  We benchmark the robustness of maximum likelihood based uncertainty
estimation methods to outliers in training data for regression tasks. Outliers
or noisy labels in training data results in degraded performances as well as
incorrect estimation of uncertainty. We propose the use of a heavy-tailed
distribution (Laplace distribution) to improve the robustness to outliers. This
property is evaluated using standard regression benchmarks and on a
high-dimensional regression task of monocular depth estimation, both containing
outliers. In particular, heavy-tailed distribution based maximum likelihood
provides better uncertainty estimates, better separation in uncertainty for
out-of-distribution data, as well as better detection of adversarial attacks in
the presence of outliers.
