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Title: A joint learning of multiple precision matrices with sign consistency Authors:  Yuan Huang - Yale University (United States) [presenting]
Abstract: The Gaussian graphical model is a popular tool for inferring the relationships among random variables, where the precision matrix has a natural interpretation of conditional independence. With high-dimensional data, sparsity of the precision matrix is often assumed, and various regularization methods have been applied for estimation. Under quite a few important scenarios, it is desirable to conduct the joint estimation of multiple precision matrices. In joint estimation, entries corresponding to the same element of multiple precision matrices form a group, and group regularization methods have been applied for estimation and identification of the sparsity structures. For many practical examples, it can be difficult to interpret the results when parameters within the same group have conflicting signs. To tackle this problem, we develop a regularization method for the joint estimation of multiple precision matrices. It effectively promotes the sign consistency of group parameters and hence can lead to more interpretable results, while still allowing for conflicting signs to achieve full flexibility. Its consistency properties are rigorously established. Simulation shows that the proposed method outperforms the competing alternatives under a variety of settings. With two data example, the proposed method leads to different and more consistent findings.