文章基本信息

标题：Selective inference for latent block models
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作者：Chihiro Watanabe ; Taiji Suzuki
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：1
页码：3137-3183
DOI：10.1214/21-EJS1853
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：62F03; 62H30; Latent Block Model; relational data analysis; selective inference