How to Approximate Inference with Subtractive Mixture Models

Lena Zellinger, Nicola Branchini, Lennert De Smet, Víctor Elvira, Nikolay Malkin, Antonio Vergari
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:5149-5157, 2026.

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 \url{https://github.com/april-tools/delta-vi.}

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-zellinger26a, title = { How to Approximate Inference with Subtractive Mixture Models }, author = {Zellinger, Lena and Branchini, Nicola and De Smet, Lennert and Elvira, V{\'i}ctor and Malkin, Nikolay and Vergari, Antonio}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {5149--5157}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/zellinger26a/zellinger26a.pdf}, url = {https://proceedings.mlr.press/v300/zellinger26a.html}, 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 \url{https://github.com/april-tools/delta-vi.} } }
Endnote
%0 Conference Paper %T How to Approximate Inference with Subtractive Mixture Models %A Lena Zellinger %A Nicola Branchini %A Lennert De Smet %A Víctor Elvira %A Nikolay Malkin %A Antonio Vergari %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-zellinger26a %I PMLR %P 5149--5157 %U https://proceedings.mlr.press/v300/zellinger26a.html %V 300 %X 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 \url{https://github.com/april-tools/delta-vi.}
APA
Zellinger, L., Branchini, N., De Smet, L., Elvira, V., Malkin, N. & Vergari, A.. (2026). How to Approximate Inference with Subtractive Mixture Models . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:5149-5157 Available from https://proceedings.mlr.press/v300/zellinger26a.html.

Related Material