Convergence Rates of Smooth Message Passing with Rounding in EntropyRegularized MAP Inference
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:30033014, 2020.
Abstract
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 discretevalued model. Linear programming (LP) relaxations in the SheraliAdams 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 entropyregularized LPs to analyze convergence rates of a class of edgebased smooth message passing algorithms to epsilonoptimality 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.
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