New Neural Estimator Improves Normalized Mutual Information Accuracy.

Petra Eerikinharju, Marko Tuononen, Ville Hautam\"aki· July 31, 2026 View original

Key takeaways

  • Normalized mutual information offers comparable dependency scores across diverse datasets.
  • Existing NMI estimators face challenges with dimensionality and numerical stability.
  • NMINE is a new neural estimator that improves NMI accuracy for continuous, multidimensional data.
  • Neural estimation is a promising direction for robust dependency measurement.

Who benefits

Data ScienceMachine LearningHealthcareFinanceResearch

Summary

Researchers propose NMINE, a fully neural estimator for normalized mutual information in continuous, multidimensional variables, combining MINE-based mutual information estimation with neural marginal entropy estimators. Experiments show it improves accuracy over existing k-nearest-neighbor methods, addressing limitations of unbounded mutual information values.

Mutual information is a crucial measure for understanding statistical dependencies, including non-linear relationships, between variables. However, its unbounded nature makes direct comparisons across different datasets or applications challenging. Normalized mutual information (NMI) addresses this by providing a standardized dependency score, but current estimation methods struggle with high dimensionality and numerical stability. A new approach, Normalized Mutual Information Neural Estimation (NMINE), introduces a fully neural estimator for NMI in continuous, multidimensional settings. This method integrates a MINE-based neural estimator for mutual information with neural estimators for marginal entropies, leveraging the Donsker-Varadhan representation for MI and learning divergence from a uniform reference for entropies. Experimental validation on Gaussian data across various dimensions demonstrates that NMINE significantly enhances accuracy compared to traditional k-nearest-neighbor-based NMI estimators. This suggests that neural estimation offers a promising path forward for more robust and accurate normalized dependency measurements in complex data environments.

Why it matters

Professionals dealing with complex, high-dimensional data can leverage this improved estimation technique to better understand underlying statistical relationships and dependencies, leading to more robust data analysis and model interpretation.

How to implement this in your domain

  1. 1Explore NMINE's open-source implementation (if available) for integrating into existing data analysis pipelines.
  2. 2Apply NMINE to analyze feature dependencies in machine learning models for improved interpretability.
  3. 3Benchmark NMINE against current mutual information estimation methods in specific use cases to assess performance gains.
  4. 4Utilize normalized dependency scores derived from NMINE for feature selection or dimensionality reduction tasks.

Original post by Petra Eerikinharju, Marko Tuononen, Ville Hautam\"aki

"arXiv:2607.27710v1 Announce Type: new Abstract: Mutual information is a general measure of statistical dependence that captures both linear and nonlinear relationships between random variables. For continuous and multidimensional variables For continuous multidimensional variable…"

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Originally posted by Petra Eerikinharju, Marko Tuononen, Ville Hautam\"aki on X · view source

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