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The joint graphical lasso for inverse covariance estimation across multiple classes
Author(s) -
Danaher Patrick,
Wang Pei,
Witten Daniela M.
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12033
Subject(s) - lasso (programming language) , graphical model , covariance , algorithm , regular polygon , joint (building) , mathematics , set (abstract data type) , gaussian , computer science , mathematical optimization , statistics , architectural engineering , physics , geometry , quantum mechanics , world wide web , engineering , programming language
Summary We consider the problem of estimating multiple related Gaussian graphical models from a high dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso , which borrows strength across the classes to estimate multiple graphical models that share certain characteristics, such as the locations or weights of non‐zero edges. Our approach is based on maximizing a penalized log‐likelihood. We employ generalized fused lasso or group lasso penalties and implement a fast alternating directions method of multipliers algorithm to solve the corresponding convex optimization problems. The performance of the method proposed is illustrated through simulated and real data examples.