Related papers: Mean-Field Analysis of Latent Variable Process Mod…
In this paper we study the cooperative behavior of agents playing the Prisoner's Dilemma game in random scale-free networks. We show that the survival of cooperation is enhanced with respect to random homogeneous graphs but, on the other…
Dynamic network data have become ubiquitous in social network analysis, with new information becoming available that captures when friendships form, when corporate transactions happen and when countries interact with each other. Flexible…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…
Latent space is one of the key concepts in generative AI, offering powerful means for creative exploration through vector manipulation. However, diffusion models like Stable Diffusion lack the intuitive latent vector control found in GANs,…
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system…
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…
Large agent networks are abundant in applications and nature and pose difficult challenges in the field of multi-agent reinforcement learning (MARL) due to their computational and theoretical complexity. While graphon mean field games and…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the…
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The…
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a…
We present a latent variable model for classification that provides a novel probabilistic interpretation of neural network softmax classifiers. We derive a variational objective to train the model, analogous to the evidence lower bound…
We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of…