A Data-Efficient Mutual Information Neural Estimator for Statistical Dependency Testing

Xiao Lin, Indranil Sur, Samuel A. Nastase, Uri Hasson, Ajay Divakaran, Mohamed R. Amer

TL;DR: A new & practical statistical test of dependency using neural networks, benchmarked on synthetic and a real fMRI datasets.

Abstract: Measuring Mutual Information (MI) between high-dimensional, continuous, random variables from observed samples has wide theoretical and practical applications. Recent works have developed accurate MI estimators through provably low-bias approximations and tight variational lower bounds assuming abundant supply of samples, but require an unrealistic number of samples to guarantee statistical significance of the estimation. In this work, we focus on improving data efficiency and propose a Data-Efficient MINE Estimator (DEMINE) that can provide a tight lower confident interval of MI under limited data, through adding cross-validation to the MINE lower bound (Belghazi et al., 2018). Hyperparameter search is employed and a novel meta-learning approach with task augmentation is developed to increase robustness to hyperparamters, reduce overfitting and improve accuracy. With improved data-efficiency, our DEMINE estimator enables statistical testing of dependency at practical dataset sizes. We demonstrate the effectiveness of DEMINE on synthetic benchmarks and a real world fMRI dataset, with application of inter-subject correlation analysis.

Keywords: mutual information, fMRI, inter-subject correation, mutual information neural estimation, meta-learning, statistical test of dependency