DeepAI AI Chat
Log In Sign Up

Approximate Sherali-Adams Relaxations for MAP Inference via Entropy Regularization

by   Jonathan N. Lee, et al.

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sherali-Adams hierarchy are widely used to attempt to solve this problem. We leverage recent work in entropy-regularized linear programming to propose an iterative projection algorithm (SMPLP) for large scale MAP inference that is guaranteed to converge to a near-optimal solution to the relaxation. With an appropriately chosen regularization constant, we show the resulting rounded solution solves the exact MAP problem whenever the LP is tight. We further provide theoretical guarantees on the number of iterations sufficient to achieve ϵ-close solutions. Finally, we show in practice that SMPLP is competitive for solving Sherali-Adams relaxations.


Inference in Graphical Models via Semidefinite Programming Hierarchies

Maximum A posteriori Probability (MAP) inference in graphical models amo...

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...

Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation

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

Exact MAP Inference by Avoiding Fractional Vertices

Given a graphical model, one essential problem is MAP inference, that is...

Distributed Anytime MAP Inference

We present a distributed anytime algorithm for performing MAP inference ...

Improving the Accuracy and Efficiency of MAP Inference for Markov Logic

In this work we present Cutting Plane Inference (CPI), a Maximum A Poste...

Automorphism Groups of Graphical Models and Lifted Variational Inference

Using the theory of group action, we first introduce the concept of the ...