# On the Information Complexity of Proper Learners for VC Classes in the Realizable Case

arXiv: https://arxiv.org/abs/2011.02970 · HTML: https://mlsanity.com/paper/2011.02970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

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

- [Information-Theoretic Analysis of Minimax Excess Risk](https://mlsanity.com/paper/2202.07537/) (2022)

## Abstract (arXiv)

We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from d log n +2 to O(d), where n is the number of i.i.d. training examples. In fact, we exhibit VC classes for which the CMI of any proper learner cannot be bounded by any real-valued function of the VC dimension only.