Optimal prediction of data with unknown abrupt change points

Jie Ding, Jiawei Zhou, Vahid Tarokh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We develop a novel methodology for predicting time series under unknown abrupt changes in data generating distributions. Based on Kolmogorov and Tikhomirov's e entropy, we propose a concept called e-predictability that quantifies the size of a model class and the maximal number of structural changes that allows the achievability of asymptotic optimal prediction. To predict under abrupt changes, our basic idea is to apply ϵ-net to discretize a nonparametric or parametric model class with an appropriately chosen e, and then apply a kinetic model averaging over the quantizers. Under reasonable assumptions, we prove that the average predictive performance is asymptotically as good as the oracle, i.e. when all the data generating distributions are known in advance. We show that the assumptions hold for a rather wide class of time variations. The results also address some puzzles related to the 'prediction-inference dilemma' in the context of change point analysis.

Original languageEnglish (US)
Title of host publication2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages928-932
Number of pages5
ISBN (Electronic)9781509059904
DOIs
StatePublished - Mar 7 2018
Externally publishedYes
Event5th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Montreal, Canada
Duration: Nov 14 2017Nov 16 2017

Publication series

Name2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings
Volume2018-January

Other

Other5th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017
CountryCanada
CityMontreal
Period11/14/1711/16/17

Bibliographical note

Funding Information:
This work is supported by Defense Advanced Research Projects Agency (DARPA) grant numbers W911NF-14-1-0508 and N66001-15-C-4028.

Keywords

  • Abrupt changes
  • Kinetic prediction
  • Kolmogorov and Tikhomirov ϵ-entropy
  • Optimal data prediction
  • Scoring rule
  • Time series
  • Tracking

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