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

arXiv: https://arxiv.org/abs/2305.09071 · HTML: https://mlsanity.com/paper/2305.09071/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 51 references that are in the map.
- First posted on arXiv 15 May 2023.

## Builds on (most cited first, 2 of 2)

- [A Mixture of Generalized Hyperbolic Distributions](https://mlsanity.com/paper/1305.1036/) (2013)
- [Flexible High-Dimensional Unsupervised Learning with Missing Data](https://mlsanity.com/paper/1706.06185/) (2017)

## Abstract (arXiv)

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.