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Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data

Yuqi Gu 1 Elena Erosheva 2, 3 Gongjun Xu 4 David Dunson 5
2 MAASAI - Modèles et algorithmes pour l’intelligence artificielle
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), JAD - Laboratoire Jean Alexandre Dieudonné, Laboratoire I3S - SPARKS - Scalable and Pervasive softwARe and Knowledge Systems
Abstract : Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of Dimension-Grouped MMMs (Gro-M 3 s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M 3 s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M 3 s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through an application to a functional disability dataset.
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https://hal.archives-ouvertes.fr/hal-03522275
Contributor : Elena Erosheva Connect in order to contact the contributor
Submitted on : Wednesday, January 12, 2022 - 2:01:41 AM
Last modification on : Thursday, March 24, 2022 - 4:49:57 PM
Long-term archiving on: : Wednesday, April 13, 2022 - 6:16:54 PM

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Yuqi Gu, Elena Erosheva, Gongjun Xu, David Dunson. Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data. 2022. ⟨hal-03522275⟩

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