Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in the high-dimensional, undersampled regimes typical of modern experiments. Recent machine learning-based estimators show promise, but their accuracy depends sensitively on dataset size, structure, and hyperparameters, with no accepted tests to detect failures. We close these gaps through a systematic evaluation of classical and neural MI estimators across standard benchmarks and new synthetic datasets tailored to challenging high-dimensional, undersampled regimes. We contribute: (i) a practical protocol for reliable MI estimation with explicit checks for statistical consistency; (ii) confidence intervals (error bars around estimates) that existing neural MI estimator do not provide; and (iii) a new class of probabilistic critics designed for high-dimensional, high-information settings. We demonstrate the effectiveness of our protocol with computational experiments, showing that it consistently matches or surpasses existing methods while uniquely quantifying its own reliability. We show that reliable MI estimation is sometimes achievable even in severely undersampled, high-dimensional datasets, provided they admit accurate low-dimensional representations. This broadens the scope of applicability of neural MI estimators and clarifies when such estimators can be trusted.

翻译：互信息（MI）是衡量两个变量间统计依赖性的基本度量，但从有限数据中准确估计互信息仍是一个众所周知的难题。目前不存在普遍可靠的估计器，且常见方法在现代实验典型的高维、欠采样场景中往往失效。近期基于机器学习的估计器展现出潜力，但其准确性高度依赖于数据集大小、结构及超参数，且缺乏公认的检测失效的测试方法。我们通过系统评估经典与神经互信息估计器，在标准基准测试和针对高维欠采样挑战场景设计的新合成数据集上填补了这些空白。我们的贡献包括：（i）具有明确统计一致性检验的可靠互信息估计实用方案；（ii）现有神经互信息估计器未能提供的置信区间（估计值误差范围）；（iii）专为高维高信息场景设计的新型概率判别器类别。我们通过计算实验证明了该方案的有效性，表明其在独特量化自身可靠性的同时，始终达到或超越现有方法。我们证明，即使在高维严重欠采样数据集中，只要数据允许精确的低维表示，可靠的互信息估计有时仍可实现。这拓宽了神经互信息估计器的适用范围，并明确了此类估计器的可信使用条件。