# Invariant Models for Causal Transfer Learning

arXiv: https://arxiv.org/abs/1507.05333 · HTML: https://mlsanity.com/paper/1507.05333/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2015.

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

- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Invariant Policy Learning: A Causal Perspective](https://mlsanity.com/paper/2106.00808/) (2021)
- [Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past](https://mlsanity.com/paper/2203.06056/) (2022)
- [Invariant Subspace Decomposition](https://mlsanity.com/paper/2404.09962/) (2024)

## Abstract (arXiv)

Methods of transfer learning try to combine knowledge from several related tasks (or domains) to improve performance on a test task. Inspired by causal methodology, we relax the usual covariate shift assumption and assume that it holds true for a subset of predictor variables: the conditional distribution of the target variable given this subset of predictors is invariant over all tasks. We show how this assumption can be motivated from ideas in the field of causality. We focus on the problem of Domain Generalization, in which no examples from the test task are observed. We prove that in an adversarial setting using this subset for prediction is optimal in Domain Generalization; we further provide examples, in which the tasks are sufficiently diverse and the estimator therefore outperforms pooling the data, even on average. If examples from the test task are available, we also provide a method to transfer knowledge from the training tasks and exploit all available features for prediction. However, we provide no guarantees for this method. We introduce a practical method which allows for automatic inference of the above subset and provide corresponding code. We present results on synthetic data sets and a gene deletion data set.