New Protocol Improves Mutual Information Estimation in High-Dimensional Data with Statistical Reliability Checks
Researchers have developed a practical protocol that enables neural network-based mutual information (MI) estimators to work reliably in high-dimensional, data-scarce settings where existing methods fail. The key insight is that when statistical dependencies have a low-dimensional latent structure, sample complexity scales with that latent dimension rather than the full data dimension. This matters because MI estimation is foundational across scientific disciplines, yet previously lacked any accepted method for detecting when neural estimators produce unreliable results.
Mutual information quantifies statistical dependence between variables and is widely used in fields ranging from neuroscience to machine learning, but accurate estimation from finite samples in high-dimensional settings has remained a persistent challenge. The authors demonstrate that neural MI estimators become tractable when the underlying dependencies admit a low-dimensional latent representation, with sample complexity governed by the latent dimensionality rather than the ambient data dimension — a result grounded theoretically in random matrix theory. Building on this, they introduce a protocol that equips neural estimators with statistical consistency checks, bias correction, and confidence intervals, addressing the critical gap that no accepted failure-detection tests previously existed. They also introduce the VSIB family of probabilistic critics, which substantially reduce bias and variance at higher MI values where standard estimators break down. The protocol is validated on synthetic benchmarks with up to 500 dimensions and as few as 256 samples, on a standard 40-dataset benchmark suite, and on real image data including noisy MNIST and CIFAR-10/100 with a ResNet-20 backbone, consistently matching or exceeding existing methods while being the only approach to report confidence intervals and flag unreliable estimates.
What's missing
The paper has not yet undergone formal peer review, as it is a preprint on arXiv. Key open questions include how the protocol performs when the low-dimensional latent structure assumption is violated or only approximately satisfied, and how computational cost scales compared to existing neural estimators in practice.
What different sources said
- arXiv stat.MLCenter
Accurate Estimation of Mutual Information in High Dimensional Data
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