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Recently skew-t mixture models have been introduced as a flexibleprobabilistic modeling technique taking into account both skewness in dataclusters and the statistical degree of freedom (S-DoF) to improve modelinggeneralizability, and robustness to heavy tails and skewness. In this paper, weshow that the state-of-the-art skew-t mixture models fundamentally suffer froma hidden phenomenon named here as "S-DoF explosion," which results in localminima in the shapes of normal kernels during the non-convex iterative processof expectation maximization. For the first time, this paper provides insightsinto the instability of the S-DoF, which can result in the divergence of thekernels from the mixture of t-distribution, losing generalizability and powerfor modeling the outliers. Thus, in this paper, we propose a regularizediterative optimization process to train the mixture model, enhancing thegeneralizability and resiliency of the technique. The resulting mixture modelis named Finite Mixture of Multivariate Regulated Skew-t (FiMReSt) Kernels,which stabilizes the S-DoF profile during optimization process of learning. Tovalidate the performance, we have conducted a comprehensive experiment onseveral real-world datasets and a synthetic dataset. The results highlight (a)superior performance of the FiMReSt, (b) generalizability in the presence ofoutliers, and (c) convergence of S-DoF.

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