Localizing differentially evolving covariance structures via scan statistics
Authors:
Ronak Mehta, Hyunwoo J. Kim, Shulei Wang, Sterling C. Johnson, Ming Yuan and Vikas Singh
Journal:
Quart. Appl. Math. 77 (2019), 357-398
MSC (2010):
Primary 53B20, 53B21, 62F03, 62P10; Secondary 62H30, 62H10
DOI:
https://doi.org/10.1090/qam/1522
Published electronically:
December 17, 2018
MathSciNet review:
3932963
Full-text PDF
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Additional Information
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.
References
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References
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Additional Information
Ronak Mehta
Affiliation:
Department of Computer Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email:
ronakrm@cs.wisc.edu
Hyunwoo J. Kim
Affiliation:
Department of Computer Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706
MR Author ID:
1145369
Email:
hwkim@cs.wisc.edu
Shulei Wang
Affiliation:
Department of Statistics, University of Wisconsin-Madison, Madison, Wisconsin 53706 and Department of Statistics, Columbia University, New York, New York 10027
MR Author ID:
1244471
Email:
shulei@stat.wisc.edu
Sterling C. Johnson
Affiliation:
Alzheimer’s Disease Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53792
MR Author ID:
1145335
Email:
scj@medicine.wisc.edu
Ming Yuan
Affiliation:
Department of Statistics, Columbia University, New York, New York 10027
MR Author ID:
674009
Email:
ming.yuan@columbia.edu
Vikas Singh
Affiliation:
Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, Wisconsin 53706
MR Author ID:
766120
Email:
vsingh@biostat.wisc.edu
Received by editor(s):
March 2, 2018
Received by editor(s) in revised form:
September 23, 2018
Published electronically:
December 17, 2018
Additional Notes:
This research was supported in part by NIH grants R01 AG040396, AG021155, EB022883 and NSF grants DMS 1265202 and CAREER award 1252725. The authors were also supported by the UW Center for Predictive Computational Phenotyping (via BD2K award AI117924) and the Wisconsin Alzheimer’s Disease Research Center (AG033514).
The first author was supported by a fellowship via training grant award T32LM012413.
The second author’s work on this project was performed at UW-Madison in 2017, before joining Amazon.
The fifth author was supported by NSF grant DMS-1803450.
Article copyright:
© Copyright 2018
Brown University
