“Modélisation stochastique et réseaux complexes : application à la dynamique d’opinions dans les réseaux sociaux”
21 Octobre 2022
Avignon Université, Campus Hannah Arendt, AT01
Cette journée du GdR et du ANR Nicetweet a pour objectif de réunir la communauté scientifique française dans le domaine de la Modélisation stochastique et des réseaux complexes avec comme domaine d’application l’étude des dynamiques d’opinion dans les réseaux sociaux.
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Cette Journée sera seulement en présentiel.
9h15-9h30 : Accueil
9h30-10h00 : Nicolas Gast (INRIA Grenoble)
Title: Computing the bias of mean field approximation (slides)
Abstract: Mean field approximation is a widely used technique to study stochastic systems composed of many interacting objects with applications from theoretical physics to biological models and artificial intelligence. In computer science, mean field approximation has been successfully used to analyze the performance of many distributed algorithms, including allocation strategies in server farms, caching algorithms and wireless protocols. In a first part, I will introduce the key concepts behind the classical mean field approximation. By using some of the classical models, I will show how the method can be applied and give ideas of where it cannot be applied. In the second part, I will talk about more recent results: first, how accurate is the approximation for finite systems, and second, how to use this result to define a refined approximation to make it applicable for a few tens of objects.
10h00-10h30 : Konstantin Avratchenkov (INRIA Sophia-Antipolis)
Title: Dynamic social learning under graph constraints (slides)
Abstract: We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively 𝛼-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. There is also an interesting and useful connection with population games and replicator dynamics. We show that for 𝛼 > 0, the asymptotic outcome concentrates around the optimum in a certain limiting sense when ‘annealed’ by letting 𝛼 → ∞ slowly. This is a joint work with V. Borkar, S. Moharir and S. Shah.
10h30-11h00 : pause café
11h-11h30 : Anastasios Giovanidis (LIP6)
Title: Ranking Online Social Users by their Influence (slides)
Abstract: In this talk I will present an original mathematical model to analyse the diffusion of posts within a generic online social platform. The main novelty is that each user is not simply considered as a node on the social graph, but is further equipped with his/her own Wall and Newsfeed, and has his/her own individual self-posting and re-posting activity. The influence probabilities to find posts from a given user on the Wall and Newsfeed of any other are derived in closed form as the solution of a linear system of equations. Using the solution, a new measure of per-user influence over the entire network can be defined, the Ψ-score. This score combines the user position on the graph with the user (re-)posting activity. In the homogeneous case where all users have the same activity rates, it is proved that the Ψ-score is equal to PageRank. Two algorithms to derive the new score for large graphs will be presented, one that allows for detailed scores and byproducts and another much faster that has a runtime of the same order as PageRank’s power iteration. The Ψ-score is compared against the empirical influence measured from very large data traces (Twitter, Weibo) and the results illustrate that it can accurately rank influencers with asymmetric (re-)posting activity for real world platforms. Furthermore, we will show how the balance equations from our model can be adapted to describe the spread of opinions in social networks, and we will apply this to an example case from the political arena, using Tweets from the 2017 presidential elections in France. Using our framework we can formulate an optimisation problem that outputs optimal recommendations in order to mitigate the serious problem of echo chambers in social platforms.
11h30-12h : Paolo Frasca (GIPSA)
Title: The closed loop between opinion formation and personalised recommendations (slides)
Abstract: This talk will present a mathematical model of the interaction between a social media user and an online platform. The model is mathematically treatable and is able to highlight the potential drawbacks of personalised recommendations. In online platforms, recommender systems are responsible for directing users to relevant content. In order to enhance the users’ engagement, recommender systems adapt their output to the reactions of the users, who are in turn affected by the recommended content. In this work, we study a tractable analytical model of a user that interacts with an online news aggregator, with the purpose of making explicit the feedback loop between the evolution of the user’s opinion and the personalised recommendation of content. We find that personalised recommendations markedly affect the evolution of opinions and favor the emergence of more extreme ones: the intensity of these effects is inherently related to the effectiveness of the recommender. We also show that by tuning the amount of randomness in the recommendation algorithm, one can seek a balance between the effectiveness of the recommendation system and its impact on the opinions.
12h00 – 14h00 : pause repas
14h00-15h00 : Ulrich Krause (Univ. Bremen)
Title: Opinion Dynamics: Questions, Answers, and further Questions (slides)
Abstract: Opinion dynamics is a fertile field with applications to such diverse topics as expert systems, dissemination of cultures, flocking of birds or robots, sensor networks, data segmentation. The talk starts with simple cases of a few interacting agents and introduces the concept of opinion formation under bounded confidence. For a more general mathematical model the following questions will be addressed:
- Which conditions guarantee convergence of the opinions to a consensus?
- How fast is the convergence and can consensus be reached in finite time?
- What can be said if there is no convergence to consensus?
- Will there be a stable fragmentation of opinions into consent and dissent?
For the answers given by various theorems two assumptions considering the interactions of agents play a major role: The principle of the third agent and the block intensity rule.
The results obtained by using these assumptions hold true not only for scalar opinions but also for higher dimensionsional ones. Though much progress has been made in recent years by researchers across the world and coming from quite different disciplines there are still many open questions considering opinion dynamics under bounded confidence. The following fundamental questions are for example still open
- When will consensus be reached in case different agents act with different confidence levels?
- How does the formation of consensus depend on the parameter of the (uniform) confidence level?
15h00-15h30 : pause café
15h30-16h00 : Vineeth VARMA (CRAN)
Title: Stochastic modeling and analysis of adaptive voter models (slides)
Abstract: Since the works of Liggett, the voter model (VM) is probably one of the most analyzed frameworks modeling social interactions. Numerous extensions and refinements have been proposed including the adaptive framework in which the graph co-evolves with the agent spins (opinions). In contrast to most existing works which look at rewiring processes for the graph evolution, we allow for three independent stochastic processes that describe the spin flip (opinion change), link creation and link breaking. Additionally we look at several link-creation rules inspired by social interactions which result in completely different dynamics and equilibria.
16h00-16h30 : C. MORARESCU (Univ. Lorraine)
Title: A hybrid model of opinion dynamics with memory-based connectivity (slides)
Abstract: Given a social network where the individuals know the identity of the other members, we present a model of opinion dynamics where the connectivity among the individuals depends on both their current and past opinions. Thus, their interactions are not only based on the present states but also on their past relationships. The model is a multi-agent system with active or inactive pairwise interactions depending on auxiliary state variables filtering the instantaneous opinions, thereby taking the past experience into account. When an interaction is (de)activated, a jump occurs, leading to a hybrid model. The proven stability properties ensure that opinions converge to local agreements/clusters as time grows. Simulation results are provided to illustrate the theoretical guarantees.
16h30-17h00 : Pierre Henri Morand (AU)
Title: Empirical validation of opinion dynamics models.
Abstract: While the theoretical literature on opinion dynamics in social networks is extremely abundant (and mobilizes conceptual tools from many academic disciplines), empirical approaches remain rare. Yet, their aim is to validate the chosen modeling hypotheses, to compare the theoretical results obtained with the observed evidences. The objective of this panel (/ talk) is to discuss some of the different empirical methods, their contributions and their limits.
17h00-17h30 : fin