Learning minimal volume uncertainty ellipsoids

TL;DR

This paper introduces a neural network-based method for learning minimal volume uncertainty ellipsoids for parameter estimation, offering computational efficiency and accuracy improvements over existing techniques.

Contribution

It proposes a differentiable optimization approach using neural networks to compute uncertainty ellipsoids with less storage and computation, applicable to real-world localization data.

Findings

Neural network approach produces smaller, accurate ellipsoids.

Method requires less storage and computation during inference.

Validated on four real-world localization datasets.

Abstract

We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of jointly Gaussian data, we prove that the optimal ellipsoid is centered around the conditional mean and shaped as the conditional covariance matrix. In more practical cases, we propose a differentiable optimization approach for approximately computing the optimal ellipsoids using a neural network with proper calibration. Compared to existing methods, our network requires less storage and less computations in inference time, leading to accurate yet smaller ellipsoids. We demonstrate these advantages on four real-world localization datasets.