Fairness Metrics

Decisions made by machine learning models can have lasting impacts, making long-term fairness a critical consideration. It has been observed that ignoring the long-term effect and directly applying fairness criterion in static settings can actually worsen bias over time. To address biases in sequential decision-making, we introduce a long-term fairness concept named Equal Long-term Benefit Rate (ELBERT). This concept is seamlessly integrated into a Markov Decision Process (MDP) to consider the future effects of actions on long-term fairness, thus providing a unified framework for fair sequential decision-making problems. ELBERT effectively addresses the temporal discrimination issues found in previous long-term fairness notions. Additionally, we demonstrate that the policy gradient of Long-term Benefit Rate can be analytically simplified to standard policy gradients. This simplification makes conventional policy optimization methods viable for reducing bias, leading to our bias mitigation approach ELBERT-PO. Extensive experiments across various diverse sequential decision-making environments consistently reveal that ELBERT-PO significantly diminishes bias while maintaining high utility. Code is available at https://github.com/umd-huang-lab/ELBERT.

Group Equivariant CNNs (G-CNNs) have shown promising efficacy in various tasks, owing to their ability to capture hierarchical features in an equivariant manner. However, their equivariance is fixed to the symmetry of the whole group, limiting adaptability to diverse partial symmetries in real-world datasets, such as limited rotation symmetry of handwritten digit images and limited color-shift symmetry of flower images. Recent efforts address this limitation, one example being Partial G-CNN which restricts the output group space of convolution layers to break full equivariance. However, such an approach still fails to adjust equivariance levels across data. In this paper, we propose a novel approach, Variational Partial G-CNN (VP G-CNN), to capture varying levels of partial equivariance specific to each data instance. VP G-CNN redesigns the distribution of the output group elements to be conditioned on input data, leveraging variational inference to avoid overfitting. This enables the model to adjust its equivariance levels according to the needs of individual data points. Additionally, we address training instability inherent in discrete group equivariance models by redesigning the reparametrizable distribution. We demonstrate the effectiveness of VP G-CNN on both toy and real-world datasets, including MNIST67-180, CIFAR10, ColorMNIST, and Flowers102. Our results show robust performance, even in uncertainty metrics.

In the machine learning ecosystem, hardware selection is often regarded as a mere utility, overshadowed by the spotlight on algorithms and data. This is especially relevant in contexts like ML-as-a-service platforms, where users often lack control over the hardware used for model deployment. This paper investigates the influence of hardware on the delicate balance between model performance and fairness. We demonstrate that hardware choices can exacerbate existing disparities, attributing these discrepancies to variations in gradient flows and loss surfaces across different demographic groups. Through both theoretical and empirical analysis, the paper not only identifies the underlying factors but also proposes an effective strategy for mitigating hardware-induced performance imbalances.

We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm's update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.

Given a dataset of individuals each described by a covariate vector, a treatment, and an observed outcome on the treatment, the goal of the individual treatment effect (ITE) estimation task is to predict outcome changes resulting from a change in treatment. A fundamental challenge is that in the observational data, a covariate’s outcome is observed only under one treatment, whereas we need to infer the difference in outcomes under two different treatments. Several existing approaches address this issue through training with inferred pseudo-outcomes, but their success relies on the quality of these pseudo-outcomes. We propose PairNet, a novel ITE estimation training strategy that minimizes losses over pairs of examples based on their factual observed outcomes. Theoretical analysis for binary treatments reveals that PairNet is a consistent estimator of ITE risk, and achieves smaller generalization error than baseline models. Empirical comparison with thirteen existing methods across eight benchmarks, covering both discrete and continuous treatments, shows that PairNet achieves significantly lower ITE error compared to the baselines. Also, it is model-agnostic and easy to implement.

