Bayesian Variational Inference for Mixed Data Mixture Models

2025/07/22 by Junyang Wang, James Bennett, Wang, Junyang +5 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2507.16545

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Heterogeneous, mixed type datasets including both continuous and categorical variables are ubiquitous, and enriches data analysis by allowing for more complex relationships and interactions to be modelled. Mixture models offer a flexible framework for capturing the underlying heterogeneity and relationships in mixed type datasets. Most current approaches for modelling mixed data either forgo uncertainty quantification and only conduct point estimation, and some use MCMC which incurs a very high computational cost that is not scalable to large datasets. This paper develops a coordinate ascent variational inference algorithm (CAVI) for mixture models on mixed (continuous and categorical) data, which circumvents the high computational cost of MCMC while retaining uncertainty quantification. We demonstrate our approach through simulation studies as well as an applied case study of the NHANES risk factor dataset. We provide theoretical justification for our method by establishing that the CAVI variational posterior mean converges locally to the true parameter value at a gap of O(1/n) from the maximum likelihood estimator. Building on this result, we show that the CAVI variational posterior contracts around the true parameter at O(n^-1/2) rate.

Citations

• A Bayesian Finite Mixture Model with Variable Selection for Data with Mixed-type Variables
• Variational Inference: A Review for Statisticians
• Model Based Clustering for Mixed Data: clustMD
• Mixture models with a prior on the number of components
• Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling

Cited by

• Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization

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