An Approximate Tensor-Based Inference Method Applied to the Game of Minesweeper

Abstract

AbstractWe propose an approximate probabilistic inference method based on the CP-tensor decomposition and apply it to the well known computer game of Minesweeper. In the method we view conditional probability tables of the exactly ℓ-out-of-k functions as tensors and approximate them by a sum of rank-one tensors. The number of the summands is min {l + 1,k − l + 1}, which is lower than their exact symmetric tensor rank, which is k. Accuracy of the approximation can be tuned by single scalar parameter. The computer game serves as a prototype for applications of inference mechanisms in Bayesian networks, which are not always tractable due to the dimensionality of the problem, but the tensor decomposition may significantly help.KeywordsBayesian NetworksProbabilistic InferenceCP Tensor DecompositionSymmetric Tensor Rank