Scalable Semidefinite Relaxation for Maximum A Posterior Estimation

by   Qixing Huang, et al.

Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimate the MAP assignment. Algorithmically, we develop an accelerated variant of the alternating direction method of multipliers (referred to as SDPAD-LR) that can effectively exploit the special structure of the new relaxation. Encouragingly, the proposed procedure allows solving SDR for large-scale problems, e.g., problems on a grid graph comprising hundreds of thousands of variables with multiple states per node. Compared with prior SDP solvers, SDPAD-LR is capable of attaining comparable accuracy while exhibiting remarkably improved scalability, in contrast to the commonly held belief that semidefinite relaxation can only been applied on small-scale MRF problems. We have evaluated the performance of SDR on various benchmark datasets including OPENGM2 and PIC in terms of both the quality of the solutions and computation time. Experimental results demonstrate that for a broad class of problems, SDPAD-LR outperforms state-of-the-art algorithms in producing better MAP assignment in an efficient manner.


page 1

page 2

page 3

page 4


Community detection using fast low-cardinality semidefinite programming

Modularity maximization has been a fundamental tool for understanding th...

Efficient semidefinite-programming-based inference for binary and multi-class MRFs

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. co...

Continuous Relaxation of MAP Inference: A Nonconvex Perspective

In this paper, we study a nonconvex continuous relaxation of MAP inferen...

A Fast Semidefinite Approach to Solving Binary Quadratic Problems

Many computer vision problems can be formulated as binary quadratic prog...

Inference in Graphical Models via Semidefinite Programming Hierarchies

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

A Practical Distributed ADMM Solver for Billion-Scale Generalized Assignment Problems

Assigning items to owners is a common problem found in various real-worl...

Probabilistic Adaptive Computation Time

We present a probabilistic model with discrete latent variables that con...

Please sign up or login with your details

Forgot password? Click here to reset