  Heteroscedastic regression is the task of supervised learning where each
label is subject to noise from a different distribution. This noise can be
caused by the labelling process, and impacts negatively the performance of the
learning algorithm as it violates the i.i.d. assumptions. In many situations
however, the labelling process is able to estimate the variance of such
distribution for each label, which can be used as an additional information to
mitigate this impact. We adapt an inverse-variance weighted mean square error,
based on the Gauss-Markov theorem, for parameter optimization on neural
networks. We introduce Batch Inverse-Variance, a loss function which is robust
to near-ground truth samples, and allows to control the effective learning
rate. Our experimental results show that BIV improves significantly the
performance of the networks on two noisy datasets, compared to L2 loss,
inverse-variance weighting, as well as a filtering-based baseline.
