The CONSORT-EHEALTH checklist is intended for authors of randomized trials evaluating webbased and Internet-based applications/interventions, including mobile interventions, electronic games (incl multiplayer games), social media, certain telehealth applications, and other interactive and/or networked electronic applications. Some of the items (e.g. all subitems under item 5description of the intervention) may also be applicable for other study designs.The goal of the CONSORT EHEALTH checklist and guideline is to be a) a guide for reporting for authors of RCTs, b) to form a basis for appraisal of an ehealth trial (in terms of validity)CONSORT-EHEALTH items/subitems are MANDATORY reporting items for studies published in the Journal of Medical Internet Research and other journals / scienti c societies endorsing the checklist.Items numbered 1., 2., 3., 4a., 4b etc are original CONSORT or CONSORT-NPT (non-pharmacologic treatment) items. Items with Roman numerals (i., ii, iii, iv etc.) are CONSORT-EHEALTH extensions/clari cations.As the CONSORT-EHEALTH checklist is still considered in a formative stage, we would ask that you also RATE ON A SCALE OF 1-5 how important/useful you feel each item is FOR THE PURPOSE OF THE CHECKLIST and reporting guideline (optional).
The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric MSE convergence rate. However, most of the previously proposed estimators have high computational complexity of at least O(N 2 ). We propose a unified method for empirical non-parametric estimation of general MI function between random vectors in R d based on N i.i.d. samples. The reduced complexity MI estimator, called the ensemble dependency graph estimator (EDGE), combines randomized locality sensitive hashing (LSH), dependency graphs, and ensemble bias-reduction methods. We prove that EDGE achieves optimal computational complexity O(N ), and can achieve the optimal parametric MSE rate of O(1/N ) if the density is d times differentiable. To the best of our knowledge EDGE is the first non-parametric MI estimator that can achieve parametric MSE rates with linear time complexity. We illustrate the utility of EDGE for the analysis of the information plane (IP) in deep learning. Using EDGE we shed light on a controversy on whether or not the compression property of information bottleneck (IB) in fact holds for ReLu and other rectification functions in deep neural networks (DNN).Recently, Shwartz-Ziv and Tishby utilized MI to study the training process in Deep Neural Networks (DNN) [16]. Let X, T and Y respectively denote the input, hidden and output layers. The authors of [16] introduced the information bottleneck (IB) that represents the tradeoff between two mutual information measures: I(X, T ) and I(T, Y ). They observed that the training process of a DNN consists of two distinct phases; 1) an initial fitting phase in which I(T, Y ) increases, and 2) a subsequent compression phase in which I(X, T ) decreases. Saxe et al in [17] countered the claim of [16], asserting that this compression property is not universal, rather it depends on the specific activation function. Specifically, they claimed that the compression property does not hold for ReLu activation functions. The authors of [16] challenged these claims, arguing that the authors of [17] had not observed compression due to poor estimates of the MI. We use our proposed rate-optimal ensemble MI estimator to explore this arXiv:1801.09125v2 [cs.IT]
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