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Recently, several methods have been proposed for estimating the mutualinformation from sample data using deep neural networks and without the knowingclosed form distribution of the data. This class of estimators is referred toas neural mutual information estimators. Although very promising, suchtechniques have yet to be rigorously bench-marked so as to establish theirefficacy, ease of implementation, and stability for capacity estimation whichis joint maximization frame-work. In this paper, we compare the differenttechniques proposed in the literature for estimating capacity and provide apractitioner perspective on their effectiveness. In particular, we study theperformance of mutual information neural estimator (MINE), smoothed mutualinformation lower-bound estimator (SMILE), and directed information neuralestimator (DINE) and provide insights on InfoNCE. We evaluated these algorithmsin terms of their ability to learn the input distributions that are capacityapproaching for the AWGN channel, the optical intensity channel, and peakpower-constrained AWGN channel. For both scenarios, we provide insightfulcomments on various aspects of the training process, such as stability,sensitivity to initialization.

Neural Capacity Estimators: How Reliable Are They?