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Activity Number: 611
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #308322
Title: Regression Trees and Forests for Nonhomogeneous Poisson Process
Author(s): Walid Mathlouthi*+ and Denis Larocque and Marc Fredette
Companies: and HEC Montréal and HEC Montreal
Keywords: Non-homogeneous Poisson Process ; Random Forests ; Recurrent events

Non-homogeneous Poisson processes (NHPP), for which the rate function varies over time, constitute a class of a very versatile model for modeling recurrent events. The existing tree-based methods for count and Poisson data were developed under the assumption of a constant rate function. We propose tree and random forest methods for NHPP. The proposed tree splitting criterion is based on the observed log-likelihood of a model with piecewise constant rate function over pre-specified intervals. The first approach builds a random forest using an aggregation of many trees built with the same intervals. The second approach builds the forest by varying the number, length, and position of the intervals from one tree to another. This produces a smooth estimate of the rate compared to the piecewise constant estimation of the first approach. The results from a simulation study, showing that the proposed models work very well, and an application with real data will be presented.

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