Neural Estimators for Conditional Mutual Information Using Nearest Neighbors Sampling
This work addresses a long-standing problem in information theory for researchers and practitioners needing reliable CMI estimators, though it is incremental as it builds on prior neural network approaches.
The paper tackles the challenge of estimating conditional mutual information (CMI) from samples by introducing a new k-nearest neighbors (k-NN) based resampling technique to train neural network classifiers, resulting in improved accuracy and reduced variance in CMI estimation compared to existing methods.
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.