# The Peaking Phenomenon in Semi-supervised Learning

arXiv: https://arxiv.org/abs/1610.05160 · HTML: https://mlsanity.com/paper/1610.05160/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2016.

## Built on by (most cited first, 5 of 5)

- [The Shape of Learning Curves: a Review](https://mlsanity.com/paper/2103.10948/) (2021)
- [A Survey of Learning Curves with Bad Behavior: or How More Data Need Not Lead to Better Performance](https://mlsanity.com/paper/2211.14061/) (2022)
- [LCDB 1.1: A Database Illustrating Learning Curves Are More Ill-Behaved Than Previously Thought](https://mlsanity.com/paper/2505.15657/) (2025)
- [Understanding the Role of Optimization in Double Descent](https://mlsanity.com/paper/2312.03951/) (2023)
- [Origins and mitigation of double descent in reduced order modeling](https://mlsanity.com/paper/2607.26414/) (2026)

## Abstract (arXiv)

For the supervised least squares classifier, when the number of training objects is smaller than the dimensionality of the data, adding more data to the training set may first increase the error rate before decreasing it. This, possibly counterintuitive, phenomenon is known as peaking. In this work, we observe that a similar but more pronounced version of this phenomenon also occurs in the semi-supervised setting, where instead of labeled objects, unlabeled objects are added to the training set. We explain why the learning curve has a more steep incline and a more gradual decline in this setting through simulation studies and by applying an approximation of the learning curve based on the work by Raudys & Duin.