New Protocol Improves Mutual Information Estimation in High-Dimensional Data with Statistical Reliability Checks
Researchers developed a new protocol for accurately estimating mutual information (MI) from high-dimensional data using neural networks, addressing a long-standing challenge in scientific computing. The key innovation is recognizing that MI estimation becomes tractable when statistical dependencies have low-dimensional latent representations, reducing sample complexity requirements. This matters because mutual information is fundamental across scientific disciplines, and reliable estimation with confidence intervals makes neural MI estimators usable as actual scientific instruments rather than unreliable black boxes.
A new arXiv preprint presents a practical protocol for reliably estimating mutual information in high-dimensional, undersampled datasets—a regime where standard approaches typically fail. The authors demonstrate that neural network-based MI estimators can achieve statistical consistency when underlying dependencies admit low-dimensional latent representations, with sample complexity governed by latent dimensionality rather than ambient dimension. The protocol includes explicit consistency checks, bias correction, and confidence intervals—features absent from existing methods. The researchers introduce a new class of probabilistic critics (VSIB family) that reduce bias and variance at higher MI values. Validation spans synthetic benchmarks (up to 500 dimensions with samples as low as 256), standard benchmark suites, and real image datasets (MNIST, CIFAR-10/100), consistently matching or exceeding existing methods while being the only approach to flag unreliable estimates and report confidence intervals.
What's missing
The preprint does not discuss computational complexity or runtime comparisons with existing methods, nor does it address potential limitations when latent dimensionality assumptions are violated or how practitioners can validate whether their data satisfies the low-dimensional latent representation assumption in real-world applications.
What different sources said
- arXiv stat.MLCenter
Accurate Estimation of Mutual Information in High Dimensional Data
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