Regularized Mutual Information Neural Estimation

With the variational lower bound of mutual information (MI), the estimation of MI can be understood as an optimization task via stochastic gradient descent. In this work, we start by showing how Mutual Information Neural Estimator (MINE) searches for the optimal function $T$ that maximizes the Donsker-Varadhan representation. With our synthetic dataset, we directly observe the neural network outputs during the optimization to investigate why MINE succeeds or fails: We discover the drifting phenomenon, where the constant term of $T$ is shifting through the optimization process, and analyze the instability caused by the interaction between the $logsumexp$ and the insufficient batch size. Next, through theoretical and experimental evidence, we propose a novel lower bound that effectively regularizes the neural network to alleviate the problems of MINE. We also introduce an averaging strategy that produces an unbiased estimate by utilizing multiple batches to mitigate the batch size limitation. Finally, we show that $L^2$ regularization achieves significant improvements in both discrete and continuous settings.Comment: 18 pages, 15 figur

MINDE: Mutual Information Neural Diffusion Estimation

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods

CNN-AIDED FACTOR GRAPHS WITH ESTIMATED MUTUAL INFORMATION FEATURES FOR SEIZURE DETECTION

We propose a convolutional neural network (CNN) aided factor graphs assisted by mutual information features estimated by a neural network for seizure detection. Specifically, we use neural mutual information estimation to evaluate the correlation between different electroencephalogram (EEG) channels as features. We then use a 1D-CNN to extract extra features from the EEG signals and use both features to estimate the probability of a seizure event. Finally, learned factor graphs are employed to capture the temporal correlation in the signal. Both sets of features from the neural mutual estimation and the 1D-CNN are used to learn the factor nodes. We show that the proposed method achieves state-of-the-art performance using 6-fold leave-four-patients-out cross-validation

Estimating mutual information and multi--information in large networks

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained with manageable computational effort. The same methods allow estimation of higher order, multi--information terms. These ideas are illustrated by analyses of gene expression, financial markets, and consumer preferences. In each case, information theoretic measures correlate with independent, intuitive measures of the underlying structures in the system

CRYPTO-MINE: Cryptanalysis via Mutual Information Neural Estimation

The use of Mutual Information (MI) as a measure to evaluate the efficiency of cryptosystems has an extensive history. However, estimating MI between unknown random variables in a high-dimensional space is challenging. Recent advances in machine learning have enabled progress in estimating MI using neural networks. This work presents a novel application of MI estimation in the field of cryptography. We propose applying this methodology directly to estimate the MI between plaintext and ciphertext in a chosen plaintext attack. The leaked information, if any, from the encryption could potentially be exploited by adversaries to compromise the computational security of the cryptosystem. We evaluate the efficiency of our approach by empirically analyzing multiple encryption schemes and baseline approaches. Furthermore, we extend the analysis to novel network coding-based cryptosystems that provide individual secrecy and study the relationship between information leakage and input distribution