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We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.
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This content will become publicly available on February 10, 2026
Large Precision Matrix Estimation with Unknown Group Structure
The estimation of large precision matrices is crucial in modern multivariate analysis. Traditional sparsity assumptions, while useful, often fall short of accurately capturing the dependencies among features. This article addresses this limitation by focusing on precision matrix estimation for multivariate data characterized by a flexible yet unknown group structure. We introduce a novel approach that begins with the detection of this unknown group structure, clustering features within the low-dimensional space defined by the leading eigenvectors of the sample covariance matrix. Following this, we employ group-wise multivariate response linear regressions, guided by the identified group memberships, to estimate the precision matrix. We rigorously establish the theoretical foundations of our proposed method for both group detection and precision matrix estimation. The superior numerical performance of our approach is demonstrated through comprehensive simulation experiments and a comparative analysis with established methods in the field. Additionally, we apply our method to a real breast cancer dataset, showcasing its practical utility and effectiveness. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
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- PAR ID:
- 10588572
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Journal of the American Statistical Association
- ISSN:
- 0162-1459
- Page Range / eLocation ID:
- 1 to 24
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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