Multivariate Uncertainty in Deep Learning

TL;DR

This paper presents methods to model and quantify multivariate uncertainty in deep learning for navigation and tracking, improving the safety and reliability of autonomous systems by incorporating both aleatoric and epistemic uncertainties.

Contribution

It introduces a novel approach to model multivariate uncertainty in neural networks, trained via Gaussian loss and end-to-end Kalman filter integration, enhancing state estimation accuracy.

Findings

Improved Kalman filter performance with accurate uncertainty modeling.

End-to-end training helps neural networks compensate for filter weaknesses.

Significant impact on visual tracking and odometry tasks.

Abstract

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes filters are typically assumed to be a fixed covariance matrix. This assumption is risky, particularly for "black box" deep learning models, in which uncertainty can vary dramatically and unexpectedly. Accurate quantification of multivariate uncertainty will allow for the full potential of deep learning to be used more safely and reliably in these applications. We show how to model multivariate uncertainty for regression problems with neural networks, incorporating both aleatoric and epistemic sources of heteroscedastic uncertainty. We train a deep uncertainty covariance matrix model in two ways: directly using a multivariate Gaussian density loss function, and indirectly using end-to-end training through a Kalman filter. We experimentally show in a visual tracking problem the large impact that accurate multivariate uncertainty quantification can have on Kalman filter performance for both in-domain and out-of-domain evaluation data. We additionally show in a challenging visual odometry problem how end-to-end filter training can allow uncertainty predictions to compensate for filter weaknesses.