  Causal modeling has been recognized as a potential solution to many
challenging problems in machine learning (ML). Here, we describe how a recently
proposed counterfactual approach developed to deconfound linear structural
causal models can still be used to deconfound the feature representations
learned by deep neural network (DNN) models. The key insight is that by
training an accurate DNN using softmax activation at the classification layer,
and then adopting the representation learned by the last layer prior to the
output layer as our features, we have that, by construction, the learned
features will fit well a (multi-class) logistic regression model, and will be
linearly associated with the labels. As a consequence, deconfounding approaches
based on simple linear models can be used to deconfound the feature
representations learned by DNNs. We validate the proposed methodology using
colored versions of the MNIST dataset. Our results illustrate how the approach
can effectively combat confounding and improve model stability in the context
of dataset shifts generated by selection biases.
