Social Learning with Partial Information Sharing

This work addresses the problem of sharing partial information within social learning strategies. In traditional social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate information from private observations to form their beliefs over a set of hypotheses; second, agents combine the entirety of their beliefs locally among neighbors. Within a sufficiently informative environment and as long as the connectivity of the network allows information to diffuse across agents, these algorithms enable agents to learn the true hypothesis. Instead of sharing the entirety of their beliefs, this work considers the case in which agents will only share their beliefs regarding one hypothesis of interest, with the purpose of evaluating its validity, and draws conditions under which this policy does not affect truth learning. We propose two approaches for sharing partial information, depending on whether agents behave in a self-aware manner or not. The results show how different learning regimes arise, depending on the approach employed and on the inherent characteristics of the inference problem. Furthermore, the analysis interestingly points to the possibility of deceiving the network, as long as the evaluated hypothesis of interest is close enough to the truth

Interplay between Topology and Social Learning over Weak Graphs

We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving part. The data collected by the agents might be heterogeneous. For example, some sub-networks might intentionally generate data from a fake hypothesis in order to influence other agents. The social learning task is accomplished via a diffusion strategy where each agent: i) updates individually its belief using its private data; ii) computes a new belief by exponentiating a linear combination of the log-beliefs of its neighbors. First, we examine what agents learn over weak graphs (social learning problem). We obtain analytical formulas for the beliefs at the different agents, which reveal how the agents' detection capability and the network topology interact to influence the beliefs. In particular, the formulas allow us to predict when a leader-follower behavior is possible, where some sending agents can control the mind of the receiving agents by forcing them to choose a particular hypothesis. Second, we consider the dual or reverse learning problem that reveals how agents learned: given a stream of beliefs collected at a receiving agent, we would like to discover the global influence that any sending component exerts on this receiving agent (topology learning problem). A remarkable and perhaps unexpected interplay between social and topology learning is observed: given $H$ hypotheses and $S$ sending components, topology learning can be feasible when $H\geq S$. The latter being only a necessary condition, we examine the feasibility of topology learning for two useful classes of problems. The analysis reveals that a critical element to enable faithful topology learning is the diversity in the statistical models of the sending sub-networks.Comment: Submitted for publicatio

Programa Conectar Igualdad -Seguimiento y evaluación

El presente documento tiene por propósito presentar los lineamientos de seguimiento y evaluación del Programa CONECTAR IGUALDAD, en particular el componente de estudios especiales

Social Learning With Partial Information Sharing

This work studies the learning abilities of agents sharing partial beliefs over social networks. The agents observe data that could have risen from one of several hypotheses and interact locally to decide whether the observations they are receiving have risen from a particular hypothesis of interest. To do so, we establish the conditions under which it is sufficient to share partial information about the agents' belief in relation to the hypothesis of interest. Some interesting convergence regimes arise

Adaptation in Online Social Learning

This work studies social learning under non-stationary conditions. Although designed for online inference, traditional social learning algorithms perform poorly under drifting conditions. To mitigate this drawback, we propose the Adaptive Social Learning (ASL) strategy. This strategy leverages an adaptive Bayesian update, where the adaptation degree can be modulated by tuning a suitable step-size parameter. The learning performance of the ASL algorithm is examined by means of a steady-state analysis. It is shown that, under the regime of small step-sizes: i) consistent learning is possible; ii) and an accurate prediction of the performance can be furnished in terms of a Gaussian approximation

Social Opinion Formation Under Communication Trends

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We study the case where agents share information about only one hypothesis, namely, the trending topic, which can be randomly changing at every iteration. We show that agents can learn the true hypothesis even if they do not discuss it, at rates comparable to traditional social learning. We also show that using one's own belief as a prior for estimating the neighbors' non-transmitted beliefs might create opinion clusters that prevent learning with full confidence. This practice, however, avoids the complete rejection of the truth.Comment: Submitted for publicatio