Matrix completion and extrapolation via kernel regression

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is formulated as a kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach performs faster than widespread methods such as alternating least squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects

Cost aware Inference for IoT Devices

Networked embedded devices (IoTs) of limitedCPU, memory and power resources are revo-lutionizing data gathering, remote monitoringand planning in many consumer and businessapplications. Nevertheless, resource limita-tions place a significant burden on their ser-vice life and operation, warranting cost-awaremethods that are capable of distributivelyscreening redundancies in device informationand transmitting informative data. We pro-pose to train a decentralized gated networkthat, given an observed instance at test-time,allows for activation of select devices to trans-mit information to a central node, which thenperforms inference. We analyze our proposedgradient descent algorithm for Gaussian fea-tures and establish convergence guaranteesunder good initialization. We conduct exper-iments on a number of real-world datasetsarising in IoT applications and show that ourmodel results in over 1.5X service life withnegligible accuracy degradation relative to aperformance achievable by a neural network.http://proceedings.mlr.press/v89/zhu19d/zhu19d.pdfPublished versio

Generalization error bounds for kernel matrix completion and extrapolation

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable algorithms. This paper analyzes the generalization error of such approaches, and presents numerical tests confirming the theoretical resultsThis work is supported by ERDF funds (TEC2013-41315-R and TEC2016-75067-C4-2), the Catalan Government (2017 SGR 578), and NSF grants(1500713, 1514056, 1711471 and 1509040).Peer ReviewedPostprint (published version