# Principled Parallel Mean-Field Inference for Discrete Random Fields

Pierre Baque*, Timur Bagautdinov*, Francois Fleuret, Pascal Fua

EPFL, IDIAP

##### Abstract

Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice, various parallel techniques are used, which either rely on ad hoc smoothing with heuristically set parameters, or put strong constraints on the type of models. In this paper, we propose a novel proximal gradient-based approach to optimizing the variational objective. It is naturally parallelizable and easy to implement. We prove its convergence, and then demonstrate that, in practice, it yields faster convergence and often finds better optima than more traditional mean-field optimization techniques. Moreover, our method is less sensitive to the choice of parameters.

##### Files

Additional proofs and evaluations.

##### Code

A version of DenseCRF with our inference is available here

##### Sample Results

We provide additional sample results for three datasets considered in the paper

Characters Inpainting

Semantic Segmentation

People Detection