The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit the structure of problems. BADMM provides a unified framework for ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM. We establish the global convergence and the O (1 /T) iteration complexity for BADMM. In some cases, BADMM can be faster than ADMM by a factor of O (n/ ln n) where n is the dimensionality. In solving the linear program of mass transportation problem, BADMM leads to massive parallelism and can easily run on GPU. BADMM is several times faster than highly optimized commercial software Gurobi.

We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors propose a new screening rule Slores for pre-filtering variables for logistic regression. This statement though sounds too simple and doesn't give the paper justice at all. The paper provides a rigorous and theoretically well founded derivation of a novel pre-screening rule which could in principle be extended to other settings as well. The method is also efficient compared to other safe rules that guarantee to discard only non-zero entries.

Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse lo gistic regression s creening rule (Slores) to identify the "0" components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that the data set needs to be scanned only once to run the screening and its computational cost is negligible compared to that of solving the sparse logistic regression problem. Moreover, Slores is independent of solvers for sparse logistic regression, thus Slores can be integrated with any existing solver to improve the efficiency. We have evaluated Slores using high-dimensional data sets from different applications. Experiments demonstrate that Slores outperforms the existing state-of-the-art screening rules and the efficiency of solving sparse logistic regression can be improved by one magnitude.

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(COL T 2005).