In this paper we present a general framework for estimating regression models subject to a user-defined level of fairness. We enforce fairness as a model selection step in which we choose the value of a ridge penalty to control the effect of sensitive attributes. We then estimate the parameters of the model conditional on the chosen penalty value. Our proposal is mathematically simple, with a solution that is partly in closed form, and produces estimates of the regression coefficients that are intuitive to interpret as a function of the level of fairness. Furthermore, it is easily extended to generalised linear models, kernelised regression models and other penalties; and it can accommodate multiple definitions of fairness. We compare our approach with the regression model from Komiyama et al. (2018), which implements a provably-optimal linear regression model; and with the fair models from Zafar et al. (2019). We evaluate these approaches empirically on six different data sets, and we find that our proposal provides better goodness of fit and better predictive accuracy for the same level of fairness. In addition, we highlight a source of bias in the original experimental evaluation in Komiyama et al. (2018).
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There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as stochastic gradient descent (SGD), where little to no explicit regularization has been employed. This work considers this issue in arguably the most basic setting: constant-stepsize SGD (with iterate averaging or tail averaging) for linear regression in the overparameterized regime. Our main result provides a sharp excess risk bound, stated in terms of the full eigenspectrum of the data covariance matrix, that reveals a bias-variance decomposition characterizing when generalization is possible: (i) the variance bound is characterized in terms of an effective dimension (specific for SGD) and (ii) the bias bound provides a sharp geometric characterization in terms of the location of the initial iterate (and how it aligns with the data covariance matrix). More specifically, for SGD with iterate averaging, we demonstrate the sharpness of the established excess risk bound by proving a matching lower bound (up to constant factors). For SGD with tail averaging, we show its advantage over SGD with iterate averaging by proving a better excess risk bound together with a nearly matching lower bound. Moreover, we reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares (minimum-norm interpolation) and ridge regression. Experimental results on synthetic data corroborate our theoretical findings.
The yaglm package aims to make the broader ecosystem of modern generalized linear models accessible to data analysts and researchers. This ecosystem encompasses a range of loss functions (e.g. linear, logistic, quantile regression), constraints (e.g. positive, isotonic) and penalties. Beyond the basic lasso/ridge, the package supports structured penalties such as the nuclear norm as well as the group, exclusive, fused, and generalized lasso. It also supports more accurate adaptive and non-convex (e.g. SCAD) versions of these penalties that often come with strong statistical guarantees at limited additional computational expense. yaglm comes with a variety of tuning parameter selection methods including: cross-validation, information criteria that have favorable model selection properties, and degrees of freedom estimators. While several solvers are built in (e.g. FISTA), a key design choice allows users to employ their favorite state of the art optimization algorithms. Designed to be user friendly, the package automatically creates tuning parameter grids, supports tuning with fast path algorithms along with parallelization, and follows a unified scikit-learn compatible API.
Restless and collapsing bandits are commonly used to model constrained resource allocation in settings featuring arms with action-dependent transition probabilities, such as the allocation of health interventions among patients [Whittle, 1988; Mate et al., 2020]. However, state-of-the-art Whittle-index-based approaches to this planning problem either do not consider fairness among arms or incentivize fairness without guaranteeing it [Mate et al., 2021]. Additionally, their optimality guarantees only apply when arms are indexable and threshold-optimal. We demonstrate that the incorporation of hard fairness constraints necessitates the coupling of arms, which undermines the tractability, and by extension, indexability of the problem. We then introduce ProbFair, a probabilistically fair stationary policy that maximizes total expected reward and satisfies the budget constraint, while ensuring a strictly positive lower bound on the probability of being pulled at each timestep. We evaluate our algorithm on a real-world application, where interventions support continuous positive airway pressure (CPAP) therapy adherence among obstructive sleep apnea (OSA) patients, as well as on a broader class of synthetic transition matrices.
Although pre-trained language models, such as BERT, achieve state-of-art performance in many language understanding tasks, they have been demonstrated to inherit strong gender bias from its training data. Existing studies addressing the gender bias issue of pre-trained models, usually recollect and build gender-neutral data on their own and conduct a second phase pre-training on the released pre-trained model with such data. However, given the limited size of the gender-neutral data and its potential distributional mismatch with the original pre-training data, catastrophic forgetting would occur during the second-phase pre-training. Forgetting on the original training data may damage the model's downstream performance to a large margin. In this work, we first empirically show that even if the gender-neutral data for second-phase pre-training comes from the original training data, catastrophic forgetting still occurs if the size of gender-neutral data is smaller than that of original training data. Then, we propose a new method, GEnder Equality Prompt (GEEP), to improve gender fairness of pre-trained models without forgetting. GEEP learns gender-related prompts to reduce gender bias, conditioned on frozen language models. Since all pre-trained parameters are frozen, forgetting on information from the original training data can be alleviated to the most extent. Then GEEP trains new embeddings of profession names as gender equality prompts conditioned on the frozen model. Empirical results show that GEEP not only achieves state-of-the-art performances on gender debiasing in various applications such as pronoun predicting and coreference resolution, but also achieves comparable results on general downstream tasks such as GLUE with original pre-trained models without much forgetting.
