Stochastic First-Order Learning for Large-Scale Flexibly Tied Gaussian Mixture Model

• URL: http://arxiv.org/abs/2212.05402v3
• Date: Sat, 11 Nov 2023 17:39:22 GMT
• Title: Stochastic First-Order Learning for Large-Scale Flexibly Tied Gaussian Mixture Model
• Authors: Mohammad Pasande, Reshad Hosseini, Babak Nadjar Araabi
• Abstract summary: We propose a new optimization algorithm on the manifold of Gaussian Mixture Models (GMMs) We observe that methods can outperform the expectation-maximization algorithm in terms of attaining better likelihood, needing fewer epochs for convergence, and consuming less time per each epoch.
• Score: 3.4546761246181696
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges of common GMMs when faced with high-dimensional data and complex densities which often demand a large number of Gaussian components. However, the expectation-maximization algorithm for fitting flexibly-tied GMMs still encounters difficulties with streaming and very large dimensional data. To overcome these challenges, this paper suggests the use of first-order stochastic optimization algorithms. Specifically, we propose a new stochastic optimization algorithm on the manifold of orthogonal matrices. Through numerous empirical results on both synthetic and real datasets, we observe that stochastic optimization methods can outperform the expectation-maximization algorithm in terms of attaining better likelihood, needing fewer epochs for convergence, and consuming less time per each epoch.

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