Learning minimal volume uncertainty ellipsoids
This work addresses uncertainty quantification in parameter estimation, offering a more efficient method for applications like localization, though it is incremental as it builds on existing ellipsoid-based approaches.
The paper tackles the problem of learning minimal volume uncertainty ellipsoids for parameter estimation by proposing a differentiable optimization approach using a neural network, which results in smaller ellipsoids with less storage and computational requirements compared to existing methods, as demonstrated on four real-world localization datasets.
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.