Distributed online expectation-maximization algorithm for Poisson mixture model

Traffic flow data, in the form of multiple time series of aggregated traffic volume observed from various vehicle detector stations, are investigated as a motivating example. By the very nature of the traffic volume observations, we model the traffic volume data from each station by a Poisson mixture model. We then propose a distributed online expectation-maximization algorithm to fit the traffic volume data under the Poisson mixture model, with the results to be used to make inference about the population attributes of the traffic flows. Apart from the finite mixture Poisson model, two forms of infinite mixture Poisson – Poisson-inverse-Gaussian model and Poisson-Gamma model – are specifically considered and analyzed in detail. Simulation study and real data analysis are also undertaken to confirm the theoretical properties that we have derived for the proposed distributed online expectation-maximization algorithms.