Related papers: Parameter Evaluation of a Simple Mean-Field Model …

Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction…

We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…

The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…

Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

We review some not well known results about marginal log-linear models, derive some new ones and show how they might be relevant in mediation analysis within logistic regression. In particular, we elaborate on the relation between…

Network autocorrelation models are widely used to evaluate the impact of social influence on some variable of interest. This is a large class of models that parsimoniously accounts for how one's neighbors influence one's own behaviors or…

Assessing drivers' interaction capabilities is crucial for understanding human driving behavior and enhancing the interactive abilities of autonomous vehicles. In scenarios involving strong interaction, existing metrics focused on…

A primary difficulty with unsupervised discovery of structure in large data sets is a lack of quantitative evaluation criteria. In this work, we propose and investigate several metrics for evaluating and comparing generative models of…

The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended…

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

The linear-in-means model is the standard empirical model of peer effects. Using choice data and exogenous group variation, we first develop a revealed preference style test for the linear-in-means model. This test is formulated as a linear…

In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…

Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of…