Many existing fairness criteria for machine learning involve equalizing or achieving some metric across protected groups such as race or gender groups. However, practitioners trying to audit or enforce such group-based criteria can easily face the problem of noisy or biased protected group information. We study this important practical problem in two ways. First, we study the consequences of naïvely only relying on noisy protected groups: we provide an upper bound on the fairness violations on the true groups G when the fairness criteria are satisfied on noisy groups Ĝ. Second, we introduce two new approaches using robust optimization that, unlike the naïve approach of only relying on Ĝ, are guaranteed to satisfy fairness criteria on the true protected groups G while minimizing a training objective. We provide theoretical guarantees that one such approach converges to an optimal feasible solution. Using two case studies, we empirically show that the robust approaches achieve better true group fairness guarantees than the naïve approach.
While many areas of machine learning have benefited from the increasing availability of large and varied datasets, the benefit to causal inference has been limited given the strong assumptions needed to ensure identifiability of causal effects; these are often not satisfied in real-world datasets. For example, many large observational datasets (e.g., case-control studies in epidemiology, click-through data in recommender systems) suffer from selection bias on the outcome, which makes the average treatment effect (ATE) unidentifiable. We propose a general algorithm to estimate causal effects from multiple data sources, where the ATE may be identifiable only in some datasets but not others. The key idea is to construct control variates using the datasets in which the ATE is not identifiable. We show theoretically that this reduces the variance of the ATE estimate. We apply this framework to inference from observational data under an outcome selection bias, assuming access to an auxiliary small dataset from which we can obtain a consistent estimate of the ATE. We construct a control variate by taking the difference of the odds ratio estimates from the two datasets. Across simulations and two case studies with real data, we show that this control variate can significantly reduce the variance of the ATE estimate.
We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, our paradigm leverages the demonstrator's behavior en route to optimality, and in particular, the exploration phase, to obtain consistent reward estimates. We develop simple and efficient reward estimation procedures for demonstrations within a class of upper-confidence-based algorithms, showing that reward estimation gets progressively easier as the regret of the algorithm increases. We match these upper bounds with information-theoretic lower bounds that apply to any demonstrator algorithm, thereby characterizing the optimal tradeoff between exploration and reward estimation. Extensive empirical evaluations on both synthetic data and simulated experimental design data from the natural sciences corroborate our theoretical results.
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