for large memory at each agent might be practically infeasible owing to the ad-hoc nature and limited sensing, computation and storage capabilities of agents in a networked setup.\
Thus, in both of the schemes above, specifically in the case which involves estimating a high-dimensional parameter, it might not be practical to estimate the entire parameter at each agent. In such a high-dimensional parameter estimation scheme, it is highly favorable to estimate only a few entries of the parameter based on the requirements of each agent, which could potentially reduce the dimensions of messages being exchanged in the network thereby reducing the implementation complexity considerably.\

Connections with Distributed Optimization {#subsec:dist_opt}
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In principle, distributed stochastic optimization, with each node interested in a few entries of the optimization variable, is more general than the distributed estimation/random fields setup studied here. Indeed, one recovers the setup here with specializing the cost functions to be quadratic. However, this is true only for a very generic formulation of distributed stochastic optimization, where no strong convexity is assumed, each node is interested in a subset of the variable of interest, and the gradient (first order) information is subject to noise, and the underlying network is random. 