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2021 Selective inference for latent block models
Chihiro Watanabe, Taiji Suzuki
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Electron. J. Statist. 15(1): 3137-3183 (2021). DOI: 10.1214/21-EJS1853


Model selection in latent block models has been a challenging but important task in the field of statistics. Specifically, a major challenge is encountered when constructing a test on a block structure obtained by applying a specific clustering algorithm to a finite size matrix. In this case, it becomes crucial to consider the selective bias in the block structure, that is, the block structure is selected from all the possible cluster memberships based on some criterion by the clustering algorithm. To cope with this problem, this study provides a selective inference method for latent block models. Specifically, we construct a statistical test on a set of row and column cluster memberships of a latent block model, which is given by a squared residue minimization algorithm. The proposed test, by its nature, includes and thus can also be used as the test on the set of row and column cluster numbers. We also propose an approximated version of the test based on simulated annealing to avoid combinatorial explosion in searching the optimal block structure. The results show that the proposed exact and approximated tests work effectively, compared to the naive test that did not take the selective bias into account.

Funding Statement

TS was partially supported by JSPS KAKENHI (18K19793, 18H03201, and 20H00576), Japan Digital Design, Fujitsu Laboratories Ltd., and JST CREST.


We would like to thank Editage ( for English language editing.


Download Citation

Chihiro Watanabe. Taiji Suzuki. "Selective inference for latent block models." Electron. J. Statist. 15 (1) 3137 - 3183, 2021.


Received: 1 May 2020; Published: 2021
First available in Project Euclid: 8 June 2021

arXiv: 2005.13273
Digital Object Identifier: 10.1214/21-EJS1853

Primary: 62F03
Secondary: 62H30

Keywords: Latent Block Model , relational data analysis , selective inference


Vol.15 • No. 1 • 2021
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