Considerable research effort has been guided towards algorithmic fairness but real-world adoption of bias reduction techniques is still scarce. Existing methods are either metric- or model-specific, require access to sensitive attributes at inference time, or carry high development or deployment costs. This work explores the unfairness that emerges when optimizing ML models solely for predictive performance, and how to mitigate it with a simple and easily deployed intervention: fairness-aware hyperparameter optimization (HO). We propose and evaluate fairness-aware variants of three popular HO algorithms: Fair Random Search, Fair TPE, and Fairband. We validate our approach on a real-world bank account opening fraud case-study, as well as on three datasets from the fairness literature. Results show that, without extra training cost, it is feasible to find models with 111% mean fairness increase and just 6% decrease in performance when compared with fairness-blind HO.
Recent research on fair regression focused on developing new fairness notions and approximation methods as target variables and even the sensitive attribute are continuous in the regression setting. However, all previous fair regression research assumed the training data and testing data are drawn from the same distributions. This assumption is often violated in real world due to the sample selection bias between the training and testing data. In this paper, we develop a framework for fair regression under sample selection bias when dependent variable values of a set of samples from the training data are missing as a result of another hidden process. Our framework adopts the classic Heckman model for bias correction and the Lagrange duality to achieve fairness in regression based on a variety of fairness notions. Heckman model describes the sample selection process and uses a derived variable called the Inverse Mills Ratio (IMR) to correct sample selection bias. We use fairness inequality and equality constraints to describe a variety of fairness notions and apply the Lagrange duality theory to transform the primal problem into the dual convex optimization. For the two popular fairness notions, mean difference and mean squared error difference, we derive explicit formulas without iterative optimization, and for Pearson correlation, we derive its conditions of achieving strong duality. We conduct experiments on three real-world datasets and the experimental results demonstrate the approach's effectiveness in terms of both utility and fairness metrics.
Improving Molecular Graph Neural Network Explainability with Orthonormalization and Induced Sparsity
Rationalizing which parts of a molecule drive the predictions of a molecular graph convolutional neural network (GCNN) can be difficult. To help, we propose two simple regularization techniques to apply during the training of GCNNs: Batch Representation Orthonormalization (BRO) and Gini regularization. BRO, inspired by molecular orbital theory, encourages graph convolution operations to generate orthonormal node embeddings. Gini regularization is applied to the weights of the output layer and constrains the number of dimensions the model can use to make predictions. We show that Gini and BRO regularization can improve the accuracy of state-of-the-art GCNN attribution methods on artificial benchmark datasets. In a real-world setting, we demonstrate that medicinal chemists significantly prefer explanations extracted from regularized models. While we only study these regularizers in the context of GCNNs, both can be applied to other types of neural networks
We investigate the problem of fair recommendation in the context of two-sided online platforms, comprising customers on one side and producers on the other. Traditionally, recommendation services in these platforms have focused on maximizing customer satisfaction by tailoring the results according to the personalized preferences of individual customers. However, our investigation reveals that such customer-centric design may lead to unfair distribution of exposure among the producers, which may adversely impact their well-being. On the other hand, a producer-centric design might become unfair to the customers. Thus, we consider fairness issues that span both customers and producers. Our approach involves a novel mapping of the fair recommendation problem to a constrained version of the problem of fairly allocating indivisible goods. Our proposed FairRec algorithm guarantees at least Maximin Share (MMS) of exposure for most of the producers and Envy-Free up to One item (EF1) fairness for every customer. Extensive evaluations over multiple real-world datasets show the effectiveness of FairRec in ensuring two-sided fairness while incurring a marginal loss in the overall recommendation quality.
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theoretical guarantees; perhaps because the resulting optimization problem is non-convex. The main contribution of this paper is a new meta-algorithm for classification that takes as input a large class of fairness constraints, with respect to multiple non-disjoint sensitive attributes, and which comes with provable guarantees. This is achieved by first developing a meta-algorithm for a large family of classification problems with convex constraints, and then showing that classification problems with general types of fairness constraints can be reduced to those in this family. We present empirical results that show that our algorithm can achieve near-perfect fairness with respect to various fairness metrics, and that the loss in accuracy due to the imposed fairness constraints is often small. Overall, this work unifies several prior works on fair classification, presents a practical algorithm with theoretical guarantees, and can handle fairness metrics that were previously not possible.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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