How to Approximate Inference with Subtractive Mixture Models

2026-04-17

AI Summary

Traditional mixture models exhibit limited expressiveness in variational inference and importance sampling, while subtractive mixture models—though more flexible—lack interpretable latent variables, hindering their direct application to approximate inference. This work presents the first systematic inference framework tailored for subtractive mixture models, introducing a novel expectation estimator and a stable, efficient learning strategy to overcome the challenges posed by their absence of explicit latent structure. Experimental results demonstrate that the proposed approach significantly outperforms baseline methods in distribution approximation tasks. The authors also release their implementation to facilitate future research in this direction.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

Problem

• subtractive mixture models
• approximate inference
• variational inference
• importance sampling
• negative coefficients

Innovation

• Subtractive Mixture Models
• Variational Inference
• Importance Sampling
• Expectation Estimation
• Distribution Approximation