Social Sensing With Minimal Resources: Profiling Agents by Simply Knowing How to Count

The focus of this paper is on profiling an ensemble of agents-where profiling refers to estimating their probability of taking different courses of actions, under different states of nature-by exploiting a recorded time series of actions made in the past, a problem relevant, among others, for modern social network applications. Agents' actions are coupled by the underlying state of nature, but are otherwise independent. This notwithstanding, agents' profiling is possible and effective, provided that some mild assumption on the agents' behaviors is met. The nonparametric profiling is performed by computing the agents' conditional type by aggregating actions that are believed to be taken under the same state of nature. The time-varying state of nature is unknown and must be inferred, and the effect of such uncertainty on the otherwise classical-type estimator is of central interest here. It is shown that a simple counting procedure leads to an asymptotically strong consistent profiling estimator in the limit of large number of agents and large number of per-agent observations. Analytical formulas are provided for finite values of both of these two parameters, and simulations are presented.