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A Min‐Max conditional covariance algorithm for structure learning of Gaussian graphical models
Author(s) -
Gao Wei,
Ye Wenna
Publication year - 2019
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11395
Subject(s) - covariance , graphical model , algorithm , gaussian , consistency (knowledge bases) , mathematics , conditional independence , computer science , conditional variance , artificial intelligence , statistics , econometrics , volatility (finance) , physics , quantum mechanics , autoregressive conditional heteroskedasticity
The Gaussian graphical models provide a useful statistical framework for analyzing the linear dependence among continuous random variables. In this paper, we propose a learning algorithm to reconstruct the graph structure of the high‐dimensional Gaussian random vector from observation data. The algorithm is constituted by two conditional covariance threshold tests to identify the presence of the edges. We present a procedure called Min‐Max conditional covariance to estimate the test statistics and prove that the proposed algorithm has high computational efficiency and asymptotic consistency. The performance of the proposed methods is confirmed through numerical simulations on synthetic data and through a real‐world application to foreign exchange data.