MAP Inference via L2-Sphere Linear Program Reformulation

05/09/2019
by   Baoyuan Wu, et al.
0

Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation methods have been developed, among which the linear programming (LP) relaxation based methods show promising performance. However, one major drawback of LP relaxation is that it is possible to give fractional solutions. Instead of presenting a tighter relaxation, in this work we propose a continuous but equivalent reformulation of the original MAP inference problem, called LS-LP. We add the L2-sphere constraint onto the original LP relaxation, leading to an intersected space with the local marginal polytope that is equivalent to the space of all valid integer label configurations. Thus, LS-LP is equivalent to the original MAP inference problem. We propose a perturbed alternating direction method of multipliers (ADMM) algorithm to optimize the LS-LP problem, by adding a sufficiently small perturbation epsilon onto the objective function and constraints. We prove that the perturbed ADMM algorithm globally converges to the epsilon-Karush-Kuhn-Tucker (epsilon-KKT) point of the LS-LP problem. The convergence rate will also be analyzed. Experiments on several benchmark datasets from Probabilistic Inference Challenge (PIC 2011) and OpenGM 2 show competitive performance of our proposed method against state-of-the-art MAP inference methods.

READ FULL TEXT

page 3

page 4

page 5

page 6

page 7

page 9

page 12

page 20

research
05/17/2013

Belief Propagation for Linear Programming

Belief Propagation (BP) is a popular, distributed heuristic for performi...
research
09/26/2013

Automorphism Groups of Graphical Models and Lifted Variational Inference

Using the theory of group action, we first introduce the concept of the ...
research
03/08/2017

Exact MAP Inference by Avoiding Fractional Vertices

Given a graphical model, one essential problem is MAP inference, that is...
research
12/17/2013

Constraint Reduction using Marginal Polytope Diagrams for MAP LP Relaxations

LP relaxation-based message passing algorithms provide an effective tool...
research
08/14/2013

Compact Relaxations for MAP Inference in Pairwise MRFs with Piecewise Linear Priors

Label assignment problems with large state spaces are important tasks es...
research
09/25/2017

Exact MAP inference in general higher-order graphical models using linear programming

This paper is concerned with the problem of exact MAP inference in gener...
research
04/14/2020

Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation

We consider the MAP-inference problem for graphical models, which is a v...

Please sign up or login with your details

Forgot password? Click here to reset