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As pairwise ranking becomes broadly employed for elections, sports competitions, recommendation, information retrieval and so on, attackers have strong motivation and incentives to manipulate or disrupt the ranking list. They could inject malicious comparisons into the training data to fool the target ranking algorithm. Such a technique is called "poisoning attack" in regression and classification tasks. In this paper, to the best of our knowledge, we initiate the first systematic investigation of data poisoning attack on the pairwise ranking algorithms, which can be generally formalized as the dynamic and static games between the ranker and the attacker, and can be modeled as certain kinds of integer programming problems mathematically. To break the computational hurdle of the underlying integer programming problems, we reformulate them into the distributionally robust optimization (DRO) problems, which are computational tractable. Based on such DRO formulations, we propose two efficient poisoning attack algorithms and establish the associated theoretical guarantees including the existence of Nash equilibrium and the generalization ability bounds. The effectiveness of the suggested poisoning attack strategies is demonstrated by a series of toy simulations and several real data experiments. These experimental results show that the proposed methods can significantly reduce the performance of the ranker in the sense that the correlation between the true ranking list and the aggregated results with toxic data can be decreased dramatically.

In this paper, we propose an efficient boosting method with theoretical guarantees for binary classification. There are three key ingredients of the proposed boosting method: a fully corrective greedy (FCG) update, a differentiable squared hinge (also called truncated quadratic) loss function, and an efficient alternating direction method of multipliers (ADMM) solver. Compared with traditional boosting methods, on one hand, the FCG update accelerates the numerical convergence rate, and on the other hand, the squared hinge loss inherits the robustness of the hinge loss for classification and maintains the theoretical benefits of the square loss in regression. The ADMM solver with guaranteed fast convergence then provides an efficient implementation for the proposed boosting method. We conduct both theoretical analysis and numerical verification to show the outperformance of the proposed method. Theoretically, a fast learning rate of order O((m/logm) -1/2 ) is proved under certain standard assumptions, where m is the size of sample set. Numerically, a series of toy simulations and real data experiments are carried out to verify the developed theory., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Recently, the spherical data processing has emerged in many applications and attracted a lot of attention. Among all the methods for dealing with the spherical data, the spherical neural networks (SNNs) method has been recognized as a very efficient tool due to SNNs possess both good approximation capability and spacial localization property. For better localized approximant, weighted approximation should be considered since different areas of the sphere may play different roles in the approximation process. In this paper, using the minimal Riesz energy points and the spherical cap average operator, we first construct a class of well-localized SNNs with a bounded sigmoidal activation function, and then study their approximation capabilities. More specifically, we establish a Jackson-type error estimate for the weighted SNNs approximation in the metric of L(p) space for the well developed doubling weights., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for convex consensus optimization. However, to the behaviors or consensus nonconvex optimization, our understanding is more limited. When we lose convexity, we cannot hope that our algorithms always return global solutions though they sometimes still do. Somewhat surprisingly, the decentralized consensus algorithms, DGD and Prox-DGD, retain most other properties that are known in the convex setting. In particular, when diminishing (or constant) step sizes are used, we can prove convergence to a (or a neighborhood of) consensus stationary solution under some regular assumptions. It is worth noting that Prox-DGD can handle nonconvex nonsmooth functions if their proximal operators can be computed. Such functions include SCAD, MCP, and $\ell _q$ quasi-norms, $q\in [0,1)$. Similarly, Prox-DGD can take the constraint to a nonconvex set with an easy projection. To establish these properties, we have to introduce a completely different line of analysis, as well as modify existing proofs that were used in the convex setting. [ABSTRACT FROM AUTHOR]

Abstract: Finding the sparset solution of an underdetermined system of linear equations y=Ax has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the most efficient and important classes of algorithms. This is mainly due to their low computational complexities, especially for large scale applications. The aim of this paper is to provide guarantees on the global convergence of a wide class of iterative thresholding algorithms. Since the thresholds of the considered algorithms are set adaptively at each iteration, we call them adaptively iterative thresholding (AIT) algorithms. As the main result, we show that as long as A satisfies a certain coherence property, AIT algorithms can find the correct support set within finite iterations, and then converge to the original sparse solution exponentially fast once the correct support set has been identified. Meanwhile, we also demonstrate that AIT algorithms are robust to the algorithmic parameters. In addition, it should be pointed out that most of the existing iterative thresholding algorithms such as hard, soft, half and smoothly clipped absolute deviation (SCAD) algorithms are included in the class of AIT algorithms studied in this paper. [Copyright &y& Elsevier]