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

arXiv: https://arxiv.org/abs/1807.07879 · HTML: https://mlsanity.com/paper/1807.07879/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2018.

## Built on by (most cited first, 8 of 8)

- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Visual Representation Learning Does Not Generalize Strongly Within the Same Domain](https://mlsanity.com/paper/2107.08221/) (2021)
- [Causal Direction of Data Collection Matters: Implications of Causal and Anticausal Learning for NLP](https://mlsanity.com/paper/2110.03618/) (2021)
- [Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features](https://mlsanity.com/paper/2307.09933/) (2023)
- [An Information-theoretical Approach to Semi-supervised Learning under Covariate-shift](https://mlsanity.com/paper/2202.12123/) (2022)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Scalable Causal Domain Adaptation](https://mlsanity.com/paper/2103.00139/) (2021)
- [On the Role of Priors in Bayesian Causal Learning](https://mlsanity.com/paper/2504.01424/) (2025)

## Abstract (arXiv)

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.