Convergence Rates of Smooth Message Passing with Rounding in Entropy-Regularized MAP Inference
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, and smooth message passing algorithms have been proposed to solve regularized versions of these LPs with great success. This paper leverages recent work in entropy-regularized LPs to analyze convergence rates of a class of edge-based smooth message passing algorithms to $\epsilon$-optimality in the relaxation. With an appropriately chosen regularization constant, we present a theoretical guarantee on the number of iterations sufficient to recover the true integral MAP solution when the LP is tight and the solution is unique.
Code (0)
등록된 구현이 없습니다.
Tasks
Combinatorial OptimizationSimilar Papers 제목 키워드 기반
Accelerated Message Passing for Entropy-Regularized MAP Inference
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. …
Elastic Graph Neural Networks
While many existing graph neural networks (GNNs) have been proven to perform $\ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNN…
Hybrid Vector Message Passing for Generalized Bilinear Factorization
In this paper, we propose a new message passing algorithm that utilizes hybrid vector message passing (HVMP) to solve the generalized bilinear factorization (GBF) problem. The proposed GBF-HVMP algorithm integrates expec…
Provably Convergent Subgraph-wise Sampling for Fast GNN Training
Subgraph-wise sampling -- a promising class of mini-batch training techniques for graph neural networks (GNNs -- is critical for real-world applications. During the message passing (MP) in GNNs, subgraph-wise sampling me…
Convergence of Some Convex Message Passing Algorithms to a Fixed Point
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. This is also known as conv…