TY - JOUR

T1 - Robust fitting of mixture models using weighted complete estimating equations

AU - Sugasawa, Shonosuke

AU - Kobayashi, Genya

N1 - Funding Information:
We would like to thank the three reviewers and the coordinating editor for their valuable comments and suggestions, which have significantly improved the paper. This work was supported by the Japan Society for the Promotion of Science (KAKENHI) Grant Numbers 18K12754 , 18K12757 , 20H00080 , 21K01421 , and 21H00699 .
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/10

Y1 - 2022/10

N2 - Mixture modeling, which considers the potential heterogeneity in data, is widely adopted for classification and clustering problems. Mixture models can be estimated using the Expectation-Maximization algorithm, which works with the complete estimating equations conditioned by the latent membership variables of the cluster assignment based on the hierarchical expression of mixture models. However, when the mixture components have light tails such as a normal distribution, the mixture model can be sensitive to outliers. This study proposes a method of weighted complete estimating equations (WCE) for the robust fitting of mixture models. Our WCE introduces weights to complete estimating equations such that the weights can automatically downweight the outliers. The weights are constructed similarly to the density power divergence for mixture models, but in our WCE, they depend only on the component distributions and not on the whole mixture. A novel expectation-estimating-equation (EEE) algorithm is also developed to solve the WCE. For illustrative purposes, a multivariate Gaussian mixture, a mixture of experts, and a multivariate skew normal mixture are considered, and how our EEE algorithm can be implemented for these specific models is described. The numerical performance of the proposed robust estimation method was examined using simulated and real datasets.

AB - Mixture modeling, which considers the potential heterogeneity in data, is widely adopted for classification and clustering problems. Mixture models can be estimated using the Expectation-Maximization algorithm, which works with the complete estimating equations conditioned by the latent membership variables of the cluster assignment based on the hierarchical expression of mixture models. However, when the mixture components have light tails such as a normal distribution, the mixture model can be sensitive to outliers. This study proposes a method of weighted complete estimating equations (WCE) for the robust fitting of mixture models. Our WCE introduces weights to complete estimating equations such that the weights can automatically downweight the outliers. The weights are constructed similarly to the density power divergence for mixture models, but in our WCE, they depend only on the component distributions and not on the whole mixture. A novel expectation-estimating-equation (EEE) algorithm is also developed to solve the WCE. For illustrative purposes, a multivariate Gaussian mixture, a mixture of experts, and a multivariate skew normal mixture are considered, and how our EEE algorithm can be implemented for these specific models is described. The numerical performance of the proposed robust estimation method was examined using simulated and real datasets.

KW - Clustering

KW - Divergence

KW - EEE algorithm

KW - Mixture of experts

KW - Skew normal mixture

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U2 - 10.1016/j.csda.2022.107526

DO - 10.1016/j.csda.2022.107526

M3 - Article

AN - SCOPUS:85130552273

SN - 0167-9473

VL - 174

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

M1 - 107526

ER -