Research Area:  Machine Learning

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.

Keywords:  
Artificial Intelligence
Machine Learning
SDE-Net
Deep Neural Nets
Bayesian methods

Author(s) Name:  Lingkai Kong, Jimeng Sun, Chao Zhang

Publisher name:  arXiv.2008.10546

DOI:  10.48550/arXiv.2008.10546

Volume Information:  

Paper Link:   https://arxiv.org/abs/2008.10546