Modeling nonlinearity in multi-dimensional dependent data

Qiuyi Han, Jie Ding, Edoardo Airoldi, Vahid Tarokh

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

1 Scopus citations

Abstract

Given massive data that may be time dependent and multi-dimensional, how to efficiently explore the underlying functional relationships across different dimensions and time lags? In this work, we propose a methodology to sequentially and adaptively model nonlinear multivariate time series data. Data at each time step and dimension is modeled as a nonlinear function of past values corrupted by noise, and the underlying nonlinear function is assumed to be approximately expandable in a spline basis. We cast the modeling of data as finding a good fit representation in the linear span of multi-dimensional spline basis, and use a variant of h-penalty regularization in order to reduce the dimensionality of representation. Using adaptive filtering techniques, we design our online algorithm to automatically tune the underlying parameters based on the minimization of the regularized sequential prediction error. We demonstrate the generality and flexibility of the proposed approach on both synthetic and real-world datasets. Moreover, we analytically investigate the performance of our algorithm by obtaining bounds of the prediction errors.

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.
Pages206-210
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

Keywords

  • Adaptive Filtering
  • Group LASSO
  • Non-linear Models
  • Spline Regression
  • Time Series

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