Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation

2026-07-03

AI Summary

Existing benchmarks for mutual information estimation are largely confined to low-dimensional, simplified distributions, limiting their ability to evaluate estimator performance on complex real-world data. This work proposes a unified benchmark framework grounded in copula theory, comprising two complementary test suites: the first systematically controls mutual information, dimensionality, and marginal complexity using synthetic data and flow-based models; the second integrates real images with controllable dependency structures, extending the classic same-pair paradigm. For the first time, this framework jointly encompasses both synthetic and real data while accounting for both dependency structure and marginal complexity. Systematic evaluation of diverse discriminative and generative estimators reveals that no single method dominates across all settings, and that fundamental limitations exist across different estimator families—limitations more effectively exposed by the newly designed tests.

Abstract

Mutual information (MI) estimation is a central problem in machine learning and statistics; however, existing benchmarks typically evaluate estimators on simplified, low-dimensional distributions, leaving their performance on complex, realistic data largely unexplored. We address this gap with a comprehensive benchmarking framework grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases. Within this framework, we propose two complementary families of tests: a copula-first family that systematically varies ground-truth MI, dimensionality, and marginal complexity using synthetic and flow-based transformations; and a marginals-first family that couples real-world image data with controlled dependency structures, extending the classic same-class-pairing paradigm. We use this suite to extensively evaluate three classes of estimators: non-parametric, discriminative, and generative. Contrary to prevailing assumptions, our results indicate that there is no universal winner: each category can systematically outperform all other estimators under specific setups. By analyzing these cases, we identify fundamental estimation barriers and propose new tests that more effectively stress these specific limitations. We share the open source code at https://github.com/VanessB/mutinfo.

Problem

• Mutual Information Estimation
• Benchmarking
• High-dimensional Data
• Real-world Data
• Estimator Evaluation

Innovation

• mutual information estimation
• copula-theoretic framework
• comprehensive benchmarking
• real-world image data
• estimator evaluation