How to Approximate Inference with Subtractive Mixture Models
For researchers in approximate inference, this work provides practical methods to leverage SMMs, though the improvements are incremental and come with additional challenges.
This paper addresses the challenge of using subtractive mixture models (SMMs) for variational inference and importance sampling, proposing new expectation estimators and learning schemes. Empirical results show that SMMs can improve approximation quality over classical MMs, but with trade-offs in stability and efficiency.
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.