The ability to properly benchmark model performance in the face of spurious correlations is important to both build better predictors and increase confidence that models are operating as intended. We demonstrate that characterizing (as opposed to simply quantifying) model mistakes across subgroups is pivotal to properly reflect model biases, which are ignored by standard metrics such as worst-group accuracy or accuracy gap. Inspired by the hypothesis testing framework, we introduce SkewSize, a principled and flexible metric that captures bias from mistakes in a model's predictions. It can be used in multi-class settings or generalised to the open vocabulary setting of generative models. SkewSize is an aggregation of the effect size of the interaction between two categorical variables: the spurious variable representing the bias attribute the model's prediction. We demonstrate the utility of SkewSize in multiple settings including: standard vision models trained on synthetic data, vision models trained on ImageNet, and large scale vision-and-language models from the BLIP-2 family. In each case, the proposed SkewSize is able to highlight biases not captured by other metrics, while also providing insights on the impact of recently proposed techniques, such as instruction tuning.

The complex and unpredictable nature of deep neural networks prevents their safe use in many high-stakes applications. There have been many techniques developed to interpret deep neural networks, but all have substantial limitations. Algorithmic tasks have proven to be a fruitful test ground for interpreting a neural network end-to-end. Building on previous work, we completely reverse engineer fully connected one-hidden layer networks that have ``grokked'' the arithmetic of the permutation groups $S_5$ and $S_6$. The models discover the true subgroup structure of the full group and converge on neural circuits that decompose the group arithmetic using the permutation group's subgroups. We relate how we reverse engineered the model's mechanisms and confirmed our theory was a faithful description of the circuit's functionality. We also draw attention to current challenges in conducting interpretability research by comparing our work to Chughtai et al. (2023) which alleges to find a different algorithm for this same problem.

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over Wasserstein distance. In this paper we prove that the infinite dimensionality of the space of probabilities drastically deteriorates its sample complexity, which is slower than any polynomial rate in the sample size. We propose a new distance that preserves many desirable properties of the former while achieving a parametric rate of convergence. In particular, our distance 1) metrizes weak convergence; 2) can be estimated numerically through samples with low complexity; 3) can be bounded analytically from above and below. The main ingredient are integral probability metrics, which lead to the name *hierarchical IPM*.

Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be represented in the derived rankings. Our work considers ranking functions: maps from individual predictions for a classification task to distributions over rankings. We focus on two aspects of ranking functions: stability to perturbations in predictions and fairness towards both individuals and subgroups. Not only is stability an important requirement for its own sake, but --- as we show --- it composes harmoniously with individual fairness in the sense of Dwork et al. (2012). While deterministic ranking functions cannot be stable aside from trivial scenarios, we show that the recently proposed uncertainty aware (UA) ranking functions of Singh et al. (2021) are stable. Our main result is that UA rankings also achieve group fairness through successful composition with multiaccurate or multicalibrated predictors. Our work demonstrates that UA rankings naturally interpolate between group and individual level fairness guarantees, while simultaneously satisfying stability guarantees important whenever machine-learned predictions are used.

Insertion/deletion metrics and their variants have been extensively applied to evaluate attribution-based explanation methods. Such metrics measure the significance of features by observing changes in model predictions as features are incrementally inserted or deleted. Given the direct connection between the attribution values and model predictions that insertion/deletion metrics enable, they are commonly used as the decisive metrics for novel attribution methods. Such influential metrics for explanation methods should be handled with great scrutiny. However, contemporary research on insertion/deletion metrics falls short of a comprehensive analysis. To address this, we propose the TRAjectory importanCE (TRACE) framework, which achieves the best scores of the insertion/deletion metric. Our contribution includes two aspects: 1) TRACE stands as the principled explanation for explaining the influence of feature deletion on model predictions. We demonstrate that TRACE is guaranteed to achieve almost optimal results both theoretically and empirically. 2) Using TRACE, we benchmark insertion/deletion metrics across all possible settings and study critical problems such as the out-of-distribution (OOD) issue, and provide practical guidance on applying these metrics in practice.

We model real-world data markets, where sellers post fixed prices and buyers are free to purchase from any set of sellers, as a simultaneous game. A key component here is the negative externality buyers induce on one another due to data purchases. Starting with a simple setting where buyers know their valuations a priori, we characterize both the existence and welfare properties of the pure Nash equilibrium in the presence of such externality. While the outcomes are bleak without any intervention, mirroring the limitations of current data markets, we prove that for a standard class of externality functions, platforms intervening through a transaction cost can lead to a pure equilibrium with strong welfare guarantees. We next consider a more realistic setting where buyers learn their valuations over time through market interactions. Our intervention is feasible here as well, and we consider learning algorithms to achieve low regret concerning both individual and cumulative utility metrics. Lastly, we analyze the promises of this intervention under a much richer externality model.

