We prove that the alpha-expansion algorithm for MAP inference always returns a globally optimal assignment for Markov Random Fields with Potts pairwise potentials, with a catch: the returned assignment is only guaranteed to be optimal in a small …

Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for the LP …

To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition assumes that …

We propose a new way to answer probabilistic queries that span multiple datapoints. We formalize reasoning about the similarity of different datapoints as the evaluation of the Bayes Factor within a hierarchical deep generative model that enforces a …

Approximate algorithms for structured prediction problems -- such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001) -- typically far exceed their theoretical performance guarantees on real-world instances. These …

Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work …

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to …

Linear programming (LP) relaxations are widely used to attempt to identify a most likely configuration of a discrete graphical model. In some cases, the LP relaxation attains an optimum vertex at an integral location and thus guarantees an exact …

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the …

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each depending on two …