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
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.
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 = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/grathwohl20a/grathwohl20a.pdf},
url = {https://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.}
}