Learning as MAP Inference in Discrete Graphical Models

We present a new formulation for attacking binary classification problems. Instead of relying on convex losses and regularisers such as in SVMs, logistic regression and boosting, or instead non-convex but continuous formulations such as those encountered in neural networks and deep belief networks, our framework entails a non-convex but \emph{discrete} formulation, where estimation amounts to finding a MAP configuration in a graphical model whose potential functions are low-dimensional discrete surrogates for the misclassification loss. We argue that such a discrete formulation can naturally account for a number of issues that are typically encountered in either the convex or the continuous non-convex paradigms, or both. By reducing the learning problem to a MAP inference problem, we can immediately translate the guarantees available for many inference settings to the learning problem itself. We empirically demonstrate in a number of experiments that this approach is promising in dealing with issues such as severe label noise, while still having global optimality guarantees.