Joint estimation of multiple graphical models from high dimensional time series

Huitong Qiu, Fang Han, Han Liu, Brian S Caffo

Research output: Contribution to journalArticle

Abstract

We consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel-based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T,n) and the dimension d can increase, we provide an explicit rate of convergence in parameter estimation. It characterizes the strength that one can borrow across different individuals and the effect of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging data illustrate the effectiveness of the method proposed.

Original languageEnglish (US)
Pages (from-to)487-504
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume78
Issue number2
DOIs
StatePublished - Mar 1 2016

Fingerprint

Multiple Models
Graphical Models
High-dimensional
Time series
Parameter Estimation
Dependent Observations
Data Dependence
Functional Magnetic Resonance Imaging
Higher Dimensions
Rate of Convergence
Vary
kernel
Experiment
Graphical models
Joint estimation
Parameter estimation

Keywords

  • Conditional independence
  • Graphical model
  • High dimensional data
  • Rate of convergence
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Joint estimation of multiple graphical models from high dimensional time series. / Qiu, Huitong; Han, Fang; Liu, Han; Caffo, Brian S.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 78, No. 2, 01.03.2016, p. 487-504.

Research output: Contribution to journalArticle

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