  We consider several estimation and learning problems that networked agents
face when making decisions given their uncertainty about an unknown variable.
Our methods are designed to efficiently deal with heterogeneity in both size
and quality of the observed data, as well as heterogeneity over time
(intermittence). The goal of the studied aggregation schemes is to efficiently
combine the observed data that is spread over time and across several network
nodes, accounting for all the network heterogeneities. Moreover, we require no
form of coordination beyond the local neighborhood of every network agent or
sensor node. The three problems that we consider are (i) maximum likelihood
estimation of the unknown given initial data sets, (ii) learning the true model
parameter from streams of data that the agents receive intermittently over
time, and (iii) minimum variance estimation of a complete sufficient statistic
from several data points that the networked agents collect over time. In each
case we rely on an aggregation scheme to combine the observations of all
agents; moreover, when the agents receive streams of data over time, we modify
the update rules to accommodate the most recent observations. In every case, we
demonstrate the efficiency of our algorithms by proving convergence to the
globally efficient estimators given the observations of all agents. We
supplement these results by investigating the rate of convergence and providing
finite-time performance guarantees.
