Score Operator Newton transport

Nisha Chandramoorthy, Florian T Schaefer, Youssef M Marzouk
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3349-3357, 2024.

Abstract

We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton method, involving an elliptic PDE, for finding a zero of a “score-residual” operator. We prove sufficient conditions for convergence to a valid transport map. Our Newton iterates can be computed by exploiting fast solvers for elliptic PDEs, resulting in new algorithms for Bayesian inference and other sampling tasks. We identify elementary settings where score-operator Newton transport achieves fast convergence while avoiding mode collapse.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-chandramoorthy24a, title = {Score Operator {N}ewton transport}, author = {Chandramoorthy, Nisha and T Schaefer, Florian and M Marzouk, Youssef}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3349--3357}, 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/chandramoorthy24a/chandramoorthy24a.pdf}, url = {https://proceedings.mlr.press/v238/chandramoorthy24a.html}, abstract = {We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton method, involving an elliptic PDE, for finding a zero of a “score-residual” operator. We prove sufficient conditions for convergence to a valid transport map. Our Newton iterates can be computed by exploiting fast solvers for elliptic PDEs, resulting in new algorithms for Bayesian inference and other sampling tasks. We identify elementary settings where score-operator Newton transport achieves fast convergence while avoiding mode collapse.} }
Endnote
%0 Conference Paper %T Score Operator Newton transport %A Nisha Chandramoorthy %A Florian T Schaefer %A Youssef M Marzouk %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-chandramoorthy24a %I PMLR %P 3349--3357 %U https://proceedings.mlr.press/v238/chandramoorthy24a.html %V 238 %X We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton method, involving an elliptic PDE, for finding a zero of a “score-residual” operator. We prove sufficient conditions for convergence to a valid transport map. Our Newton iterates can be computed by exploiting fast solvers for elliptic PDEs, resulting in new algorithms for Bayesian inference and other sampling tasks. We identify elementary settings where score-operator Newton transport achieves fast convergence while avoiding mode collapse.
APA
Chandramoorthy, N., T Schaefer, F. & M Marzouk, Y.. (2024). Score Operator Newton transport. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3349-3357 Available from https://proceedings.mlr.press/v238/chandramoorthy24a.html.

Related Material