Mutual information (MI) quantifies statistical dependence between variables and is widely used across scientific disciplines, yet accurate estimation from finite data remains notoriously difficult. Common approaches fail in high-dimensional, undersampled regimes ($N \lesssim K$) typical of modern experiments, and no accepted tests exist to detect when neural network-based estimators fail, making them effectively unusable as scientific instruments. We show that neural MI estimators can be made reliable when the statistical dependencies admit a low-dimensional latent representation. Sample complexity is then governed by the latent dimensionality $K_Z \ll K$ rather than the ambient dimension -- a regime shift we confirm empirically and ground theoretically via random matrix theory. Building on this insight, we develop a practical protocol that provides neural estimators with explicit statistical consistency checks, bias correction, and confidence intervals. We additionally introduce a new class of probabilistic critics (the VSIB family) that substantially reduce bias and variance at higher MI values where standard estimators break down. We validate the protocol on synthetic benchmarks ($K=500$, $N$ as low as $256$), on the standard 40-dataset benchmark suite of Czyz et al. (2023), on noisy MNIST ($K=784$), and on CIFAR-10/100 ($K=3072$) with a ResNet-20 backbone. Our protocol consistently matches or exceeds existing methods while being the only approach to report confidence intervals and flag unreliable estimates, achieving reliable MI detection well below the ambient pixel dimension on real images.

翻译：互信息（MI）量化变量之间的统计依赖性，广泛应用于各科学领域，但基于有限数据进行精确估计一直是公认的难题。在当代实验典型的高维、欠采样情形（N ≲ K）下，常用方法均告失效，且目前尚无公认的检验标准可检测基于神经网络的估计器何时失效，这使其实际上无法作为科学工具使用。我们证明：当统计依赖关系存在低维潜在表示时，神经互信息估计器可以变得可靠。此时样本复杂度由潜在维度 K_Z ≪ K 而非环境维度主导——这一机制转换我们通过实验确认，并基于随机矩阵理论从理论上加以论证。基于这一见解，我们开发了一套实用协议，为神经估计器提供显式统计一致性检验、偏差校正和置信区间。此外，我们引入了一类新型概率评判器（VSIB族），在标准估计器失效的较高MI值区间显著降低偏差和方差。我们在合成基准测试（K=500，N低至256）、Czyz等（2023）的标准40数据集基准套件、含噪MNIST（K=784）以及基于ResNet-20骨干网络的CIFAR-10/100（K=3072）上验证了该协议。我们的协议始终优于或持平现有方法，且是唯一能够报告置信区间并标记不可靠估计的方法，在真实图像上可靠地实现了远低于环境像素维度的MI检测。