Related papers: Statistical inference versus mean field limit for …
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…
Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions is essential for targeted recommendations that could improve our health and…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
Optimization of human-AI teams hinges on the AI's ability to tailor its interaction to individual human teammates. A common hypothesis in adaptive AI research is that minor differences in people's predisposition to trust can significantly…
In arXiv:1301.6911, Cerf and Gorny constructed a model of self-organized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising Curie-Weiss model. The fluctuations of the magnetization of this…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
This paper investigates the model for pedestrian flow firstly proposed in [Cristiani et al., DOI:10.1137/140962413]. The model assumes that each individual in the crowd moves in a known domain, aiming at minimizing a given cost functional.…
Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$…
Finding a basis/coordinate system that can efficiently represent an input data stream by viewing them as realizations of a stochastic process is of tremendous importance in many fields including data compression and computational…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the…
Agents can achieve effective interaction with previously unknown other agents by maintaining beliefs over a set of hypothetical behaviours, or types, that these agents may have. A current limitation in this method is that it does not…
Principled accountability for autonomous decision-making in uncertain environments requires distinguishing intentional outcomes from negligent designs from actual accidents. We propose analyzing the behavior of autonomous agents through a…
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…
Mean-field reinforcement learning (MF-RL) scales multi-agent RL to large populations by reducing each agent's dependence on others to a single summary statistic -- the mean action. However, this reduction requires every agent to act at…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…