SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates
Lingkai Kong, Jimeng Sun, Chao Zhang
Abstract
Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large number of parameters. Non-Bayesian methods are simple to implement but often conflate different sources of uncertainties and require huge computing resources. We propose a new method for quantifying uncertainties of DNNs from a dynamical system perspective. The core of our method is to view DNN transformations as state evolution of a stochastic dynamical system and introduce a Brownian motion term for capturing epistemic uncertainty. Based on this perspective, we propose a neural stochastic differential equation model (SDE-Net) which consists of (1) a drift net that controls the system to fit the predictive function; and (2) a diffusion net that captures epistemic uncertainty. We theoretically analyze the existence and uniqueness of the solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.
BibTeX
@InProceedings{pmlr-v119-kong20b,
title = {{SDE}-Net: Equipping Deep Neural Networks with Uncertainty Estimates},
author = {Kong, Lingkai and Sun, Jimeng and Zhang, Chao},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {5405--5415},
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/kong20b/kong20b.pdf},
url = {https://proceedings.mlr.press/v119/kong20b.html},
abstract = {Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large number of parameters. Non-Bayesian methods are simple to implement but often conflate different sources of uncertainties and require huge computing resources. We propose a new method for quantifying uncertainties of DNNs from a dynamical system perspective. The core of our method is to view DNN transformations as state evolution of a stochastic dynamical system and introduce a Brownian motion term for capturing epistemic uncertainty. Based on this perspective, we propose a neural stochastic differential equation model (SDE-Net) which consists of (1) a drift net that controls the system to fit the predictive function; and (2) a diffusion net that captures epistemic uncertainty. We theoretically analyze the existence and uniqueness of the solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.}
}