Model selection for Gaussian latent block clustering with the integrated classification likelihood

Lomet, Aurore; Govaert, Gérard; Grandvalet, Yves

doi:10.1007/s11634-013-0161-3

Cited by 11 publications

(12 citation statements)

References 16 publications

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“…The Latent block models (LBM), also known as bipartite stochastic block models and introduced in [15], are generative probabilistic models enabling to cluster jointly the rows and the columns of a data matrix denoted R. These co-clustering models assume a homogeneous block structure of the whole data matrix. This structure is unveiled by the reordering of rows and columns according to their respective cluster index; for k 1 row clusters and k 2 column clusters, the reordering reveals k 1 × k 2 homogeneous blocks in the data matrix being possibly binary [15] categorical [24], or quantitative [27,16].…”

Section: A the Latent Block Modelsmentioning

confidence: 99%

Stereotype-aware collaborative filtering

Frisch¹,

Léger²,

Grandvalet³

2021

Annals of Computer Science and Information Systems

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In collaborative filtering, recommendations are made using user feedback on a few products. In this paper, we show that even if sensitive attributes are not used to fit the models, a disparate impact may nevertheless affect recommendations. We propose a definition of fairness for the recommender system that expresses that the ranking of items should be independent of sensitive attribute. We design a coclustering of users and items that processes exogenous sensitive attributes to remove their influence to return fair recommendations. We prove that our model ensures approximately fair recommendations provided that the classification of users approximately respects statistical parity.

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Section: A the Latent Block Modelsmentioning

confidence: 99%

Stereotype-aware collaborative filtering

Frisch¹,

Léger²,

Grandvalet³

2021

Annals of Computer Science and Information Systems

Self Cite

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“…For the following discussion, we explain the case where the noise is generated by a normal distribution with zero mean and standard deviation σ for simplicity. Such a model can be applied to relational data matrices with continuous entries, and it has been called the Gaussian latent block model [24,25]. Here, B kh is the mean of entries in the (k, h)-th block under the null hypothesis:…”

Section: Problem Setting and Statistical Model For Goodness-of-fit Te...mentioning

confidence: 99%

Goodness-of-fit Test for Latent Block Models

Watanabe

Suzuki

2019

Preprint

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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.

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“…Estimation of the block number In addition, a specific expression of the ICL criterion (3) can be invoked for selecting the pair (K, L) (see [32] and [26] which provide ICL expressions for the Gaussian situation and for the Bernoulli/multinomial case, respectively).…”

Section: Model-based Co-clusteringmentioning

confidence: 99%

Unifying data units and models in (co-)clustering

Biernacki

Lourme

2018

Adv Data Anal Classif

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Statisticians are already aware that any modelling process issue (exploration, prediction) is wholly data unit dependent, to the extend that it should be impossible to provide a statistical outcome without specifying the couple (unit,model). In this work, this general principle is formalized with a particular focus in model-based clustering and co-clustering in the case of possibly mixed data types (continuous and/or categorical and/or counting features), being also the opportunity to revisit what the related data units are. Such a formalization allows to raise three important spots: (i) the couple (unit,model) is not identifiable so that different interpretations unit/model of the same whole modelling process are always possible; (ii) combining different "classical" units with different "classical" models should be an interesting opportunity for a cheap, wide and meaningful enlarging of the whole modelling process family designed by the couple (unit,model); (iii) if necessary, this couple, up to the non identifiability property, could be selected by any traditional model selection criterion. Some experiments on real data sets illustrate in detail practical benefits from the previous three spots.

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Model selection for Gaussian latent block clustering with the integrated classification likelihood

Cited by 11 publications

References 16 publications

Stereotype-aware collaborative filtering

Stereotype-aware collaborative filtering

Goodness-of-fit Test for Latent Block Models

Unifying data units and models in (co-)clustering

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