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.

Extraneous variables are variables that are irrelevant for a certain task, but heavily affect the distribution of the available data. In this work, we show that the presence of such variables can degrade the performance of deep-learning models. We study three datasets where there is a strong influence of known extraneous variables: classification of upper-body movements in stroke patients, annotation of surgical activities, and recognition of corrupted images. Models trained with batch normalization learn features that are highly dependent on the extraneous variables. In batch normalization, the statistics used to normalize the features are learned from the training set and fixed at test time, which produces a mismatch in the presence of varying extraneous variables. We demonstrate that estimating the feature statistics adaptively during inference, as in instance normalization, addresses this issue, producing normalized features that are more robust to changes in the extraneous variables. This results in a significant gain in performance for different network architectures and choices of feature statistics.

Electronic Medical Records (EMR) are a rich source of patient information, including measurements reflecting physiologic signs and administered therapies. Identifying which variables are useful in predicting clinical outcomes can be challenging. Advanced algorithms such as deep neural networks were designed to process high-dimensional inputs containing variables in their measured form, thus bypass separate feature selection or engineering steps. We investigated the effect of extraneous input variables on the predictive performance of Recurrent Neural Networks (RNN) by including in the input vector extraneous variables randomly drawn from theoretical and empirical distributions. RNN models using different input vectors (EMR variables; EMR and extraneous variables; extraneous variables only) were trained to predict three clinical outcomes: in-ICU mortality, 72-hour ICU re-admission, and 30-day ICU-free days. The measured degradations of the RNN's predictive performance with the addition of extraneous variables to EMR variables were negligible.