Title: Applications of Efficient Statistical Inference over Continuous Higher-Order Distributions
Statistical inference in high-dimensional continuous probability distributions is a computationally challenging task. One method that has proven successful in a wide class of applications is belief propagation, which estimates the marginal of each variable in a distribution. Historically, belief propagation has only been practical only for a
restricted subclass of inference problems known as pairwise-connected Markov Random Fields. In this talk, I describe methods of efficient belief propagation for higher-order factors. These methods make possible several previously intractable applications. First, I show how these techniques can be applied to the inference of 3D shape from shading in single images. This approach to shape-from-shading not only produces state of the art results, but also demonstrates the flexibility to generalize to more complex depth inference problems.
Secondly, I show applications towards learning the parameters of higher-order Markov and conditional random fields. Finally, I demonstrate how these techniques can be applied towards binary classification, outperforming SVMs and expectation propagation on linear classification problems.