# How much does your data exploration overfit? Controlling bias via information usage

arXiv: https://arxiv.org/abs/1511.05219 · HTML: https://mlsanity.com/paper/1511.05219/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2015.

## Built on by (most cited first, 30 of 95)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Information-Theoretic Generalization Bounds for Stochastic Gradient Descent](https://mlsanity.com/paper/2102.00931/) (2021)
- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
- [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)
- [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)
- [Knowledge Overshadowing Causes Amalgamated Hallucination in Large Language Models](https://mlsanity.com/paper/2407.08039/) (2024)
- [FedSWA: Improving Generalization in Federated Learning with Highly Heterogeneous Data via Momentum-Based Stochastic Controlled Weight Averaging](https://mlsanity.com/paper/2507.20016/) (2025)
- [Fine-Tuning Language Models via Epistemic Neural Networks](https://mlsanity.com/paper/2211.01568/) (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)
- [Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion](https://mlsanity.com/paper/2502.21278/) (2025)
- [Information-Theoretic Analysis of Unsupervised Domain Adaptation](https://mlsanity.com/paper/2210.00706/) (2022)
- [Generalization Bounds with Data-dependent Fractal Dimensions](https://mlsanity.com/paper/2302.02766/) (2023)
- [Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective](https://mlsanity.com/paper/2410.01720/) (2024)
- [Characterizing and Understanding the Generalization Error of Transfer Learning with Gibbs Algorithm](https://mlsanity.com/paper/2111.01635/) (2021)
- [Online-to-PAC Conversions: Generalization Bounds via Regret Analysis](https://mlsanity.com/paper/2305.19674/) (2023)
- [Information Complexity of Stochastic Convex Optimization: Applications to Generalization and Memorization](https://mlsanity.com/paper/2402.09327/) (2024)
- [Empirical Risk Minimization with Relative Entropy Regularization](https://mlsanity.com/paper/2211.06617/) (2022)
- [Information-Theoretic Bounds on the Moments of the Generalization Error of Learning Algorithms](https://mlsanity.com/paper/2102.02016/) (2021)
- [Learning via Wasserstein-Based High Probability Generalisation Bounds](https://mlsanity.com/paper/2306.04375/) (2023)
- [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)

Modern data is messy and high-dimensional, and it is often not clear a priori what are the right questions to ask. Instead, the analyst typically needs to use the data to search for interesting analyses to perform and hypotheses to test. This is an adaptive process, where the choice of analysis to be performed next depends on the results of the previous analyses on the same data. Ultimately, which results are reported can be heavily influenced by the data. It is widely recognized that this process, even if well-intentioned, can lead to biases and false discoveries, contributing to the crisis of reproducibility in science. But while %the adaptive nature of exploration any data-exploration renders standard statistical theory invalid, experience suggests that different types of exploratory analysis can lead to disparate levels of bias, and the degree of bias also depends on the particulars of the data set. In this paper, we propose a general information usage framework to quantify and provably bound the bias and other error metrics of an arbitrary exploratory analysis. We prove that our mutual information based bound is tight in natural settings, and then use it to give rigorous insights into when commonly used procedures do or do not lead to substantially biased estimation. Through the lens of information usage, we analyze the bias of specific exploration procedures such as filtering, rank selection and clustering. Our general framework also naturally motivates randomization techniques that provably reduces exploration bias while preserving the utility of the data analysis. We discuss the connections between our approach and related ideas from differential privacy and blinded data analysis, and supplement our results with illustrative simulations.