# On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models

arXiv: https://arxiv.org/abs/2205.04641 · HTML: https://mlsanity.com/paper/2205.04641/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 15 of 15)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Causal Interpretability for Machine Learning -- Problems, Methods and Evaluation](https://mlsanity.com/paper/2003.03934/) (2020)
- [Marginal Singularity, and the Benefits of Labels in Covariate-Shift](https://mlsanity.com/paper/1803.01833/) (2018)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Stable Prediction across Unknown Environments](https://mlsanity.com/paper/1806.06270/) (2018)
- [Joint Geometrical and Statistical Alignment for Visual Domain Adaptation](https://mlsanity.com/paper/1705.05498/) (2017)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [An improper estimator with optimal excess risk in misspecified density estimation and logistic regression](https://mlsanity.com/paper/1912.10784/) (2019)
- [Generalization in anti-causal learning](https://mlsanity.com/paper/1812.00524/) (2018)
- [Minimax optimal approaches to the label shift problem in non-parametric settings](https://mlsanity.com/paper/2003.10443/) (2020)
- [Entropic Causal Inference: Identifiability and Finite Sample Results](https://mlsanity.com/paper/2101.03501/) (2021)
- [Semi-Supervised Learning: the Case When Unlabeled Data is Equally Useful](https://mlsanity.com/paper/2005.11018/) (2020)

## Built on by (most cited first, 4 of 4)

- [Unified Source-Free Domain Adaptation](https://mlsanity.com/paper/2403.07601/) (2024)
- [On the Role of Priors in Bayesian Causal Learning](https://mlsanity.com/paper/2504.01424/) (2025)
- [Semi-Supervised Learning under General Causal Models](https://mlsanity.com/paper/2510.22567/) (2025)
- [An Expectation-Maximization Algorithm for Domain Adaptation in Gaussian Causal Models](https://mlsanity.com/paper/2601.03459/) (2026)

## Abstract (arXiv)

Recent advancements in unsupervised domain adaptation (UDA) and semi-supervised learning (SSL), particularly incorporating causality, have led to significant methodological improvements in these learning problems. However, a formal theory that explains the role of causality in the generalization performance of UDA/SSL is still lacking. In this paper, we consider the UDA/SSL scenarios where we access m labelled source data and n unlabelled target data as training instances under different causal settings with a parametric probabilistic model. We study the learning performance (e.g., excess risk) of prediction in the target domain from an information-theoretic perspective. Specifically, we distinguish two scenarios: the learning problem is called causal learning if the feature is the cause and the label is the effect, and is called anti-causal learning otherwise. We show that in causal learning, the excess risk depends on the size of the source sample at a rate of O(frac1m) only if the labelling distribution between the source and target domains remains unchanged. In anti-causal learning, we show that the unlabelled data dominate the performance at a rate of typically O(frac1n). These results bring out the relationship between the data sample size and the hardness of the learning problem with different causal mechanisms.