Localizing differentially evolving covariance structures via scan statistics

Ronak Mehta, Hyun Woo Kim, Shulei Wang, Sterling C. Johnson, Ming Yuan, Vikas Singh

Research output: Contribution to journalArticle

Abstract

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant groupwise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. Evaluating on U.S. census data, we identify groups of states with cultural and legal overlap related to baby name trends and drug usage. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.

Original languageEnglish
Pages (from-to)357-398
Number of pages42
JournalQuarterly of Applied Mathematics
Volume77
Issue number2
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes

Fingerprint

Scan Statistic
Covariance Structure
Statistics
Graph Partition
Familywise Error Rate
Distinct
Effect Size
Alzheimer's Disease
Subset
Census
Graphical Models
Risk Factors
Model Analysis
Graph in graph theory
Parametric Model
Error Bounds
Covariates
Overlap
Drugs
Generalise

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Localizing differentially evolving covariance structures via scan statistics. / Mehta, Ronak; Kim, Hyun Woo; Wang, Shulei; Johnson, Sterling C.; Yuan, Ming; Singh, Vikas.

In: Quarterly of Applied Mathematics, Vol. 77, No. 2, 01.01.2019, p. 357-398.

Research output: Contribution to journalArticle

Mehta, Ronak ; Kim, Hyun Woo ; Wang, Shulei ; Johnson, Sterling C. ; Yuan, Ming ; Singh, Vikas. / Localizing differentially evolving covariance structures via scan statistics. In: Quarterly of Applied Mathematics. 2019 ; Vol. 77, No. 2. pp. 357-398.
@article{4414f36160aa419bb2183783a6fb1395,
title = "Localizing differentially evolving covariance structures via scan statistics",
abstract = "Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant groupwise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. Evaluating on U.S. census data, we identify groups of states with cultural and legal overlap related to baby name trends and drug usage. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.",
author = "Ronak Mehta and Kim, {Hyun Woo} and Shulei Wang and Johnson, {Sterling C.} and Ming Yuan and Vikas Singh",
year = "2019",
month = "1",
day = "1",
doi = "10.1090/qam/1522",
language = "English",
volume = "77",
pages = "357--398",
journal = "Quarterly of Applied Mathematics",
issn = "0033-569X",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - Localizing differentially evolving covariance structures via scan statistics

AU - Mehta, Ronak

AU - Kim, Hyun Woo

AU - Wang, Shulei

AU - Johnson, Sterling C.

AU - Yuan, Ming

AU - Singh, Vikas

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant groupwise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. Evaluating on U.S. census data, we identify groups of states with cultural and legal overlap related to baby name trends and drug usage. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.

AB - Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant groupwise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. Evaluating on U.S. census data, we identify groups of states with cultural and legal overlap related to baby name trends and drug usage. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.

UR - http://www.scopus.com/inward/record.url?scp=85063666529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063666529&partnerID=8YFLogxK

U2 - 10.1090/qam/1522

DO - 10.1090/qam/1522

M3 - Article

VL - 77

SP - 357

EP - 398

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

SN - 0033-569X

IS - 2

ER -