B0345
Title: Nonparametric neighborhood selection in graphical models
Authors: Yuedong Wang - University of California - Santa Barbara (United States) [presenting]
Abstract: The neighbourhood selection method directly explores the conditional dependence structure and has been widely used to construct undirected graphical models. However, there is little research on nonparametric methods for neighbourhood selection with mixed data except for some special cases with discrete data. A fully nonparametric neighbourhood selection method is presented under a consolidated smoothing spline ANOVA (SS ANOVA) decomposition framework. The proposed model is flexible and contains many existing models as special cases. The proposed method provides a unified framework for mixed data without any restrictions on the type of each random variable. We detect edges by applying an $L1$ regularization to interactions in the SS ANOVA decomposition. An iterative procedure is proposed to compute the estimates and establish the convergence rates for conditional density and interactions. Simulations indicate that the proposed methods perform well under Gaussian and non-Gaussian settings. The proposed methods are illustrated, using two real data examples.
