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Causal modeling has been recognized as a potential solution to manychallenging problems in machine learning (ML). Here, we describe how a recentlyproposed counterfactual approach developed to deconfound linear structuralcausal models can still be used to deconfound the feature representationslearned by deep neural network (DNN) models. The key insight is that bytraining an accurate DNN using softmax activation at the classification layer,and then adopting the representation learned by the last layer prior to theoutput layer as our features, we have that, by construction, the learnedfeatures will fit well a (multi-class) logistic regression model, and will belinearly associated with the labels. As a consequence, deconfounding approachesbased on simple linear models can be used to deconfound the featurerepresentations learned by DNNs. We validate the proposed methodology usingcolored versions of the MNIST dataset. Our results illustrate how the approachcan effectively combat confounding and improve model stability in the contextof dataset shifts generated by selection biases.

Causality-aware counterfactual confounding adjustment for feature representations learned by deep models