Robust fitting of mixture models using weighted complete estimating equations

Shonosuke Sugasawa, Genya Kobayashi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number107526
JournalComputational Statistics and Data Analysis
Publication statusPublished - 2022 Oct
Externally publishedYes


  • Clustering
  • Divergence
  • EEE algorithm
  • Mixture of experts
  • Skew normal mixture

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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