论文标题
混合模型与重尾组件中的非涉及分位数变化检测方法
A Non-Iterative Quantile Change Detection Method in Mixture Model with Heavy-Tailed Components
论文作者
论文摘要
混合模型的估计参数具有广泛的应用，从分类问题到估计复杂分布。当前有关估计混合物密度参数的当前文献都是基于迭代期望最大化（EM）型算法，这些算法需要使用对潜在标签变量的期望或使用贝叶斯规则从此类潜伏标签的条件分布中产生样品的期望。此外，当组件的数量未知时，由于众所周知的标签切换问题\ cite {Richardson1997bayesian}，该问题在计算上变得更加要求。在本文中，我们提出了一种基于变更点方法的强大而快速的方法，以确定即使组件重尾，几乎适用于任何位置尺度家庭的混合组件数量（例如，凯奇）。我们通过将我们的方法与使用模拟数据和实际案例研究的文献中可用的一些流行方法进行比较，介绍了几个数值插图。所提出的方法显示的速度比某些竞争方法快500倍，并且在通过拟合优度测试估算混合物分布方面也更准确。
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.
