Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samples

Covariate shift in the test data is a common practical phenomena that can significantly downgrade both the accuracy and the fairness performance of the model. Ensuring fairness across different sensitive groups under covariate shift is of paramount importance due to societal implications like criminal justice. We operate in the unsupervised regime where only a small set of unlabeled test samples along with a labeled training set is available. Towards improving fairness under this highly challenging yet realistic scenario, we make three contributions. First is a novel composite weighted entropy based objective for prediction accuracy which is optimized along with a representation matching loss for fairness. We experimentally verify that optimizing with our loss formulation outperforms a number of state-of-the-art baselines in the pareto sense with respect to the fairness-accuracy tradeoff on several standard datasets. Our second contribution is a new setting we term Asymmetric Covariate Shift that, to the best of our knowledge, has not been studied before. Asymmetric covariate shift occurs when distribution of covariates of one group shifts significantly compared to the other groups and this happens when a dominant group is over-represented. While this setting is extremely challenging for current baselines, We show that our proposed method significantly outperforms them. Our third contribution is theoretical, where we show that our weighted entropy term along with prediction loss on the training set approximates test loss under covariate shift. Empirically and through formal sample complexity bounds, we show that this approximation to the unseen test loss does not depend on importance sampling variance which affects many other baselines.Comment: Accepted at The 38th Annual AAAI Conference on Artificial Intelligence (AAAI 2024

JAWS: Predictive Inference Under Covariate Shift

We propose \textbf{JAWS}, a series of wrapper methods for distribution-free uncertainty quantification tasks under covariate shift, centered on our core method \textbf{JAW}, the \textbf{JA}ckknife+ \textbf{W}eighted with likelihood-ratio weights. JAWS also includes computationally efficient \textbf{A}pproximations of JAW using higher-order influence functions: \textbf{JAWA}. Theoretically, we show that JAW relaxes the jackknife+'s assumption of data exchangeability to achieve the same finite-sample coverage guarantee even under covariate shift. JAWA further approaches the JAW guarantee in the limit of either the sample size or the influence function order under mild assumptions. Moreover, we propose a general approach to repurposing any distribution-free uncertainty quantification method and its guarantees to the task of risk assessment: a task that generates the estimated probability that the true label lies within a user-specified interval. We then propose \textbf{JAW-R} and \textbf{JAWA-R} as the repurposed versions of proposed methods for \textbf{R}isk assessment. Practically, JAWS outperform the state-of-the-art predictive inference baselines in a variety of biased real world data sets for both interval-generation and risk-assessment auditing tasks

Stochastic Methods in Optimization and Machine Learning

Stochastic methods are indispensable to the modeling, analysis and design of complex systems involving randomness. In this thesis, we show how simulation techniques and simulation-based computational methods can be applied to a wide spectrum of applied domains including engineering, optimization and machine learning. Moreover, we show how analytical tools in statistics and computer science including empirical processes, probably approximately correct learning, and hypothesis testing can be used in these contexts to provide new theoretical results. In particular, we apply these techniques and present how our results can create new methodologies or improve upon existing state-of-the-art in three areas: decision making under uncertainty (chance-constrained programming, stochastic programming), machine learning (covariate shift, reinforcement learning) and estimation problems arising from optimization (gradient estimate of composite functions) or stochastic systems (solution of stochastic PDE). The work in the above three areas will be organized into six chapters, where each area contains two chapters. In Chapter 2, we study how to obtain feasible solutions for chance-constrained programming using data-driven, sampling-based scenario optimization (SO) approach. When the data size is insufficient to statistically support a desired level of feasibility guarantee, we explore how to leverage parametric information, distributionally robust optimization and Monte Carlo simulation to obtain a feasible solution of chance-constrained programming in small-sample situations. In Chapter 3, We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse. We utilize results from the Vapnik-Chervonenkis (VC) dimension and Probably Approximately Correct learning to provide a general framework. In Chapter 4, we design a robust importance re-weighting method for estimation/learning problem in the covariate shift setting that improves the best-know rate. In Chapter 5, we develop a model-free reinforcement learning approach to solve constrained Markov decision processes (MDP). We propose a two-stage procedure that generates policies with simultaneous guarantees on near-optimality and feasibility. In Chapter 6, we use multilevel Monte Carlo to construct unbiased estimators for expectations of random parabolic PDE. We obtain estimators with finite variance and finite expected computational cost, but bypassing the curse of dimensionality. In Chapter 7, we introduce unbiased gradient simulation algorithms for solving stochastic composition optimization (SCO) problems. We show that the unbiased gradients generated by our algorithms have finite variance and finite expected computational cost