---
title: "Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.03487v1"
permalink: "https://feed.astralor.com/items/itm_56adf7b6247dd18e98929e70"
published: "2026-07-03T16:55:55.000Z"
score: 76
channel: "ai"
tags: ["Copula Theory","Mutual Information Estimation","Causal Inference","Benchmark","Representation Learning"]
---

# Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation

## AI commentary

> This paper overturns the intuition that one estimator class always wins—it's a must-read for AI practitioners in representation learning, causal discovery, or information theory. The copula-based unified framework is elegant and the open-source code enables easy reproduction and extension.

## At a glance

Mutual information (MI) estimation is a central problem in machine learning and statistics. Existing benchmarks mostly evaluate estimators on simplified, low-dimensional distributions. This paper proposes a comprehensive benchmarking framework grounded in a unified copula-theoretic perspective, introducing two complementary families: copula-first and marginals-first. Extensive evaluation of non-parametric, discriminative, and generative estimators reveals no universal winner, with each class outperforming others under specific setups, highlighting fundamental estimation barriers.

## Key points

- Unified MI benchmarks via copula theory, with two new test families.
- Systematic evaluation of non-parametric, discriminative, and generative estimators reveals no universal winner.
- Identifies fundamental estimation barriers and proposes targeted stress tests.

## Full text

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.

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