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We analyze two communication-efficient algorithms for distributed optimization in statistical settings involving large-scale data sets. The first algorithm is a standard averaging method that distributes the N data samples evenly to m machines, performs separate minimization on each subset, and then averages the estimates. We provide a sharp analysis of this average mixture algorithm, showing that under a reasonable set of conditions, the combined parameter achieves mean-squared error (MSE) that decays as O(N −1 + (N/m) −2 ). Whenever m ≤ √ N , this guarantee matches the best possible rate achievable by a centralized algorithm having access to all N samples. The second algorithm is a novel method, based on an appropriate form of bootstrap subsampling. Requiring only a single round of communication, it has mean-squared error that decays as O(N −1 + (N/m) −3 ), and so is more robust to the amount of parallelization. In addition, we show that a stochastic gradient-based method attains mean-squared error decaying as O(N −1 + (N/m) −3/2 ), easing computation at the expense of a potentially slower MSE rate. We also provide an experimental evaluation of our methods, investigating their performance both on simulated data and on a large-scale regression problem from the internet search domain. In particular, we show that our methods can be used to efficiently solve an advertisement prediction problem from the Chinese SoSo Search Engine, which involves logistic regression with N ≈ 2.4 × 10 8 samples and d ≈ 740,000 covariates.

We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to minimize the overall empirical loss, which is the average of the local empirical losses. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the results for distributed ridge regression, logistic regression and binary classification with a smoothed hinge loss. In a standard setting for supervised learning, the required number of communication rounds of the algorithm does not increase with the sample size, and only grows slowly with the number of machines.

Light field imaging has emerged as a technology allowing to capture richer visual information from our world. As opposed to traditional photography, which captures a 2D projection of the light in the scene integrating the angular domain, light fields collect radiance from rays in all directions, demultiplexing the angular information lost in conventional photography. On the one hand, this higher-dimensional representation of visual data offers powerful capabilities for scene understanding, and substantially improves the performance of traditional computer vision problems such as depth sensing, post-capture refocusing, segmentation, video stabilization, material classification, etc. On the other hand, the high-dimensionality of light fields also brings up new challenges in terms of data capture, data compression, content editing and display. Taking these two elements together, research in light field image processing has become increasingly popular in the computer vision, computer graphics and signal processing communities. In this article, we present a comprehensive overview and discussion of research in this field over the past 20 years. We focus on all aspects of light field image processing, including basic light field representation and theory, acquisition, super-resolution, depth estimation, compression, editing, processing algorithms for light field display, and computer vision applications of light field data. Index Terms-Light field imaging, light field processing.

Current treatments for chronic diabetic wounds remain unsatisfactory due to the lack of ideal wound dressings that can integrate matching mechanical strength, fast self‐healability, facile dressing change, and multiple therapeutic effects into one system. In this work, benefiting from the catechol groups and therapeutic effect of epigallocatechin‐3‐gallate (EGCG, green tea derivative), a smart hydrogel dressing can be conveniently obtained through copolymerization of the complex formed by EGCG and 3‐acrylamido phenylboronic acid (APBA) (the formation of boronate ester bond) and acrylamide. The resulting hydrogel features adequate mechanical properties, self‐healing capability, and tissue adhesiveness. Otherwise, the substantial release of EGCG can not only realize anti‐oxidation, antibacterial, anti‐inflammatory and proangiogenic effect, and modulation of macrophage polarization to accelerate wound healing, but also facilitate easy dressing change. This advanced hydrogel provides a facile and effective way for diabetic chronic wound management and may be extended for the therapy of other complicated wound healings.