Inference for Heterogeneous Graphical Models using Doubly High-Dimensional Linear-Mixed Models
arxiv(2024)
摘要
Motivated by the problem of inferring the graph structure of functional
connectivity networks from multi-level functional magnetic resonance imaging
data, we develop a valid inference framework for high-dimensional graphical
models that accounts for group-level heterogeneity. We introduce a
neighborhood-based method to learn the graph structure and reframe the problem
as that of inferring fixed effect parameters in a doubly high-dimensional
linear mixed model. Specifically, we propose a LASSO-based estimator and a
de-biased LASSO-based inference framework for the fixed effect parameters in
the doubly high-dimensional linear mixed model, leveraging random matrix theory
to deal with challenges induced by the identical fixed and random effect design
matrices arising in our setting. Moreover, we introduce consistent estimators
for the variance components to identify subject-specific edges in the inferred
graph. To illustrate the generality of the proposed approach, we also adapt our
method to account for serial correlation by learning heterogeneous graphs in
the setting of a vector autoregressive model. We demonstrate the performance of
the proposed framework using real data and benchmark simulation studies.
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