# Learnability with Indirect Supervision Signals

arXiv: https://arxiv.org/abs/2006.08791 · HTML: https://mlsanity.com/paper/2006.08791/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Universal Information Extraction as Unified Semantic Matching](https://mlsanity.com/paper/2301.03282/) (2023)
- [Prompting in the Dark: Assessing Human Performance in Prompt Engineering for Data Labeling When Gold Labels Are Absent](https://mlsanity.com/paper/2502.11267/) (2025)
- [Creating Training Sets via Weak Indirect Supervision](https://mlsanity.com/paper/2110.03484/) (2021)
- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [On Regularization and Inference with Label Constraints](https://mlsanity.com/paper/2307.03886/) (2023)
- [Rethinking Remaining Useful Life Prediction with Scarce Time Series Data: Regression under Indirect Supervision](https://mlsanity.com/paper/2504.09206/) (2025)
- [Learning Stable Predictors from Weak Supervision under Distribution Shift](https://mlsanity.com/paper/2604.05002/) (2026)

## Abstract (arXiv)

Learning from indirect supervision signals is important in real-world AI applications when, often, gold labels are missing or too costly. In this paper, we develop a unified theoretical framework for multi-class classification when the supervision is provided by a variable that contains nonzero mutual information with the gold label. The nature of this problem is determined by (i) the transition probability from the gold labels to the indirect supervision variables and (ii) the learner's prior knowledge about the transition. Our framework relaxes assumptions made in the literature, and supports learning with unknown, non-invertible and instance-dependent transitions. Our theory introduces a novel concept called separation, which characterizes the learnability and generalization bounds. We also demonstrate the application of our framework via concrete novel results in a variety of learning scenarios such as learning with superset annotations and joint supervision signals.