Mixtures of regressions using matrix-variate heavy-tailed distributions

IF 1.4 4区计算机科学 Q2 STATISTICS & PROBABILITY Advances in Data Analysis and Classification Pub Date : 2024-03-16 DOI:10.1007/s11634-024-00585-7

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Abstract

Finite mixtures of regressions (FMRs) are powerful clustering devices used in many regression-type analyses. Unfortunately, real data often present atypical observations that make the commonly adopted normality assumption of the mixture components inadequate. Thus, to robustify the FMR approach in a matrix-variate framework, we introduce ten FMRs based on the matrix-variate t and contaminated normal distributions. Furthermore, once one of our models is estimated and the observations are assigned to the groups, different procedures can be used for the detection of the atypical points in the data. An ECM algorithm is outlined for maximum likelihood parameter estimation. By using simulated data, we show the negative consequences (in terms of parameter estimates and inferred classification) of the wrong normality assumption in the presence of heavy-tailed clusters or noisy matrices. Such issues are properly addressed by our models instead. Additionally, over the same data, the atypical points detection procedures are also investigated. A real-data analysis concerning the relationship between greenhouse gas emissions and their determinants is conducted, and the behavior of our models in the presence of heterogeneity and atypical observations is discussed.

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使用矩阵变量重尾分布的回归混合物

摘要有限回归混合物（FMR）是许多回归类型分析中使用的强大聚类工具。遗憾的是，真实数据经常出现非典型观测结果，这使得通常采用的混合物成分正态性假设变得不充分。因此，为了在矩阵变量框架中稳健地使用 FMR 方法，我们引入了十种基于矩阵变量 t 和污染正态分布的 FMR。此外，一旦估算出我们的模型之一并将观测值分配到组中，就可以使用不同的程序来检测数据中的非典型点。我们概述了一种用于最大似然参数估计的 ECM 算法。通过使用模拟数据，我们展示了在存在重尾聚类或噪声矩阵的情况下，错误的正态性假设所带来的负面影响（在参数估计和推断分类方面）。而我们的模型可以妥善解决这些问题。此外，我们还对同一数据的非典型点检测程序进行了研究。对温室气体排放及其决定因素之间的关系进行了真实数据分析，并讨论了我们的模型在存在异质性和非典型观测时的行为。

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来源期刊

Advances in Data Analysis and Classification STATISTICS & PROBABILITY-

CiteScore

3.40

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The international journal Advances in Data Analysis and Classification (ADAC) is designed as a forum for high standard publications on research and applications concerning the extraction of knowable aspects from many types of data. It publishes articles on such topics as structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering, and pattern recognition methods; strategies for modeling complex data and mining large data sets; methods for the extraction of knowledge from data, and applications of advanced methods in specific domains of practice. Articles illustrate how new domain-specific knowledge can be made available from data by skillful use of data analysis methods. The journal also publishes survey papers that outline, and illuminate the basic ideas and techniques of special approaches.