Reparameterized Variational Rejection Sampling

Martin Jankowiak, Du Phan
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:739-747, 2024.

Abstract

Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method–Reparameterized Variational Rejection Sampling (RVRS)–offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well suited for black-box inference, especially for models with local latent variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-jankowiak24a, title = {Reparameterized Variational Rejection Sampling}, author = {Jankowiak, Martin and Phan, Du}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {739--747}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/jankowiak24a/jankowiak24a.pdf}, url = {https://proceedings.mlr.press/v238/jankowiak24a.html}, abstract = {Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method–Reparameterized Variational Rejection Sampling (RVRS)–offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well suited for black-box inference, especially for models with local latent variables.} }
Endnote
%0 Conference Paper %T Reparameterized Variational Rejection Sampling %A Martin Jankowiak %A Du Phan %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-jankowiak24a %I PMLR %P 739--747 %U https://proceedings.mlr.press/v238/jankowiak24a.html %V 238 %X Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method–Reparameterized Variational Rejection Sampling (RVRS)–offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well suited for black-box inference, especially for models with local latent variables.
APA
Jankowiak, M. & Phan, D.. (2024). Reparameterized Variational Rejection Sampling. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:739-747 Available from https://proceedings.mlr.press/v238/jankowiak24a.html.

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