Structural graphical lasso for learning mouse brain connectivity

Sen Yang, Qian Sun, Shuiwang Ji, Peter Wonka, Ian Davidson, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Scopus citations

Abstract

Investigations into brain connectivity aim to recover networks of brain regions connected by anatomical tracts or by functional associations. The inference of brain networks has recently attracted much interest due to the increasing availability of high-resolution brain imaging data. Sparse inverse covariance estimation with lasso and group lasso penalty has been demonstrated to be a powerful approach to discover brain networks. Motivated by the hierarchical structure of the brain networks, we consider the problem of estimating a graphical model with tree-structural regularization in this paper. The regularization encourages the graphical model to exhibit a brain-like structure. Specifically, in this hierarchical structure, hundreds of thousands of voxels serve as the leaf nodes of the tree. A node in the intermediate layer represents a region formed by voxels in the subtree rooted at that node. The whole brain is considered as the root of the tree. We propose to apply the tree-structural regularized graphical model to estimate the mouse brain network. However, the dimensionality of whole-brain data, usually on the order of hundreds of thousands, poses significant computational challenges. Efficient algorithms that are capable of estimating networks from high-dimensional data are highly desired. To address the computational challenge, we develop a screening rule which can quickly identify many zero blocks in the estimated graphical model, thereby dramatically reducing the computational cost of solving the proposed model. It is based on a novel insight on the relationship between screening and the so-called proximal operator that we first establish in this paper. We perform experiments on both synthetic data and real data from the Allen Developing Mouse Brain Atlas; results demonstrate the effectiveness and efficiency of the proposed approach.

Original languageEnglish (US)
Title of host publicationKDD 2015 - Proceedings of the 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery
Pages1385-1394
Number of pages10
ISBN (Electronic)9781450336642
DOIs
StatePublished - Aug 10 2015
Event21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015 - Sydney, Australia
Duration: Aug 10 2015Aug 13 2015

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Volume2015-August

Conference

Conference21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015
CountryAustralia
CitySydney
Period8/10/158/13/15

Keywords

  • Brain networks
  • Graphical lasso
  • Proximal operator
  • Screening
  • Second-order method
  • Tree-structural regularization

ASJC Scopus subject areas

  • Software
  • Information Systems

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