# Tightening Mutual Information Based Bounds on Generalization Error

arXiv: https://arxiv.org/abs/1901.04609 · HTML: https://mlsanity.com/paper/1901.04609/

## Key facts

- Cited by 117 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2019.

## Built on by (most cited first, 30 of 117)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Information-theoretic generalization bounds for black-box learning algorithms](https://mlsanity.com/paper/2110.01584/) (2021)
- [Generalization Bounds For Meta-Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2109.14595/) (2021)
- [Tighter expected generalization error bounds via Wasserstein distance](https://mlsanity.com/paper/2101.09315/) (2021)
- [On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications](https://mlsanity.com/paper/2110.03128/) (2021)
- [Towards a Unified Information-Theoretic Framework for Generalization](https://mlsanity.com/paper/2111.05275/) (2021)
- [On the Generalization of Diffusion Model](https://mlsanity.com/paper/2305.14712/) (2023)
- [A New Family of Generalization Bounds Using Samplewise Evaluated CMI](https://mlsanity.com/paper/2210.06422/) (2022)
- [Generalization Bounds using Lower Tail Exponents in Stochastic Optimizers](https://mlsanity.com/paper/2108.00781/) (2021)
- [Generalization Bounds via Convex Analysis](https://mlsanity.com/paper/2202.04985/) (2022)
- [Single Trajectory Nonparametric Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2202.08311/) (2022)
- [Rate-Distortion Theoretic Generalization Bounds for Stochastic Learning Algorithms](https://mlsanity.com/paper/2203.02474/) (2022)
- [Tighter Information-Theoretic Generalization Bounds from Supersamples](https://mlsanity.com/paper/2302.02432/) (2023)
- [Limitations of Information-Theoretic Generalization Bounds for Gradient Descent Methods in Stochastic Convex Optimization](https://mlsanity.com/paper/2212.13556/) (2022)
- [An Information-theoretical Approach to Semi-supervised Learning under Covariate-shift](https://mlsanity.com/paper/2202.12123/) (2022)
- [Information Theoretic Lower Bounds for Information Theoretic Upper Bounds](https://mlsanity.com/paper/2302.04925/) (2023)
- [More PAC-Bayes bounds: From bounded losses, to losses with general tail behaviors, to anytime validity](https://mlsanity.com/paper/2306.12214/) (2023)
- [Understanding Generalization via Leave-One-Out Conditional Mutual Information](https://mlsanity.com/paper/2206.14800/) (2022)
- [Generalization Bounds for Noisy Iterative Algorithms Using Properties of Additive Noise Channels](https://mlsanity.com/paper/2102.02976/) (2021)
- [Information-Theoretic Analysis of Unsupervised Domain Adaptation](https://mlsanity.com/paper/2210.00706/) (2022)
- [Information Complexity and Generalization Bounds](https://mlsanity.com/paper/2105.01747/) (2021)
- [Characterizing and Understanding the Generalization Error of Transfer Learning with Gibbs Algorithm](https://mlsanity.com/paper/2111.01635/) (2021)
- [Rate-Distortion Theoretic Bounds on Generalization Error for Distributed Learning](https://mlsanity.com/paper/2206.02604/) (2022)
- [Generalization Error Bounds for Deep Neural Networks Trained by SGD](https://mlsanity.com/paper/2206.03299/) (2022)
- [Information Complexity of Stochastic Convex Optimization: Applications to Generalization and Memorization](https://mlsanity.com/paper/2402.09327/) (2024)
- [Information-Theoretic Bounds on the Moments of the Generalization Error of Learning Algorithms](https://mlsanity.com/paper/2102.02016/) (2021)
- [Time-Independent Information-Theoretic Generalization Bounds for SGLD](https://mlsanity.com/paper/2311.01046/) (2023)
- [Information-Theoretic Characterization of the Generalization Error for Iterative Semi-Supervised Learning](https://mlsanity.com/paper/2110.00926/) (2021)
- [Tighter Expected Generalization Error Bounds via Convexity of Information Measures](https://mlsanity.com/paper/2202.12150/) (2022)
- [What You See is What You Get: Principled Deep Learning via Distributional Generalization](https://mlsanity.com/paper/2204.03230/) (2022)

## Abstract (arXiv)

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the learning algorithm. The bound is derived under more general conditions on the loss function than in existing studies; nevertheless, it provides a tighter characterization of the generalization error. Examples of learning algorithms are provided to demonstrate the the tightness of the bound, and to show that it has a broad range of applicability. Application to noisy and iterative algorithms, e.g., stochastic gradient Langevin dynamics (SGLD), is also studied, where the constructed bound provides a tighter characterization of the generalization error than existing results. Finally, it is demonstrated that, unlike existing bounds, which are difficult to compute and evaluate empirically, the proposed bound can be estimated easily in practice.