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