Fast Bayesian Inference in Dirichlet Process Mixture Models.

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Bayesian nonparametric methods are gaining traction for large, high-dimensional data.
• Current Markov chain Monte Carlo (MCMC) algorithms are often computationally infeasible for these settings.
• Faster algorithms are crucial for practical application of Bayesian nonparametric methods.

Purpose of the Study:

• To propose a fast algorithm for inference in Dirichlet process mixture (DPM) models.
• To enable efficient model selection and comparison between parametric and nonparametric alternatives.
• To provide a computationally tractable approach for large-scale Bayesian nonparametric analysis.

Main Methods:

• A sequential greedy search algorithm is proposed for cluster partitioning, treating it as a model selection problem.
• Utilizing conjugate priors allows for closed-form posteriors conditional on the selected partition.
• The approach facilitates Bayes factor testing of parametric versus nonparametric models.

Main Results:

• The proposed algorithm demonstrates efficiency in simulation studies compared to existing fast nonparametric methods.
• The method was successfully applied to three real-world datasets, including a large epidemiologic study.
• Matlab code is provided for reproducibility of simulations and data analyses.

Conclusions:

• The developed sequential greedy algorithm offers a computationally efficient alternative for DPM model inference.
• This method enhances the practical applicability of Bayesian nonparametric approaches in large and high-dimensional data scenarios.
• The ability to perform model comparison using Bayes factors adds significant value for data analysis.