標(biāo)題：A mean-field opinion model on hypergraphs: From modeling to inference
報(bào)告時(shí)間：2024年06月21日（星期五）15:30-16:30
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院二樓會(huì)議室
主講人：褚偉奇
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)介：
The perspectives and opinions of people change and spread through social interactions on a daily basis. In the study of opinion dynamics, one often models social entities (such as Facebook accounts) as nodes and their relationships (such as friendships) as edges, and examines how opinions evolve as dynamical processes on networks, including graphs, hypergraphs, multi-layer networks, etc. In the first part of my talk, I will introduce a model of opinion dynamics and derive its mean-field limit as the total number of agents goes to infinity. The mean-field opinion density satisfies a kinetic equation of Kac type. We prove properties of the solution of this equation, including nonnegativity, conservativity, and steady-state convergence. The parameters of such opinion models play a nontrivial role in shaping the dynamics and can also be in the form of functions. In reality, it is often impractical to measure these parameters directly. In the second part of the talk, I will approach the problem from an inverse perspective and present how to infer the parameters from limited partial observations. I will provide sufficient conditions of measurement for two scenarios, such that one is able to identify the parameters uniquely. I will also provide a numerical algorithm of the inference when the data set only has a limited number of data points.
主講人簡(jiǎn)介：
褚偉奇，2014年學(xué)士畢業(yè)于北京大學(xué)，2019年博士畢業(yè)于美國(guó)賓夕法尼亞州立大學(xué)，2019-2023年在美國(guó)加州大學(xué)洛杉磯分校任訪(fǎng)問(wèn)助理教授，于2023年入職美國(guó)馬薩諸塞大學(xué)-阿默斯特分校任助理教授。研究方向?yàn)槎喑叨冉?，?shù)據(jù)科學(xué)，動(dòng)力系統(tǒng)和網(wǎng)絡(luò)科學(xué)。
