Sparse median graphs estimation in a high-dimensional semiparametric model

Fang Han, Xiaoyan Han, Han Liu, Brian S Caffo

Research output: Contribution to journalArticle

Abstract

We propose a unified framework for conducting inference on complex aggregated data in high-dimensional settings. We assume the data are a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.

Original languageEnglish (US)
Pages (from-to)1397-1426
Number of pages30
JournalAnnals of Applied Statistics
Volume10
Issue number3
DOIs
StatePublished - Sep 1 2016

Fingerprint

Median Graph
Sparse Graphs
Semiparametric Model
Numerical analysis
High-dimensional
Recovery
Robust Estimation
Numerical Analysis
Rate of Convergence
Upper bound
Estimator
Graph in graph theory
Modeling
Median
Semiparametric model
Graph
Graphics
Model

Keywords

  • Complex aggregated data
  • Graphical model
  • High-dimensional statistics
  • Median graph
  • Semiparametric model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

Cite this

Sparse median graphs estimation in a high-dimensional semiparametric model. / Han, Fang; Han, Xiaoyan; Liu, Han; Caffo, Brian S.

In: Annals of Applied Statistics, Vol. 10, No. 3, 01.09.2016, p. 1397-1426.

Research output: Contribution to journalArticle

Han, Fang ; Han, Xiaoyan ; Liu, Han ; Caffo, Brian S. / Sparse median graphs estimation in a high-dimensional semiparametric model. In: Annals of Applied Statistics. 2016 ; Vol. 10, No. 3. pp. 1397-1426.
@article{f6cd6ac4abe34ff2ab6c24cc2be4c00b,
title = "Sparse median graphs estimation in a high-dimensional semiparametric model",
abstract = "We propose a unified framework for conducting inference on complex aggregated data in high-dimensional settings. We assume the data are a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.",
keywords = "Complex aggregated data, Graphical model, High-dimensional statistics, Median graph, Semiparametric model",
author = "Fang Han and Xiaoyan Han and Han Liu and Caffo, {Brian S}",
year = "2016",
month = "9",
day = "1",
doi = "10.1214/16-AOAS940",
language = "English (US)",
volume = "10",
pages = "1397--1426",
journal = "Annals of Applied Statistics",
issn = "1932-6157",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

TY - JOUR

T1 - Sparse median graphs estimation in a high-dimensional semiparametric model

AU - Han, Fang

AU - Han, Xiaoyan

AU - Liu, Han

AU - Caffo, Brian S

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We propose a unified framework for conducting inference on complex aggregated data in high-dimensional settings. We assume the data are a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.

AB - We propose a unified framework for conducting inference on complex aggregated data in high-dimensional settings. We assume the data are a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.

KW - Complex aggregated data

KW - Graphical model

KW - High-dimensional statistics

KW - Median graph

KW - Semiparametric model

UR - http://www.scopus.com/inward/record.url?scp=84990898378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990898378&partnerID=8YFLogxK

U2 - 10.1214/16-AOAS940

DO - 10.1214/16-AOAS940

M3 - Article

AN - SCOPUS:84990898378

VL - 10

SP - 1397

EP - 1426

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

SN - 1932-6157

IS - 3

ER -