Semi-Supervised Learning for Deep Causal Generative Models

Developing models that can answer questions of the form "How would $x$ change if $y$ had been $z$?" is fundamental for advancing medical image analysis. Training causal generative models that address such counterfactual questions, though, currently requires that all relevant variables have been observed and that corresponding labels are available in training data. However, clinical data may not have complete records for all patients and state of the art causal generative models are unable to take full advantage of this. We thus develop, for the first time, a semi-supervised deep causal generative model that exploits the causal relationships between variables to maximise the use of all available data. We explore this in the setting where each sample is either fully labelled or fully unlabelled, as well as the more clinically realistic case of having different labels missing for each sample. We leverage techniques from causal inference to infer missing values and subsequently generate realistic counterfactuals, even for samples with incomplete labels.