Event
Sean Lawlor, McGill University
Friday, November 4, 2016 15:30
Burnside Hall
room 1205, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Time-Varying Mixtures of Markov Chains: An Application to Traffic Modeling.
Time-varying mixture models are useful for representing complex, dynamic distributions. Components in the mixture model can appear and disappear, and persisting components can evolve. This allows great flexibility in streaming data applications where the model can be adjusted as new data arrives. Fitting a mixture model, especially when the model order varies with time, with computational guarantees which can meet real-time requirements is difficult with existing algorithms. Multiple issues exist with existing approximate inference methods ranging from estimation of the model order to random restarts due to the ability to converge to different local minima. Monte-Carlo methods can be used to estimate the parameters of the generating distribution and estimate the model order, but when the distribution of each mixand has a high-dimensional parameter space, they suffer from the curse of dimensionality and can take far too long to converge. This paper proposes a generative model for time-varying mixture models, tailored for mixtures of discrete-time Markov chains. A novel, deterministic inference procedure is introduced and is shown to be suitable for applications requiring real-time estimation. The method is guaranteed to converge to a local maximum of the posterior likelihood at each time step with a computational complexity which is low enough for real-time applications. As a motivating application, we model and predict traffic patterns in a transportation network. Experiments illustrate the performance of the scheme and offer insights regarding tuning of the parameters of the algorithm. The experiments also investigate the predictive power of the fitted model compared to less complex models and demonstrate the superiority of the mixture model approach for prediction of traffic routes in real data.