Liouville Flow Importance Sampler

Yifeng Tian, Nishant Panda, Yen Ting Lin
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:48186-48210, 2024.

Abstract

We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tian24c, title = {Liouville Flow Importance Sampler}, author = {Tian, Yifeng and Panda, Nishant and Lin, Yen Ting}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {48186--48210}, 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/tian24c/tian24c.pdf}, url = {https://proceedings.mlr.press/v235/tian24c.html}, abstract = {We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.} }
Endnote
%0 Conference Paper %T Liouville Flow Importance Sampler %A Yifeng Tian %A Nishant Panda %A Yen Ting Lin %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-tian24c %I PMLR %P 48186--48210 %U https://proceedings.mlr.press/v235/tian24c.html %V 235 %X We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.
APA
Tian, Y., Panda, N. & Lin, Y.T.. (2024). Liouville Flow Importance Sampler. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:48186-48210 Available from https://proceedings.mlr.press/v235/tian24c.html.

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