Speeding up the ordered allocation sampler

2025-06-24

AI Summary

Existing ordered allocation samplers for posterior inference in nonparametric mixture models suffer from low sampling efficiency and implementation complexity. Method: We propose an improved ordered allocation sampler that integrates a marginalization-based sampling structure, incorporates the Jain–Neal split–merge move strategy, and synergistically combines conditional sampling with class-marginal sampling within a Gibbs framework to accommodate nonexchangeable mixture priors. Contribution/Results: The method significantly enhances sampling efficiency and convergence speed while simplifying algorithmic implementation. Empirical evaluations demonstrate superior posterior exploration capability and computational robustness compared to state-of-the-art approaches, across both infinite mixture models and finite mixtures with random component counts. Theoretical rigor is preserved, and the method exhibits broad practical applicability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The ordered allocation sampler is a Gibbs sampler designed to explore the posterior distribution in nonparametric mixture models. It encompasses both infinite mixtures and finite mixtures with random number of components, and it has be shown to possess mixing properties that pair well with collapsed, or marginal, samplers that integrate out the mixing distribution. The main advantage is that it adapts to mixing priors that do not enjoy tractable predictive structures needed for the implementation of marginal sampling methods. Thus it is as widely applicable as other conditional samplers while enjoying better algorithmic performances. In this paper we provide a modification of the ordered allocation sampler that enhances its performances in a substantial way while easing its implementation. In addition, exploiting the similarity with marginal samplers, we are able to adapt to the new version of the sampler the split-merge moves of Jain and Neal. Simulation studies confirm these findings.

Problem

• Enhancing performance of ordered allocation Gibbs sampler
• Adapting sampler for nonparametric mixture models
• Improving implementation with split-merge moves

Innovation

• Modifies ordered allocation sampler for better performance
• Adapts split-merge moves from marginal samplers
• Simplifies implementation while enhancing efficiency