Diagonal Gaussian Mixture Models and Higher Order Tensor Decompositions

2024/01/02 by Bingni Guo, Guo, Bingni, Jiawang Nie +3
Computer Science · Mathematics · #15A69 #65F99 #Algorithms and Data Compression #Blind Source Separation Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2401.01337

openalex publication_date 2024/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies how to recover parameters in diagonal Gaussian mixture models using tensors. High-order moments of the Gaussian mixture model are estimated from samples. They form incomplete symmetric tensors generated by hidden parameters in the model. We propose to use generating polynomials to compute incomplete symmetric tensor approximations. The obtained decomposition is utilized to recover parameters in the model. We prove that our recovered parameters are accurate when the estimated moments are accurate. Using high-order moments enables our algorithm to learn Gaussian mixtures with more components. For a given model dimension and order, we provide an upper bound of the number of components in the Gaussian mixture model that our algorithm can compute.

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