Multivariate Uncertainty in Deep Learning

Area of Science:

• Robotics and Autonomous Systems
• Machine Learning
• State Estimation

Background:

• State estimation in autonomous systems relies on Kalman filters, often assuming fixed measurement uncertainties.
• Deep learning models introduce variable, unpredictable uncertainties, posing risks to traditional methods.
• Accurate multivariate uncertainty quantification is vital for safe and reliable deep learning integration.

Purpose of the Study:

• To develop a method for modeling multivariate uncertainty in neural networks for regression problems.
• To incorporate both aleatoric and epistemic sources of heteroscedastic uncertainty.
• To evaluate the impact of accurate uncertainty quantification on state estimation performance.

Main Methods:

• Developed a deep uncertainty covariance matrix model for neural networks.
• Trained the model directly using a multivariate Gaussian density loss function.
• Employed end-to-end training through a Kalman filter for indirect model optimization.

Main Results:

• Demonstrated significant performance improvements in a visual tracking task using accurate multivariate uncertainty.
• Showcased the benefits for both in-domain and out-of-domain evaluation data.
• Illustrated how end-to-end filter training enables uncertainty predictions to mitigate Kalman filter weaknesses in visual odometry.

Conclusions:

• Accurate multivariate uncertainty modeling is essential for robust deep learning in state estimation.
• The proposed methods enhance the safety and reliability of autonomous vehicle and robotics applications.
• End-to-end training offers a powerful approach to leverage uncertainty predictions for improved filter performance.