  We consider the problem of estimation of a function by a system consisting of
two agents and a fusion center. The two agents collect data comprising of
samples of an independent variable and the corresponding value of a dependent
variable. The objective of the system is to collaboratively estimate the
function without any exchange of data among the members of the system. To this
end, we propose the following framework. The agents are given a set of features
using which they construct suitable function spaces to formulate and solve the
estimation problems locally. The estimated functions are uploaded to a fusion
space where an optimization problem is solved to fuse the estimates (also known
as meta-learning) to obtain the system estimate of the mapping. The fused
function is then downloaded by the agents to gather knowledge about the other
agents estimate of the function. With respect to the framework, we present the
following: a systematic construction of fusion space given the features of the
agents; the derivation of an uploading operator for the agents to upload their
estimated functions to a fusion space; the derivation of a downloading operator
for the fused function to be downloaded. Through an example on least squares
regression, we illustrate the distributed estimation architecture that has been
developed.
