Many structured prediction tasks involve complex models where inference is computationally intractable, but where it can be well approximated using a linear programming relaxation. Previous approaches for learning for structured prediction (e.g., cuttingplane, subgradient methods, perceptron

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified

Approximate MAP inference in graphical models is an important and challenging prob-lem for many domains including computer vi-sion, computational biology and natural lan-guage understanding. Current state-of-the-art approaches employ convex relaxations of these problems as surrogate objectives

We use the property of unimodular functions to perform approximate inference with dual decomposition in binary labeled graphs. Exact inference is possible for a subclass of binary labeled graphs that have unimodular functions. We call such graphs unimodular graphs. These are graphs where

We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise a novel class of iterative solutions to the stochastic

In this paper, we propose combining augmented Lagrangian optimization with the dual decomposition method to obtain a fast algorithm for approximate MAP (maximum a posteriori) inference on factor graphs. We also show how the proposed algorithm can efficiently handle problems with (possibly global

. Specifically, a natural relaxation of the dual formulation gives rise to exact iterative solutions to the finite and infinite horizon stochastic optimal control problem, while direct application of Bayesian inference methods yields instances of risk sensitive control. 1

log-determinant maximization problem that can be solved efficiently by interior point methods, thereby providing approximations to the exact marginals. We show how a slightly weakened log-determinant relaxation can be solved even more efficiently by a dual reformulation. When applied to denoising

of the bound is determined by a permutation, or elimination order, of the model variables. Optimizing this bound results in an upper bound on the log partition function, and also yields an approximation to the model marginals. The optimization problem is convex, and is in fact a dual of a geometric program. We

We investigate dual decomposition for joint MAP inference of many strings. Given an arbitrary graphical model, we decompose it into small acyclic sub-models, whose MAP configurations can be found by finite-state composition and dynamic programming. We force the solutions of these subproblems