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Goodness-of-fit test for latent block models

Author

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  • Watanabe, Chihiro
  • Suzuki, Taiji

Abstract

Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster numbers of latent block models. Recent studies have constructed statistical-test-based methods for stochastic block models, which assume that the observed matrix is a square symmetric matrix and that the cluster assignments are the same for rows and columns. In this study, we developed a new goodness-of-fit test for latent block models to test whether an observed data matrix fits a given set of row and column cluster numbers, or it consists of more clusters in at least one direction of the row and the column. To construct the test method, we used a result from the random matrix theory for a sample covariance matrix. We experimentally demonstrated the effectiveness of the proposed method by showing the asymptotic behavior of the test statistic and measuring the test accuracy.

Suggested Citation

  • Watanabe, Chihiro & Suzuki, Taiji, 2021. "Goodness-of-fit test for latent block models," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:csdana:v:154:y:2021:i:c:s016794732030181x
    DOI: 10.1016/j.csda.2020.107090
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    References listed on IDEAS

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    3. Kehui Chen & Jing Lei, 2018. "Network Cross-Validation for Determining the Number of Communities in Network Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 241-251, January.
    4. Tianxi Li & Elizaveta Levina & Ji Zhu, 2020. "Network cross-validation by edge sampling," Biometrika, Biometrika Trust, vol. 107(2), pages 257-276.
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