# Generalization Error Bounds via mth Central Moments of the Information Density

arXiv: https://arxiv.org/abs/2004.09148 · HTML: https://mlsanity.com/paper/2004.09148/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Generalization Bounds via Convex Analysis](https://mlsanity.com/paper/2202.04985/) (2022)
- [Information Complexity and Generalization Bounds](https://mlsanity.com/paper/2105.01747/) (2021)
- [Supervised Learning as Lossy Compression: Characterizing Generalization and Sample Complexity via Finite Blocklength Analysis](https://mlsanity.com/paper/2602.04107/) (2026)
- [Pool-based Active Learning as Noisy Lossy Compression: Characterizing Label Complexity via Finite Blocklength Analysis](https://mlsanity.com/paper/2602.05333/) (2026)

## Abstract (arXiv)

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both for the case in which a new hypothesis is randomly generated every time the algorithm is used - as often assumed in the probably approximately correct (PAC)-Bayesian literature - and in the single-draw case, where the hypothesis is extracted only once. For this last scenario, we present a novel bound that is explicit in the central moments of the information density. The bound reveals that the higher the order of the information density moment that can be controlled, the milder the dependence of the generalization bound on the desired confidence level. Furthermore, we use tools from binary hypothesis testing to derive a second bound, which is explicit in the tail of the information density. This bound confirms that a fast decay of the tail of the information density yields a more favorable dependence of the generalization bound on the confidence level.