Graphical Models by Using a Joint Regression Quantiles Approach

• Activity Number: 190
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Hyonho Chun* and Myung Hee Lee and Ji Hwan Oh
• Companies: and Colorado State University and Purdue University
• Keywords: Graphical Models ; Conditional Quantiles ; Component Selection ; Generalized Additive Models

Abstract

A graphical model can be used for describing interrelationships among multiple biological entities such as genes, proteins and metabolites, in which a graph is used to encode conditional independences that are fairly challenging to be inferred without a specific distributional assumption. In many cases, the multivariate Gaussian assumption is made partly for its simplicity but the assumption is violated in many biological datasets. To resolve the problem, we relax the Gaussian assumption by modeling the conditional quantiles flexibly. In fact, the conditional quantiles bear sucient and necessary information to infer the conditional independences under the Gaussian assumption. We demonstrate the advantages of our approach using simulation studies and apply our method to an interesting real biological dataset, where a considerable amount of the dataset violates the Gaussian assumption due to unknown contamination.