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LOCALIZING DIFFERENTIALLY EVOLVING COVARIANCE STRUCTURES VIA SCAN STATISTICS.

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This study introduces a new method to detect group differences in feature trends using graphical models. It identifies specific feature subsets showing significant variations across conditions, outperforming full-model analyses.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Analysis

Background:

  • Coupled graphical models analyze longitudinal data from related sources.
  • Detecting group-level differences in feature trends is challenging due to small effect sizes.
  • Identifying differential signals within feature subsets is crucial for nuanced analysis.

Purpose of the Study:

  • To develop a parametric model for estimating trends in SPD matrices based on covariates.
  • To generalize scan statistics for graph structures to identify feature subsets with group-wise differences.
  • To analyze group-level differences in temporal dependency structures.

Main Methods:

  • Parametric modeling of SPD matrices trends.
  • Generalization of scan statistics to graph structures for subset searching.
  • Theoretical analysis of Family Wise Error Rate (FWER) and error bounds.

Main Results:

  • Identified overlapping groups of US states based on baby name and drug usage trends.
  • Discovered scientifically relevant group differences in Alzheimer's disease risk cohort.
  • Demonstrated that subset analysis reveals significant differences missed by full-graph models.

Conclusions:

  • The proposed method effectively detects group-wise differences in feature trends within specific subsets.
  • This approach enhances the identification of subtle yet significant patterns across disparate conditions.
  • The findings have implications for analyzing complex datasets in social science and healthcare.