A Sparse Conditional Graphical Model for Non-Independent Measurements

• Activity Number: 15
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Hyonho Chun*+
• Keywords: Gaussian graphical model ; Non-independence ; Genetics

Abstract

For the purpose of inferring a network, we consider a sparse Gaussian graphical model (SGGM) without independent assumption across measurements. This often occurs in genetic studies with model organisms in which data are obtained by combining multiple lines of inbred organisms or by using outbred animals. Ignoring such population structures would produce false connections in a graph structure, but most research in graph inference is focused on independent cases. On the other hand, in regression settings, a random effect model has been widely used in order to account for correlations among observations. Besides its effectiveness, the random effect model has a generality; the model can be stated within a framework of penalized least squares. This generality makes it very flexible for utilization in settings other than regression. In this manuscript, we adopt the random effect model to the SGGM. Our formulation fits into the recently developed conditional Gaussian graphical model in which the population structures are modeled as predictors and the graph is determined by a conditional precision matrix. The proposed approach is applied to the network inference problem of two data