A Non-Iterative Quantile Change Detection Method in Mixture Model with Heavy-Tailed Components

TL;DR

This paper introduces a fast, non-iterative change-point based method for estimating the number of components in mixture models, especially effective with heavy-tailed distributions, outperforming traditional iterative algorithms in speed and accuracy.

Contribution

The paper presents a novel non-iterative change-point detection approach for mixture models that is robust, fast, and applicable to heavy-tailed components, addressing limitations of existing EM-based methods.

Findings

Method is up to 500 times faster than existing algorithms.

More accurate in estimating mixture distributions according to goodness-of-fit tests.

Effective for heavy-tailed distributions like Cauchy.

Abstract

Estimating parameters of mixture model has wide applications ranging from classification problems to estimating of complex distributions. Most of the current literature on estimating the parameters of the mixture densities are based on iterative Expectation Maximization (EM) type algorithms which require the use of either taking expectations over the latent label variables or generating samples from the conditional distribution of such latent labels using the Bayes rule. Moreover, when the number of components is unknown, the problem becomes computationally more demanding due to well-known label switching issues \cite{richardson1997bayesian}. In this paper, we propose a robust and quick approach based on change-point methods to determine the number of mixture components that works for almost any location-scale families even when the components are heavy tailed (e.g., Cauchy). We present several numerical illustrations by comparing our method with some of popular methods available in the literature using simulated data and real case studies. The proposed method is shown be as much as 500 times faster than some of the competing methods and are also shown to be more accurate in estimating the mixture distributions by goodness-of-fit tests.