We argue that the estimation of the mutual information between high dimensional continuous random variables is achievable by gradient descent over neural networks. This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE is backpropable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results demonstrate substantial added flexibility and improvement in these settings.
In REF , Belghazi et al. present a Mutual Information Neural Estimator (MINE) that estimates mutual information between high dimensional continuous random variables by gradient descent over neural networks.
MINE: Mutual Information Neural Estimation
ICML 2018
Computer Science Mathematics