# Semi-Supervised Learning: the Case When Unlabeled Data is Equally Useful

arXiv: https://arxiv.org/abs/2005.11018 · HTML: https://mlsanity.com/paper/2005.11018/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2020.

## Built on by (most cited first, 9 of 9)

- [An Information-theoretical Approach to Semi-supervised Learning under Covariate-shift](https://mlsanity.com/paper/2202.12123/) (2022)
- [Information-Theoretic Characterization of the Generalization Error for Iterative Semi-Supervised Learning](https://mlsanity.com/paper/2110.00926/) (2021)
- [On the Generalization for Transfer Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2207.05377/) (2022)
- [Fast Rate Generalization Error Bounds: Variations on a Theme](https://mlsanity.com/paper/2205.03131/) (2022)
- [How Does Pseudo-Labeling Affect the Generalization Error of the Semi-Supervised Gibbs Algorithm?](https://mlsanity.com/paper/2210.08188/) (2022)
- [Fast Rate Information-theoretic Bounds on Generalization Errors](https://mlsanity.com/paper/2303.14658/) (2023)
- [On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models](https://mlsanity.com/paper/2205.04641/) (2022)
- [Advances in Electron Microscopy with Deep Learning](https://mlsanity.com/paper/2101.01178/) (2021)
- [Fast Rates for Semi-Supervised Learning via Data-Augmentation Graph Regularization](https://mlsanity.com/paper/2607.07513/) (2026)

## Abstract (arXiv)

Semi-supervised learning algorithms attempt to take advantage of relatively inexpensive unlabeled data to improve learning performance. In this work, we consider statistical models where the data distributions can be characterized by continuous parameters. We show that under certain conditions on the distribution, unlabeled data is equally useful as labeled date in terms of learning rate. Specifically, let n, m be the number of labeled and unlabeled data, respectively. It is shown that the learning rate of semi-supervised learning scales as O(1/n) if m~ n, and scales as O(1/n1+γ) if m~ n1+γ for some γ>0, whereas the learning rate of supervised learning scales as O(1/n).