We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional distributions. Under these assumptions, we establish an Ω(K log K) labeled sample complexity bound without imposing parametric assumptions, where K is the number of classes. Our results suggest that even in nonparametric settings it is possible to learn a near-optimal classifier using only a few labeled samples. Unlike previous theoretical work which focuses on binary classification, we consider general multiclass classification (K > 2), which requires solving a difficult permutation learning problem. This permutation defines a classifier whose classification error is controlled by the Wasserstein distance between mixing measures, and we provide finite-sample results characterizing the behaviour of the excess risk of this classifier. Finally, we describe three algorithms for computing these estimators based on a connection to bipartite graph matching, and perform experiments to illustrate the superiority of the MLE over the majority vote estimator.

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

The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments and games. However, these traditional games are limited because they are typically designed based on heuristics. In this paper, we formulate the task of designing behavior diagnostic games that elicit distinguishable behavior as a mutual information maximization problem, which can be solved by optimizing a variational lower bound. Our framework is instantiated by using prospect theory to model varying player traits, and Markov Decision Processes to parameterize the games. We validate our approach empirically, showing that our designed games can successfully distinguish among players with different traits, outperforming manually-designed ones by a large margin.

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

The statistical decision theoretic foundations of modern machine learning have largely focused on the minimization of the expectation of some loss function for a given task. However, seminal results in behavioral economics have shown that human decision-making is based on different risk measures than the expectation of any given loss function. In this paper, we pose the following simple question: in contrast to minimizing expected loss, could we minimize a better human-aligned risk measure? While this might not seem natural at first glance, we analyze the properties of such a revised risk measure, and surprisingly show that it might also better align with additional desiderata like fairness that have attracted considerable recent attention. We focus in particular on a class of human-aligned risk measures inspired by cumulative prospect theory. We empirically study these risk measures, and demonstrate their improved performance on desiderata such as fairness, in contrast to the traditional workhorse of expected loss minimization.

The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments and games. However, these traditional games are limited because they are typically designed based on heuristics. In this paper, we formulate the task of designing behavior diagnostic games that elicit distinguishable behavior as a mutual information maximization problem, which can be solved by optimizing a variational lower bound. Our framework is instantiated by using prospect theory to model varying player traits, and Markov Decision Processes to parameterize the games. We validate our approach empirically, showing that our designed games can successfully distinguish among players with different traits, outperforming manually-designed ones by a large margin.