A0403
Title: Combining smoothing spline with conditional Gaussian graphical model for density and graph estimation
Authors: Yuedong Wang - University of California - Santa Barbara (United States) [presenting]
Abstract: Multivariate density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships, whereas a graphical structure can be used to build models for density estimation. The goal is to construct a consolidated framework that can perform both density and graph estimation. Denote $Z$ as the random vector of interest with density function $f(z)$. Splitting $Z$ into two parts, $Z=(X, Y)$ and writing $f(z)=f(x)f(y|x)$, where $f(x)$ is the density function of $X$ and $f(y|x)$ is the conditional density of $Y|X=x$. A semiparametric framework is proposed that models $f(x)$ nonparametrically using a smoothing spline ANOVA (SS ANOVA) model and $f(y|x)$ parametrically using a conditional Gaussian graphical model (cGGM). Combining the flexibility of the SSANOVA model with the succinctness of the cGGM, this framework allows us to deal with high-dimensional data without assuming a joint Gaussian distribution. A back-fitting estimation procedure is proposed for the cGGM with a computationally efficient approach for the selection of tuning parameters. A geometric inference approach is also developed for edge selection. Asymptotic convergence properties are established for both the parameter and density estimation. The performance of the proposed method is evaluated through extensive simulation studies and real data applications.
