# Convergence Behavior of an Adversarial Weak Supervision Method

arXiv: https://arxiv.org/abs/2405.16013 · HTML: https://mlsanity.com/paper/2405.16013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 63 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 21 of 21)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [Fine-Tuning Pre-trained Language Model with Weak Supervision: A Contrastive-Regularized Self-Training Approach](https://mlsanity.com/paper/2010.07835/) (2020)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Learning from Rules Generalizing Labeled Exemplars](https://mlsanity.com/paper/2004.06025/) (2020)
- [Denoising Multi-Source Weak Supervision for Neural Text Classification](https://mlsanity.com/paper/2010.04582/) (2020)
- [End-to-End Weak Supervision](https://mlsanity.com/paper/2107.02233/) (2021)
- [Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing](https://mlsanity.com/paper/1411.4086/) (2014)
- [Learning Hyper Label Model for Programmatic Weak Supervision](https://mlsanity.com/paper/2207.13545/) (2022)
- [Rekall: Specifying Video Events using Compositions of Spatiotemporal Labels](https://mlsanity.com/paper/1910.02993/) (2019)
- [Generalized Maximum Entropy for Supervised Classification](https://mlsanity.com/paper/2007.05447/) (2020)
- [Optimally Combining Classifiers Using Unlabeled Data](https://mlsanity.com/paper/1503.01811/) (2015)
- [Minimax Optimal Convergence Rates for Estimating Ground Truth from Crowdsourced Labels](https://mlsanity.com/paper/1310.5764/) (2013)
- [Optimal Binary Classifier Aggregation for General Losses](https://mlsanity.com/paper/1510.00452/) (2015)
- [Dependency Structure Misspecification in Multi-Source Weak Supervision Models](https://mlsanity.com/paper/2106.10302/) (2021)

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

- [Reliable Programmatic Weak Supervision with Confidence Intervals for Label Probabilities](https://mlsanity.com/paper/2508.03896/) (2025)

## Abstract (arXiv)

Labeling data via rules-of-thumb and minimal label supervision is central to Weak Supervision, a paradigm subsuming subareas of machine learning such as crowdsourced learning and semi-supervised ensemble learning. By using this labeled data to train modern machine learning methods, the cost of acquiring large amounts of hand labeled data can be ameliorated. Approaches to combining the rules-of-thumb falls into two camps, reflecting different ideologies of statistical estimation. The most common approach, exemplified by the Dawid-Skene model, is based on probabilistic modeling. The other, developed in the work of Balsubramani-Freund and others, is adversarial and game-theoretic. We provide a variety of statistical results for the adversarial approach under log-loss: we characterize the form of the solution, relate it to logistic regression, demonstrate consistency, and give rates of convergence. On the other hand, we find that probabilistic approaches for the same model class can fail to be consistent. Experimental results are provided to corroborate the theoretical results.