An “Estimate & Score Algorithm” for simultaneous pa- rameter estimation and reconstruction of missing data on social networks

Dynamic activity involving social networks often has distinctive temporal patterns that can be exploited in situations involving incomplete information. Gang rivalry networks in particular show a high degree of temporal clustering of activity associated with retaliatory behavior. A recent study of a Los Angeles gang network shows that known gang activity between rivals can be modeled as a self-exciting point process on an edge of the rivalry network. In real-life situations, data is incomplete and law-enforcement agencies may not know which gang is involved. However, even when gang activity is highly stochastic, localized excitations in parts of the known dataset can help identify gangs responsible for unsolved crimes. Previous work successfully incorporated the observed clustering in time of the data to identify gangs responsible unsolved crimes. However, the authors assumed that the parameters of the model are known, when in reality they have to be estimated from the data itself. We propose an iterative method that simultaneously estimates the parameters in the underlying point process and assigns weights to the unknown events with a directly calculable score function. The results of the estimation, weights, error propagation, convergence and runtime are presented.