# Stratified Learning: A General-Purpose Statistical Method for Improved Learning under Covariate Shift

arXiv: https://arxiv.org/abs/2106.11211 · HTML: https://mlsanity.com/paper/2106.11211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 125 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [FCNs in the Wild: Pixel-level Adversarial and Constraint-based Adaptation](https://mlsanity.com/paper/1612.02649/) (2016)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Unsupervised domain adaptation in brain lesion segmentation with adversarial networks](https://mlsanity.com/paper/1612.08894/) (2016)
- [Virtual-to-real Deep Reinforcement Learning: Continuous Control of Mobile Robots for Mapless Navigation](https://mlsanity.com/paper/1703.00420/) (2017)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift](https://mlsanity.com/paper/2006.14988/) (2020)
- [High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation](https://mlsanity.com/paper/1404.7063/) (2014)
- [Nearest Neighbor-based Importance Weighting](https://mlsanity.com/paper/2102.02291/) (2021)
- [Feature-Level Domain Adaptation](https://mlsanity.com/paper/1512.04829/) (2015)
- [A CNN adapted to time series for the classification of Supernovae](https://mlsanity.com/paper/1901.00461/) (2019)

## Built on by (most cited first, 1 of 1)

- [PICZL: Image-based Photometric Redshifts for AGN](https://mlsanity.com/paper/2411.07305/) (2024)

## Abstract (arXiv)

We propose a simple, statistically principled, and theoretically justified method to improve supervised learning when the training set is not representative, a situation known as covariate shift. We build upon a well-established methodology in causal inference, and show that the effects of covariate shift can be reduced or eliminated by conditioning on propensity scores. In practice, this is achieved by fitting learners within strata constructed by partitioning the data based on the estimated propensity scores, leading to approximately balanced covariates and much-improved target prediction. We demonstrate the effectiveness of our general-purpose method on two contemporary research questions in cosmology, outperforming state-of-the-art importance weighting methods. We obtain the best reported AUC (0.958) on the updated "Supernovae photometric classification challenge", and we improve upon existing conditional density estimation of galaxy redshift from Sloan Data Sky Survey (SDSS) data.