# Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching

arXiv: https://arxiv.org/abs/2306.04376 · HTML: https://mlsanity.com/paper/2306.04376/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [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)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [NYTRO: When Subsampling Meets Early Stopping](https://mlsanity.com/paper/1510.05684/) (2015)
- [On the potential benefits of entropic regularization for smoothing Wasserstein estimators](https://mlsanity.com/paper/2210.06934/) (2022)

## Built on by (most cited first, 5 of 5)

- [Kernel Density Estimation for Multiclass Quantification](https://mlsanity.com/paper/2401.00490/) (2023)
- [On the Interconnections of Calibration, Quantification, and Classifier Accuracy Prediction under Dataset Shift](https://mlsanity.com/paper/2505.11380/) (2025)
- [Prior shift estimation for positive unlabeled data through the lens of kernel embedding](https://mlsanity.com/paper/2502.21194/) (2025)
- [Robust Label Shift Quantification](https://mlsanity.com/paper/2502.03174/) (2025)
- [Geometry-Aware Bayesian Quantification via Compositional Data Analysis](https://mlsanity.com/paper/2607.04977/) (2026)

## Abstract (arXiv)

Quantification learning deals with the task of estimating the target label distribution under label shift. In this paper, we first present a unifying framework, distribution feature matching (DFM), that recovers as particular instances various estimators introduced in previous literature. We derive a general performance bound for DFM procedures, improving in several key aspects upon previous bounds derived in particular cases. We then extend this analysis to study robustness of DFM procedures in the misspecified setting under departure from the exact label shift hypothesis, in particular in the case of contamination of the target by an unknown distribution. These theoretical findings are confirmed by a detailed numerical study on simulated and real-world datasets. We also introduce an efficient, scalable and robust version of kernel-based DFM using the Random Fourier Feature principle.