Differentiable Annealed Importance Sampling Minimizes The Jensen-Shannon Divergence Between Initial and Target Distribution

Johannes Zenn, Robert Bamler
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:58448-58469, 2024.

Abstract

Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing, among others, over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized KL divergence (Jensen-Shannon divergence) between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) in that its initial distribution is a parametric fit to an intractable target distribution. We empirically evaluate the usefulness of the initial distribution as a variational distribution on synthetic and real-world data, observing that it often provides more accurate uncertainty estimates than standard VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zenn24a, title = {Differentiable Annealed Importance Sampling Minimizes The Jensen-Shannon Divergence Between Initial and Target Distribution}, author = {Zenn, Johannes and Bamler, Robert}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {58448--58469}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zenn24a/zenn24a.pdf}, url = {https://proceedings.mlr.press/v235/zenn24a.html}, abstract = {Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing, among others, over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized KL divergence (Jensen-Shannon divergence) between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) in that its initial distribution is a parametric fit to an intractable target distribution. We empirically evaluate the usefulness of the initial distribution as a variational distribution on synthetic and real-world data, observing that it often provides more accurate uncertainty estimates than standard VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).} }
Endnote
%0 Conference Paper %T Differentiable Annealed Importance Sampling Minimizes The Jensen-Shannon Divergence Between Initial and Target Distribution %A Johannes Zenn %A Robert Bamler %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zenn24a %I PMLR %P 58448--58469 %U https://proceedings.mlr.press/v235/zenn24a.html %V 235 %X Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing, among others, over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized KL divergence (Jensen-Shannon divergence) between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) in that its initial distribution is a parametric fit to an intractable target distribution. We empirically evaluate the usefulness of the initial distribution as a variational distribution on synthetic and real-world data, observing that it often provides more accurate uncertainty estimates than standard VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).
APA
Zenn, J. & Bamler, R.. (2024). Differentiable Annealed Importance Sampling Minimizes The Jensen-Shannon Divergence Between Initial and Target Distribution. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:58448-58469 Available from https://proceedings.mlr.press/v235/zenn24a.html.

Related Material