Distributed Learning from Interactions in Social Networks

We consider a network scenario in which agents can evaluate each other according to a score graph that models some interactions. The goal is to design a distributed protocol, run by the agents, that allows them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We show that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependencies of scores and states, we provide a relaxed probabilistic model that ultimately leads to a parameter-hyperparameter estimator amenable to distributed computation. To highlight the appropriateness of the proposed relaxation, we demonstrate the distributed estimators on a social interaction set-up for user profiling.Comment: This submission is a shorter work (for conference publication) of a more comprehensive paper, already submitted as arXiv:1706.04081 (under review for journal publication). In this short submission only one social set-up is considered and only one of the relaxed estimators is proposed. Moreover, the exhaustive analysis, carried out in the longer manuscript, is completely missing in this versio

An Empirical Bayes Approach for Distributed Estimation of Spatial Fields

In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes approach in which the spatial field is modeled as a Gaussian Process, whose mean function is described by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline

Machine Learning

Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience

Simulation based bayesian econometric inference: principles and some recent computational advances.

In this paper we discuss several aspects of simulation basedBayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluatingintegrals by simulation methods is a crucial ingredientin Bayesian inference. Next, the most popular and well-knownsimulation techniques are discussed, the Metropolis-Hastingsalgorithm and Gibbs sampling (being the most popular Markovchain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed samplingmethods: adaptive radial based direction sampling [ARDS],which makes use of a transformation to radial coordinates,and neural network sampling, which makes use of a neural network approximation to the posterior distribution ofinterest. Both methods are especially useful in cases wherethe posterior distribution is not well-behaved, in the senseof having highly non-elliptical shapes. The simulationtechniques are illustrated in several example models, suchas a model for the real US GNP and models for binary data ofa US recession indicator.