  In this paper, we address the problem of how to robustly train a ConvNet for
regression, or deep robust regression. Traditionally, deep regression employs
the L2 loss function, known to be sensitive to outliers, i.e. samples that
either lie at an abnormal distance away from the majority of the training
samples, or that correspond to wrongly annotated targets. This means that,
during back-propagation, outliers may bias the training process due to the high
magnitude of their gradient. In this paper, we propose DeepGUM: a deep
regression model that is robust to outliers thanks to the use of a
Gaussian-uniform mixture model. We derive an optimization algorithm that
alternates between the unsupervised detection of outliers using
expectation-maximization, and the supervised training with cleaned samples
using stochastic gradient descent. DeepGUM is able to adapt to a continuously
evolving outlier distribution, avoiding to manually impose any threshold on the
proportion of outliers in the training set. Extensive experimental evaluations
on four different tasks (facial and fashion landmark detection, age and head
pose estimation) lead us to conclude that our novel robust technique provides
reliability in the presence of various types of noise and protection against a
high percentage of outliers.
