Nonparametric Neighborhood Selection in Graphical Models

The neighborhood selection method directly explores the conditional dependence structure and has been widely used to construct undirected graphical models. However, except for some special cases with discrete data, there is little research on nonparametric methods for neighborhood selection with mixed data. This paper develops a fully nonparametric neigh-borhood selection method under a consolidated smoothing spline ANOVA (SS ANOVA) decomposition framework. The proposed model is flexible and contains many existing mod-els 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 apply-ing an L1 regularization to interactions in the SS ANOVA decomposition. We propose an iterative procedure to compute the estimates and establish the convergence rates for con-ditional density and interactions. Simulations indicate that the proposed methods perform well under Gaussian and non-Gaussian settings. We illustrate the proposed methods using two real data examples.

Automated summary

This paper presents a nonparametric neighborhood selection method under a unified framework for mixed data, which performs well in simulations and real data examples.