  Unlike machines, humans learn through rapid, abstract model-building. The
role of a teacher is not simply to hammer home right or wrong answers, but
rather to provide intuitive comments, comparisons, and explanations to a pupil.
This is what the Learning Under Privileged Information (LUPI) paradigm
endeavors to model by utilizing extra knowledge only available during training.
We propose a new LUPI algorithm specifically designed for Convolutional Neural
Networks (CNNs) and Recurrent Neural Networks (RNNs). We propose to use a
heteroscedastic dropout (i.e. dropout with a varying variance) and make the
variance of the dropout a function of privileged information. Intuitively, this
corresponds to using the privileged information to control the uncertainty of
the model output. We perform experiments using CNNs and RNNs for the tasks of
image classification and machine translation. Our method significantly
increases the sample efficiency during learning, resulting in higher accuracy
with a large margin when the number of training examples is limited. We also
theoretically justify the gains in sample efficiency by providing a
generalization error bound decreasing with $O(\frac{1}{n})$, where $n$ is the
number of training examples, in an oracle case.
