Data-Efficient Mutual Information Neural Estimator.

Measuring Mutual Information (MI) between high-dimensional, continuous, random variables from observed samples has wide theoretical and practical applications. While traditional MI methods, such as (Kraskov et al. 2004), capable of capturing MI between low-dimensional signals, they fall short when dimensionality increases and are not scalable. Existing neural approaches, such as MINE (Belghazi et al. 2018), searches for a d-dimensional neural network that maximizes a variational lower bound for mutual information estimation; however, this requires O(d log d) observed samples to prevent the neural network from overfitting. For practical mutual information estimation in real world applications, data is not always available at a surplus, especially in cases where acquisition of the data is prohibitively expensive, for example in fMRI analysis. We introduce a scalable, data-efficient mutual information estimator. By coupling a learning-based view of the MI lower bound with meta-learning, DEMINE achieves high-confidence estimations irrespective of network size and with improved accuracy at practical dataset sizes. We demonstrate the effectiveness of DEMINE on synthetic benchmarks as well as a real world application of fMRI inter-subject correlation analysis.