# Lifting Weak Supervision To Structured Prediction

arXiv: https://arxiv.org/abs/2211.13375 · HTML: https://mlsanity.com/paper/2211.13375/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 24 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Snorkel: Rapid Training Data Creation with Weak Supervision](https://mlsanity.com/paper/1711.10160/) (2017)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Training Complex Models with Multi-Task Weak Supervision](https://mlsanity.com/paper/1810.02840/) (2018)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [A Consistent Regularization Approach for Structured Prediction](https://mlsanity.com/paper/1605.07588/) (2016)
- [Cross-Modal Data Programming Enables Rapid Medical Machine Learning](https://mlsanity.com/paper/1903.11101/) (2019)
- [Universalizing Weak Supervision](https://mlsanity.com/paper/2112.03865/) (2021)
- [Concentration in unbounded metric spaces and algorithmic stability](https://mlsanity.com/paper/1309.1007/) (2013)
- [Overton: A Data System for Monitoring and Improving Machine-Learned Products](https://mlsanity.com/paper/1909.05372/) (2019)
- [A Structured Prediction Approach for Label Ranking](https://mlsanity.com/paper/1807.02374/) (2018)
- [Graph Structured Prediction Energy Networks](https://mlsanity.com/paper/1910.14670/) (2019)
- [Manifold Structured Prediction](https://mlsanity.com/paper/1806.09908/) (2018)

## Built on by (most cited first, 10 of 10)

- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [A transfer learning framework for weak-to-strong generalization](https://mlsanity.com/paper/2405.16236/) (2024)
- [Time To Impeach LLM-as-a-Judge: Programs are the Future of Evaluation](https://mlsanity.com/paper/2506.10403/) (2025)
- [Geometry-Aware Adaptation for Pretrained Models](https://mlsanity.com/paper/2307.12226/) (2023)
- [Mitigating Source Bias for Fairer Weak Supervision](https://mlsanity.com/paper/2303.17713/) (2023)
- [Embroid: Unsupervised Prediction Smoothing Can Improve Few-Shot Classification](https://mlsanity.com/paper/2307.11031/) (2023)
- [Pearls from Pebbles: Improved Confidence Functions for Auto-labeling](https://mlsanity.com/paper/2404.16188/) (2024)
- [ScriptoriumWS: A Code Generation Assistant for Weak Supervision](https://mlsanity.com/paper/2502.12366/) (2025)
- [Reliable Programmatic Weak Supervision with Confidence Intervals for Label Probabilities](https://mlsanity.com/paper/2508.03896/) (2025)
- [Codifying the Judge: Scalable Evaluation via Program Distillation](https://mlsanity.com/paper/2607.22561/) (2026)

## Abstract (arXiv)

Weak supervision (WS) is a rich set of techniques that produce pseudolabels by aggregating easily obtained but potentially noisy label estimates from a variety of sources. WS is theoretically well understood for binary classification, where simple approaches enable consistent estimation of pseudolabel noise rates. Using this result, it has been shown that downstream models trained on the pseudolabels have generalization guarantees nearly identical to those trained on clean labels. While this is exciting, users often wish to use WS for structured prediction, where the output space consists of more than a binary or multi-class label set: e.g. rankings, graphs, manifolds, and more. Do the favorable theoretical properties of WS for binary classification lift to this setting? We answer this question in the affirmative for a wide range of scenarios. For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings and tensor decompositions, providing a nearly-consistent noise rate estimator. For labels in constant-curvature Riemannian manifolds, we introduce new invariants that also yield consistent noise rate estimation. In both cases, when using the resulting pseudolabels in concert with a flexible downstream model, we obtain generalization guarantees nearly identical to those for models trained on clean data. Several of our results, which can be viewed as robustness guarantees in structured prediction with noisy labels, may be of independent interest. Empirical evaluation validates our claims and shows the merits of the proposed method.