Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition

Differential Games of Competition in Online Content Diffusion

Access to online contents represents a large share of the Internet traffic. Most such contents are multimedia items which are user-generated, i.e., posted online by the contents' owners. In this paper we focus on how those who provide contents can leverage online platforms in order to profit from their large base of potential viewers. Actually, platforms like Vimeo or YouTube provide tools to accelerate the dissemination of contents, i.e., recommendation lists and other re-ranking mechanisms. Hence, the popularity of a content can be increased by paying a cost for advertisement: doing so, it will appear with some priority in the recommendation lists and will be accessed more frequently by the platform users. Ultimately, such acceleration mechanism engenders a competition among online contents to gain popularity. In this context, our focus is on the structure of the acceleration strategies which a content provider should use in order to optimally promote a content given a certain daily budget. Such a best response indeed depends on the strategies adopted by competing content providers. Also, it is a function of the potential popularity of a content and the fee paid for the platform advertisement service. We formulate the problem as a differential game and we solve it for the infinite horizon case by deriving the structure of certain Nash equilibria of the game

Online Multi-Agent Decentralized Byzantine-robust Gradient Estimation

In this paper, we propose an iterative scheme for distributed Byzantineresilient estimation of a gradient associated with a black-box model. Our algorithm is based on simultaneous perturbation, secure state estimation and two-timescale stochastic approximations. We also show the performance of our algorithm through numerical experiments

Online Learning with Adversaries: A Differential-Inclusion Analysis

We introduce an observation-matrix-based framework for fully asynchronous online Federated Learning (FL) with adversaries. In this work, we demonstrate its effectiveness in estimating the mean of a random vector. Our main result is that the proposed algorithm almost surely converges to the desired mean $\mu.$ This makes ours the first asynchronous FL method to have an a.s. convergence guarantee in the presence of adversaries. We derive this convergence using a novel differential-inclusion-based two-timescale analysis. Two other highlights of our proof include (a) the use of a novel Lyapunov function to show that $\mu$ is the unique global attractor for our algorithm's limiting dynamics, and (b) the use of martingale and stopping-time theory to show that our algorithm's iterates are almost surely bounded.Comment: 6 pages, 2 figure

Posting behavior in Social Networks and Content Active Filtering

International audience—In this paper, we have two objectives: First we model the posting behavior in Social Networks in topics which have negative externalities, and the second objective is to propose content active filtering in order to increase content diversity. By negative externalities, we mean that when the quantity of posted contents about some topic increases the popularity of posted contents decreases. We introduce a dynamical model to describe the posting behavior of users taking into account these externalities. Our model is based on stochastic approximations and sufficient conditions are provided to ensure its convergence to a unique rest point. We provide a close form of this rest point. Content Active Filtering (CAF) are actions taken by the administrator of the Social Network in order to promote some objectives related to the quantity of contents posted in various topics. As objective of the CAF we shall consider maximizing the diversity of posted contents

Controlling the Katz-Bonacich Centrality in Social Network: Application to gossip in Online Social Networks

International audienceRecent papers studied the control of spectral centrality measures of a network by manipulating the topology of the network. We extend these works by focusing on a specific spectral centrality measure, the Katz-Bonacich centrality. The optimization of the Katz-Bonacich centrality using a topological control is called the Katz-Bonacich optimization problem. We first prove that this problem is equivalent to a linear optimization problem. Thus, in the context of large graphs, we can use state of the art algorithms. We provide a specific applications of the Katz-Bonacich centrality minimization problem based on the minimization of gossip propagation and make some experiments on real networks