An RKHS Approach to Estimating High-Dimensional Graphs

• Activity Number: 463
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kuang-Yao Lee*+ and Bing Li and Hongyu Zhao
• Companies: Yale and Penn State and Yale
• Keywords: additive conditional independence ; reproducing kernel ; additive conditional covariance operator ; covariance selection ; sparsity ; heterogeneity

Abstract

We present a new method for estimating graphs in high-dimensional setting. Our method is based on additive conditional independence - a newly proposed statistical relation by Li, Chun, and Zhao (2014). The concept of additive conditional independence aims at relaxing the two assumptions mostly considered in existing methods, a joint (copula) gaussianity among nodes or linear associations between nodes. In the meantime, unlike the fully specified conditional independence, additive conditional independence avoids the loss of efficiency by multivariate smoothing - which makes it especially suitable for fitting large scale graphs. We show that at the population level the additive conditional independence can be characterized by identifying nonlinear patterns between variables. We also develop an estimating procedure and demonstrate it using simulations and actual data sets.