer signiﬁcant drops in worst-groupaccuracy, when evaluated based on their robust risk.
In contrast, tree-based models show “metric robustness” – that is, tree-based models which perform best according to a robust risk measure stillachieve worst-group accuracy near the highest-accuracy model of the same class (here, XGBoost).
Conclusion
The ﬁeld of machine learning has made signiﬁcant progress in the past several years in identifying andaddressing various challenges which can contribute to real-world performance disparities.
However,our results suggest that another form of progress not widely acknowledged as having implicationsfor fairness or robustness – advances in tabular data modeling with tree-based algorithms – havesimilar, if not greater, impact in practice than the state of the art in robust neural network learning orfairness-enhancing methods.
Our results suggest that tree-based algorithms are a surprisingly strongbaseline for subgroup robustness in tabular data, and that future work should compare against, andimprove upon, the subgroup robustness of tree-based models.
Our work suggests that, in practice,tree-based ensembles are an effective default for tasks where subgroup robustness is desired.
In addition to being surprising, given the attention and effort dedicated to the recent advances inrobust and fair learning, our results are important because they suggest that subgroup robustnesson par with existing state of the art can be achieved with tree-based classiﬁers that are easier andcomputationally cheaper to tune and train than either robust or fairness-enhancing models, whichtend to scale poorly with dataset size (in both n and d ).
Our work thus contributes a critical baseline,similar to how other recent works have contributed much-needed baselines in areas of machinelearning affected by the rapid proliferation of new methods [52, 60, 40].
Our ﬁndings are limited to the set of hyperparameters and models explored in our experiments – asuperset of those considered across the prior works discussed above (e.g. [55, 67]).
Our ﬁndings donot demonstrate that robust learning methods cannot achieve subgroup robustness on par with e.g.
XGBoost, but merely that this is not achieved with the conﬁgurations widely used in the literature.
Future work should investigate the subgroup robustness of non-MLP models trained using robusttechniques.
While our experiments do not identify the cause of trees’ subgroup robustness, it is likely that this isa consequence of their strong performance on tabular data.
These ﬁndings can be also viewed as ananalogue of the empirical relationship between in-distribution and out-of-distribution accuracy incomputer vision documented in [42] but now demonstrated for the tabular domain.
It is possible thatthese improvements are due to ( i ) an inductive bias in tree-based models beter suited to modelingdifferences in subpopulations in tabular data, or ( ii ) the ensembling used by the tree-based models inthis work.
We leave an identiﬁcation of such causal factors to future work.