  Learning invariant representations is a critical first step in a number of
machine learning tasks. A common approach corresponds to the so-called
information bottleneck principle in which an application dependent function of
mutual information is carefully chosen and optimized. Unfortunately, in
practice, these functions are not suitable for optimization purposes since
these losses are agnostic of the metric structure of the parameters of the
model. We introduce a class of losses for learning representations that are
invariant to some extraneous variable of interest by inverting the class of
contrastive losses, i.e., inverse contrastive loss (ICL). We show that if the
extraneous variable is binary, then optimizing ICL is equivalent to optimizing
a regularized MMD divergence. More generally, we also show that if we are
provided a metric on the sample space, our formulation of ICL can be decomposed
into a sum of convex functions of the given distance metric. Our experimental
results indicate that models obtained by optimizing ICL achieve significantly
better invariance to the extraneous variable for a fixed desired level of
accuracy. In a variety of experimental settings, we show applicability of ICL
for learning invariant representations for both continuous and discrete
extraneous variables.
