FiMReSt: Finite Mixture of Multivariate Regulated Skew-t Kernels -- A Flexible Probabilistic Model for Multi-Clustered Data with Asymmetrically-Scattered Non-Gaussian Kernels

• URL: http://arxiv.org/abs/2305.09071v1
• Date: Mon, 15 May 2023 23:53:59 GMT
• Title: FiMReSt: Finite Mixture of Multivariate Regulated Skew-t Kernels -- A Flexible Probabilistic Model for Multi-Clustered Data with Asymmetrically-Scattered Non-Gaussian Kernels
• Authors: Sarmad Mehrdad, S. Farokh Atashzar
• Abstract summary: We propose a regularized iterative optimization process to train the mixture model, enhancing the generalizability and power for modeling the skews. The resulting mixture model is named Finite Mixture of Multi Regulated Skewt (FiMStss) To validate the performance, we have conducted a comprehensive experiment on several real-world datasets and a synthetic dataset.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently skew-t mixture models have been introduced as a flexible probabilistic modeling technique taking into account both skewness in data clusters and the statistical degree of freedom (S-DoF) to improve modeling generalizability, and robustness to heavy tails and skewness. In this paper, we show that the state-of-the-art skew-t mixture models fundamentally suffer from a hidden phenomenon named here as "S-DoF explosion," which results in local minima in the shapes of normal kernels during the non-convex iterative process of expectation maximization. For the first time, this paper provides insights into the instability of the S-DoF, which can result in the divergence of the kernels from the mixture of t-distribution, losing generalizability and power for modeling the outliers. Thus, in this paper, we propose a regularized iterative optimization process to train the mixture model, enhancing the generalizability and resiliency of the technique. The resulting mixture model is named Finite Mixture of Multivariate Regulated Skew-t (FiMReSt) Kernels, which stabilizes the S-DoF profile during optimization process of learning. To validate the performance, we have conducted a comprehensive experiment on several real-world datasets and a synthetic dataset. The results highlight (a) superior performance of the FiMReSt, (b) generalizability in the presence of outliers, and (c) convergence of S-DoF.

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