The Max-Product Algorithm Viewed as Linear Data-Fusion: A Distributed Detection Scenario

Younes Abdi; Tapani Ristaniemi

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arXiv · 1909.09402

The Max-Product Algorithm Viewed as Linear Data-Fusion: A Distributed Detection Scenario

Younes Abdi·Tapani Ristaniemi

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Abstract

In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis test conducted by a max-product iteration over a binary-valued pairwise Markov random field and show that the decision variables obtained are linear combinations of the local log-likelihood ratios observed in the network. Then, we use these linear combinations to formulate the system performance in terms of the false-alarm and detection probabilities. Our findings indicate that, in the hypothesis test concerned, the optimal performance of the max-product algorithm is obtained by an optimal linear data-fusion scheme and the behavior of the max-product algorithm is very similar to the behavior of the sum-product algorithm. Consequently, we demonstrate that the optimal performance of the max-product iteration is closely achieved via a linear version of the sum-product algorithm which is optimized based on statistics received at each node from its one-hop neighbors. Finally, we verify our observations via computer simulations.

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Younes Abdi, Tapani Ristaniemi. 2020-04-29. The Max-Product Algorithm Viewed as Linear Data-Fusion: A Distributed Detection Scenario. https://arxiv.org/abs/1909.09402

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