A Minimax Approach to Supervised Learning

NeurIPS 2016  ·  Farzan Farnia, David Tse ·

Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of probability distributions $\Gamma$ on $(X,Y)$, what is the optimal decision rule minimizing the worst-case expected loss over $\Gamma$? In this paper, we address this question by introducing a generalization of the principle of maximum entropy... Applying this principle to sets of distributions with marginal on $X$ constrained to be the empirical marginal from the data, we develop a general minimax approach for supervised learning problems. While for some loss functions such as squared-error and log loss, the minimax approach rederives well-knwon regression models, for the 0-1 loss it results in a new linear classifier which we call the maximum entropy machine. The maximum entropy machine minimizes the worst-case 0-1 loss over the structured set of distribution, and by our numerical experiments can outperform other well-known linear classifiers such as SVM. We also prove a bound on the generalization worst-case error in the minimax approach. read more

PDF Abstract NeurIPS 2016 PDF NeurIPS 2016 Abstract


  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.