Date: 2016-11-04

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Piché: Analysis of survival data arising from different groups, whereby the data in each group is scarce, but abundant overall, is a common issue in applied statistics. Bayesian nonparametrics are tools of choice to handle such datasets given their ability to share information across groups. In this presentation, we will compare three popular Bayesian nonparametric methods on the modeling of survival functions coming from related heterogeneous groups. Specifically, we will first compare the modeling accuracy of the Dirichlet process, the hierarchical Dirichlet process, and the nested Dirichlet process on simulated datasets of different sizes, where groups differ in shape or in expectation, and finally we will compare the models on real world injury datasets.

Lawlor: 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.

Speaker

Sean Lawlor is a Doctoral Candidate in Electrical Engineering from the Department of Electrical and Computer Engineering, McGill University

Alexandre Piché is a MSc student in our Department. His supervisor is Russell Steele.