Stochastic classifiers arise in a number of machine learning problems, and have become especially prominent of late, as they often result from constrained optimization problems, e.g. for fairness, churn, or custom losses. Despite their utility, the inherent randomness of stochastic classifiers may cause them to be problematic to use in practice for a variety of practical reasons. In this paper, we attempt to answer the theoretical question of how well a stochastic classifier can be approximated by a deterministic one, and compare several different approaches, proving lower and upper bounds. We also experimentally investigate the pros and cons of these methods, not only in regard to how successfully each deterministic classifier approximates the original stochastic classifier, but also in terms of how well each addresses the other issues that can make stochastic classifiers undesirable.

Neural Information Processing Systems http://nips.cc/

Stochastic classifiers arise in a number of machine learning problems, and have become especially prominent of late, as they often result from constrained optimization problems, e.g. for fairness, churn, or custom losses. Despite their utility, the inherent randomness of stochastic classifiers may cause them to be problematic to use in practice for a variety of practical reasons. In this paper, we attempt to answer the theoretical question of how well a stochastic classifier can be approximated by a deterministic one, and compare several different approaches, proving lower and upper bounds. We also experimentally investigate the pros and cons of these methods, not only in regard to how successfully each deterministic classifier approximates the original stochastic classifier, but also in terms of how well each addresses the other issues that can make stochastic classifiers undesirable.

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to satisfy non-linear rate constraints such as predictive parity fairness, distribution divergences or churn ratios. We extend previous two-player game approaches for constrained optimization to an approach with three players to decouple the classifier rates from the non-linear objective, and seek to find an equilibrium of the game. Our approach generalizes many existing algorithms, and makes possible new algorithms with more flexibility and tighter handling of non-linear rate constraints. We provide convergence guarantees for convex functions of rates, and show how our methodology can be extended to handle sums-of-ratios of rates. Experiments on different fairness tasks confirm the efficacy of our approach.

Neural Information Processing Systems http://nips.cc/