Graphical LASSO with Auxiliary Information: Application to Neural Connectivity

• Activity Number: 177
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Giuseppe Vinci* and Robert Kass and Valerie Ventura and Matthew A. Smith
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University and University of Pittsburgh
• Keywords: Graphical LASSO ; Sparsity ; High-dimensionality ; Empirical Bayes ; False Discovery Rate ; Macaque visual cortex

Abstract

Gaussian Graphical Models are built on estimates of the precision matrix C. The Graphical LASSO (G-LASSO, Friedman et al., Biostatistics 2008) provides reasonable sparse solutions, as a compromise between estimation accuracy and dimensionality. The G-LASSO estimate of C is the maximum a posteriori solution of the Gaussian likelihood combined with a Laplace prior on C with unique parameter 'lambda', which controls the overall sparsity of the estimator. However, in some applications, additional information about the structure of C can be available through some auxiliary variable W. For instance, the strength of the conditional dependence of two neurons' activities decreases with interneural distance. We propose an Empirical Bayes method to incorporate the auxiliary information carried by W in the G-LASSO optimization algorithm. The proposed procedure is related to the False Discovery Rate regression methodology of Scott et al. (JASA 2015), and can lead to lower False Nondiscovery Rate of edge detection. We apply these methods to data from macaque visual cortex to infer neural connectivity.