How to Approximate Inference with Subtractive Mixture Models

TL;DR

This paper explores how subtractive mixture models can be used for variational inference and importance sampling, proposing new estimators and learning schemes to address their unique challenges.

Contribution

It introduces methods to effectively utilize subtractive mixture models for inference tasks, overcoming the lack of latent variable semantics.

Findings

Proposed expectation estimators for importance sampling with SMMs.

Developed learning schemes for variational inference using SMMs.

Empirical evaluation demonstrates the effectiveness of the proposed methods.

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.