Post-Selection Inference for Segmentation Methods in Changepoint Detection

• Activity Number: 510 - New Developments in Time Series Analysis and Change Point Detection
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Sangwon Hyun* and Kevin Lin and Max G'sell and Ryan Tibshirani
• Companies: Carnegie Mellon University and Carnegie Mellon University, Statistics Department and Carnegie Mellon University and Carnegie Mellon University
• Keywords: Changepoint detection ; Post-selection inference ; Binary segmentation

Abstract

There is a recent body of literature on methods for valid post-selection inference on model quantities after having applied adaptive algorithms to recover that model. In this paper, we present the application of post-selection inference tools developed in Lee et al (2016), Tibshirani et al (2016), and Fithian et al (2014) for segmentation-type algorithms for detecting changepoints from data. The algorithms discussed include standard/circular/wild binary segmentation and scan statistics. The main contributions of this work include characterizing polyhedral selection events of segmentation algorithms, specifying several tests types -- targeted tests of user-defined model quantities and model goodness of fit tests -- and numerical experimentation on real and synthetic data to compare against comparable fused lasso inference tools developed in Hyun et al (2016). In particular, a careful application of the tools to DNA copy number variation (CNV) data is presented to demonstrate the usefulness in a scientific application.