Semi-Generative Modelling: Covariate-Shift Adaptation with Cause and Effect Features

Current methods for covariate-shift adaptation use unlabelled data to compute importance weights or domain-invariant features, while the final model is trained on labelled data only. Here, we consider a particular case of covariate shift which allows us also to learn from unlabelled data, that is, combining adaptation with semi-supervised learning. Using ideas from causality, we argue that this requires learning with both causes, XC, and effects, XE, of a target variable, Y, and show how this setting leads to what we call a semi-generative model, P(Y,XE|XC,θ). Our approach is robust to domain shifts in the distribution of causal features and leverages unlabelled data by learning a direct map from causes to effects. Experiments on synthetic data demonstrate significant improvements in classification over purely-supervised and importance-weighting baselines.