Neural Estimators for Conditional Mutual Information Using Nearest Neighbors Sampling

TL;DR

This paper introduces a k-NN based resampling technique for neural estimators of conditional mutual information, improving estimation accuracy and variance compared to existing methods.

Contribution

It presents a novel k-NN resampling method for neural CMI estimation, with proven consistency and experimental validation of improved performance.

Findings

Enhanced accuracy of CMI estimates

Reduced variance of estimators

Validated effectiveness through experiments

Abstract

The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k nearest neighbors (k-NN), to perform the resampling and derive high-confidence concentration bounds for the sample average. Then the technique is employed to train a neural network classifier and the CMI is estimated accordingly. We propose three estimators using this technique and prove their consistency, make a comparison between them and similar approaches in the literature, and experimentally show improvements in estimating the CMI in terms of accuracy and variance of the estimators.