Learning minimal volume uncertainty ellipsoids

arXiv:2405.02441v1 Announce Type: new
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 …

abstract arxiv coverage cs.lg data mean probability prove stat.ml type uncertainty