Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling

Will Grathwohl, Kuan-Chieh Wang, Joern-Henrik Jacobsen, David Duvenaud, Richard Zemel
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:3732-3747, 2020.

Abstract

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-grathwohl20a, title = {Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling}, author = {Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Joern-Henrik and Duvenaud, David and Zemel, Richard}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {3732--3747}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/grathwohl20a/grathwohl20a.pdf}, url = { http://proceedings.mlr.press/v119/grathwohl20a.html }, abstract = {We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.} }
Endnote
%0 Conference Paper %T Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling %A Will Grathwohl %A Kuan-Chieh Wang %A Joern-Henrik Jacobsen %A David Duvenaud %A Richard Zemel %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-grathwohl20a %I PMLR %P 3732--3747 %U http://proceedings.mlr.press/v119/grathwohl20a.html %V 119 %X We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.
APA
Grathwohl, W., Wang, K., Jacobsen, J., Duvenaud, D. & Zemel, R.. (2020). Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:3732-3747 Available from http://proceedings.mlr.press/v119/grathwohl20a.html .

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