Structured Prediction by Conditional Risk Minimization

Abstract: We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of output labels, we first estimate the conditional risk function by solving a (possibly infinite) collection of regularized least squares problems. A prediction is made by solving an inference problem that minimizes the estimated conditional risk function over the output space. We show that this approach enables, in some cases, efficient training and inference without explicitly introducing a convex surrogate for the original loss function, even when it is discontinuous. Empirical evaluations on real-world and synthetic data sets demonstrate the effectiveness of our method in adapting to a variety of loss functions.