# From Biased Selective Labels to Pseudo-Labels: An Expectation-Maximization Framework for Learning from Biased Decisions

arXiv: https://arxiv.org/abs/2406.18865 · HTML: https://mlsanity.com/paper/2406.18865/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 100 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 30 of 39)

- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [Learning with Feature-Dependent Label Noise: A Progressive Approach](https://mlsanity.com/paper/2103.07756/) (2021)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Beyond Class-Conditional Assumption: A Primary Attempt to Combat Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.05458/) (2020)
- [Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels](https://mlsanity.com/paper/2105.04522/) (2021)
- [Fair Classification with Group-Dependent Label Noise](https://mlsanity.com/paper/2011.00379/) (2020)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Instance-dependent Label-noise Learning under a Structural Causal Model](https://mlsanity.com/paper/2109.02986/) (2021)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Like trainer, like bot? Inheritance of bias in algorithmic content moderation](https://mlsanity.com/paper/1707.01477/) (2017)
- [Ground(less) Truth: A Causal Framework for Proxy Labels in Human-Algorithm Decision-Making](https://mlsanity.com/paper/2302.06503/) (2023)
- [A Human-Centered Review of the Algorithms used within the U.S. Child Welfare System](https://mlsanity.com/paper/2003.03541/) (2020)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Instance-Dependent Noisy Label Learning via Graphical Modelling](https://mlsanity.com/paper/2209.00906/) (2022)
- [Centrality and Consistency: Two-Stage Clean Samples Identification for Learning with Instance-Dependent Noisy Labels](https://mlsanity.com/paper/2207.14476/) (2022)
- [What You See Is What You Get? The Impact of Representation Criteria on Human Bias in Hiring](https://mlsanity.com/paper/1909.03567/) (2019)
- [Does Fair Ranking Improve Minority Outcomes? Understanding the Interplay of Human and Algorithmic Biases in Online Hiring](https://mlsanity.com/paper/2012.00423/) (2020)
- [On Non-Random Missing Labels in Semi-Supervised Learning](https://mlsanity.com/paper/2206.14923/) (2022)
- [Counterfactual Prediction Under Outcome Measurement Error](https://mlsanity.com/paper/2302.11121/) (2023)
- [Fast Threshold Tests for Detecting Discrimination](https://mlsanity.com/paper/1702.08536/) (2017)

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

- [Causal Label Recovery in Payment Networks](https://mlsanity.com/paper/2605.29272/) (2026)
- [Beyond the Training Distribution: Evaluating Predictions Under Distribution Shift and Selection Bias](https://mlsanity.com/paper/2606.14506/) (2026)
- [A Bayesian Model for Multi-stage Censoring](https://mlsanity.com/paper/2511.11684/) (2025)
- [Long-term Fairness with Selective Labels](https://mlsanity.com/paper/2605.22291/) (2026)

## Abstract (arXiv)

Selective labels occur when label observations are subject to a decision-making process; e.g., diagnoses that depend on the administration of laboratory tests. We study a clinically-inspired selective label problem called disparate censorship, where labeling biases vary across subgroups and unlabeled individuals are imputed as "negative" (i.e., no diagnostic test = no illness). Machine learning models naively trained on such labels could amplify labeling bias. Inspired by causal models of selective labels, we propose Disparate Censorship Expectation-Maximization (DCEM), an algorithm for learning in the presence of disparate censorship. We theoretically analyze how DCEM mitigates the effects of disparate censorship on model performance. We validate DCEM on synthetic data, showing that it improves bias mitigation (area between ROC curves) without sacrificing discriminative performance (AUC) compared to baselines. We achieve similar results in a sepsis classification task using clinical data.