# ReTaSA: A Nonparametric Functional Estimation Approach for Addressing Continuous Target Shift

arXiv: https://arxiv.org/abs/2401.16410 · HTML: https://mlsanity.com/paper/2401.16410/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 8 of 8)

- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Fisher consistency for prior probability shift](https://mlsanity.com/paper/1701.05512/) (2017)
- [ELSA: Efficient Label Shift Adaptation through the Lens of Semiparametric Models](https://mlsanity.com/paper/2305.19123/) (2023)

## Built on by (most cited first, 2 of 2)

- [Positive and Unlabeled Data: Model, Estimation, Inference, and Classification](https://mlsanity.com/paper/2407.09735/) (2024)
- [Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression](https://mlsanity.com/paper/2609.15785/) (2026)

## Abstract (arXiv)

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.