A general belief in fair classification is that fairness constraints incur a trade-off with accuracy, which biased data may worsen. Contrary to this belief, Blum & Stangl (2019) show that fair classification with equal opportunity constraints even on extremely biased data can recover optimally accurate and fair classifiers on the original data distribution. Their result is interesting because it demonstrates that fairness constraints can implicitly rectify data bias and simultaneously overcome a perceived fairness-accuracy trade-off. Their data bias model simulates under-representation and label bias in underprivileged population, and they show the above result on a stylized data distribution with i.i.d. label noise, under simple conditions on the data distribution and bias parameters. We propose a general approach to extend the result of Blum & Stangl (2019) to different fairness constraints, data bias models, data distributions, and hypothesis classes. We strengthen their result, and extend it to the case when their stylized distribution has labels with Massart noise instead of i.i.d. noise. We prove a similar recovery result for arbitrary data distributions using fair reject option classifiers. We further generalize it to arbitrary data distributions and arbitrary hypothesis classes, i.e., we prove that for any data distribution, if the optimally accurate classifier in a given hypothesis class is fair and robust, then it can be recovered through fair classification with equal opportunity constraints on the biased distribution whenever the bias parameters satisfy certain simple conditions. Finally, we show applications of our technique to time-varying data bias in classification and fair machine learning pipelines.

Standard empirical risk minimization (ERM) models may prioritize learning spurious correlations between spurious features and true labels, leading to poor accuracy on groups where these correlations do not hold. Mitigating this issue often requires expensive spurious attribute (group) labels or relies on trained ERM models to infer group labels when group information is unavailable. However, the significant performance gap in worst-group accuracy between using pseudo group labels and using oracle group labels inspires us to consider further improving group robustness through preciser group inference. Therefore, we propose GIC, a novel method that accurately infers group labels, resulting in improved worst-group performance. GIC trains a spurious attribute classifier based on two key properties of spurious correlations: (1) high correlation between spurious attributes and true labels, and (2) variability in this correlation between datasets with different group distributions. Empirical studies on multiple datasets demonstrate the effectiveness of GIC in inferring group labels, and combining GIC with various downstream invariant learning methods improves worst-group accuracy, showcasing its powerful flexibility. Additionally, through analyzing the misclassifications in GIC, we identify an interesting phenomenon called semantic consistency, which may contribute to better decoupling the association between spurious attributes and labels, thereby mitigating spurious correlation. The code for GIC is available at [https://github.com/yujinhanml/GIC9](https://github.com/yujinhanml/GIC).

Despite achieving promising fairness-error trade-offs, in-processing mitigation techniques for group fairness cannot be employed in numerous practical applications with limited computation resources or no access to the training pipeline of the prediction model. In these situations, post-processing is a viable alternative. However, current methods are tailored to specific problem settings and fairness definitions and hence, are not as broadly applicable as in-processing. In this work, we propose a framework that turns any regularized in-processing method into a post-processing approach. This procedure prescribes a way to obtain post-processing techniques for a much broader range of problem settings than the prior post-processing literature. We show theoretically and through extensive experiments that our framework preserves the good fairness-error trade-offs achieved with in-processing and can improve over the effectiveness of prior post-processing methods. Finally, we demonstrate several advantages of a modular mitigation strategy that disentangles the training of the prediction model from the fairness mitigation, including better performance on tasks with partial group labels.

