Related papers: Asymptotic Learning on Bayesian Social Networks
The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes to the probability distributions represented by BNs. One application scenario is the process of knowledge acquisition of an observer interacting with a system. In…
Non-Bayesian social learning is a framework for distributed hypothesis testing aimed at learning the true state of the environment. Traditionally, the agents are assumed to receive observations conditioned on the same true state, although…
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
This paper studies asynchronous message passing (AMP), a new paradigm for applying neural network based learning to graphs. Existing graph neural networks use the synchronous distributed computing model and aggregate their neighbors in each…
We study the Bayesian model of opinion exchange of fully rational agents arranged on a network. In this model, the agents receive private signals that are indicative of an unkown state of the world. Then, they repeatedly announce the state…
Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed…
Many socioeconomic phenomena, such as technology adoption, collaborative problem-solving, and content engagement, involve a collection of agents coordinating to take a common action, aligning their decisions to maximize their individual…
Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs…
We study continuous-time consensus dynamics for multi-agent systems with undirected switching interaction graphs. We establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of…
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical"$ $ graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works…
In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for…
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
Data-driven graph learning models a network by determining the strength of connections between its nodes. The data refers to a graph signal which associates a value with each graph node. Existing graph learning methods either use simplified…
An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network…
Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…
In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe…