Related papers: Mean-Field Approximation of Dynamics on Networks
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks, and the internet of things. Due to bandwidth…
In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or,…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…
We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…
This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep…
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 typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion or disease should be modelled over a hypergraph rather than a standard graph. The use of hyperedges…
Reckoning of pairwise dynamical correlations significantly improves the accuracy of mean-field theories and plays an important role in the investigation of dynamical processes on complex networks. In this work, we perform a nonperturbative…
Weight distribution largely impacts the epidemic spreading taking place on top of networks. This paper studies a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The…
In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study…
Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a…
Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These…
Studies on social networks have proved that endogenous and exogenous factors influence dynamics. Two streams of modeling exist on explaining the dynamics of social networks: 1) models predicting links through network properties, and 2)…
For models whose evolution takes place on a network it is often necessary to augment the mean-field approach by considering explicitly the degree dependence of average quantities (heterogeneous mean-field). Here we introduce the degree…