We initiate a systematic study of worst-group risk minimization under $(\epsilon, \delta)$-differential privacy (DP). The goal is to privately find a model that approximately minimizes the maximal risk across $p$ sub-populations (groups) with different distributions, where each group distribution is accessed via a sample oracle. We first present a new algorithm that achieves excess worst-group population risk of $\tilde{O}(\frac{p\sqrt{d}}{K\epsilon} + \sqrt{\frac{p}{K}})$, where $K$ is the total number of samples drawn from all groups and $d$ is the problem dimension. Our rate is nearly optimal when each distribution is observed via a fixed-size dataset of size $K/p$. Our result is based on a new stability-based analysis for the generalization error. In particular, we show that $\Delta$-uniform argument stability implies $\tilde{O}(\Delta + \frac{1}{\sqrt{n}})$ generalization error w.r.t. the worst-group risk, where $n$ is the number of samples drawn from each sample oracle. Next, we propose an algorithmic framework for worst-group population risk minimization using any DP online convex optimization algorithm as a subroutine. Hence, we give another excess risk bound of $\tilde{O}\left( \sqrt{\frac{d^{1/2}}{\epsilon K}} +\sqrt{\frac{p}{K\epsilon^2}} + \sqrt{\frac{p}{K}} \right)$. Assuming the typical setting of $\epsilon=\Theta(1)$, this bound is more favorable than our first bound in a certain range of $p$ as a function of $K$ and $d$. Finally, we study differentially private worst-group *empirical* risk minimization in the offline setting, where each group distribution is observed by a fixed-size dataset. We present a new algorithm with nearly optimal excess risk of $\tilde{O}(\frac{p\sqrt{d}}{K\epsilon})$.

Machine learning models are increasingly used in societal applications, yet legal and privacy concerns demand that they very often be kept confidential. Consequently, there is a growing distrust about the fairness properties of these models in the minds of consumers, who are often at the receiving end of model predictions. To this end, we propose *Fairproof* -- a system that uses Zero-Knowledge Proofs (a cryptographic primitive) to publicly verify the fairness of a model, while maintaining confidentiality. We also propose a fairness certification algorithm for fully-connected neural networks which is befitting to ZKPs and is used in this system. We implement *Fairproof* in Gnark and demonstrate empirically that our system is practically feasible. Code is available at https://github.com/infinite-pursuits/FairProof.

We propose a standardized version of fairness measures for continuous scores with a reasonable interpretation based on the Wasserstein distance. Our measures are easily computable and well suited for quantifying and interpreting the strength of group disparities as well as for comparing biases across different models, datasets, or time points. We derive a link between the different families of existing fairness measures for scores and show that the proposed standardized fairness measures outperform ROC-based fairness measures because they are more explicit and can quantify significant biases that ROC-based fairness measures miss.

This paper considers the scenario in which there are multiple institutions, each with a limited capacity for candidates, and candidates, each with preferences over the institutions. A central entity evaluates the utility of each candidate to the institutions, and the goal is to select candidates for each institution in a way that maximizes utility while also considering the candidates' preferences. The paper focuses on the setting in which candidates are divided into multiple groups and the observed utilities of candidates in some groups are biased--systematically lower than their true utilities. The first result is that, in these biased settings, prior algorithms can lead to selections with sub-optimal true utility and significant discrepancies in the fraction of candidates from each group that get their preferred choices. Subsequently, an algorithm is presented along with proof that it produces selections that achieve near-optimal group fairness with respect to preferences while also nearly maximizing the true utility under distributional assumptions. Further, extensive empirical validation of these results in real-world and synthetic settings, in which the distributional assumptions may not hold, are presented.

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters that are cohesive in that close by pairs of nodes are assigned to the same cluster with high probability. We consider the additional aspect of *individual fairness* -- pairs of nodes at comparable distances should be separated with comparable probability. We show that classic decomposition procedures do not satisfy this property. We present novel algorithms that achieve various trade-offs between this property and additional desiderata of connectivity of the clusters and optimality in number of clusters. We show that our individual fairness bounds may be difficult to improve by tying the improvement to resolving a major open question in metric embeddings. We finally show the efficacy of our algorithms on real planar networks modeling Congressional redistricting.

Ensuring privacy-preserving inference on cryptographically secure data is a well-known computational challenge. To alleviate the bottleneck of costly cryptographic computations in non-linear activations, recent methods have suggested linearizing a targeted portion of these activations in neural networks. This technique results in significantly reduced runtimes with often negligible impacts on accuracy. In this paper, we demonstrate that such computational benefits may lead to increased fairness costs. Specifically, we find that reducing the number of ReLU activations disproportionately decreases the accuracy for minority groups compared to majority groups. To explain these observations, we provide a mathematical interpretation under restricted assumptions about the nature of the decision boundary, while also showing the prevalence of this problem across widely used datasets and architectures. Finally, we show how a simple procedure altering the finetuning step for linearized models can serve as an effective mitigation strategy.