A0886
Title: Density and graph estimation with smoothing splines and conditional Gaussian graphical models
Authors: Anna Liu - University of Massachusetts, Amherst (United States) [presenting]
Abstract: 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. Denote $Z$ as the vector of interest with density $f(z)$. The goal is to obtain simultaneously an estimate of $f(z)$ and an estimate of the conditional independence network for $Z$. This goal is approached by splitting $Z$ into two parts, $Z = (X^T , Y^T )^T$, and decomposing $f(z)$ as $f(x)f(y|x)$. A semiparametric framework that models $f(x)$ nonparametrically is proposed using a smoothing spline ANOVA (SS ANOVA) model and $f(y|x)$ parametrically using a conditional Gaussian graphical model (cGGM). This flexible framework allows for dealing with high-dimensional data without the Gaussian assumption. The contributions are a new edge selection algorithm for the conditional independence network, new theoretical results for both the overall density and the parameter estimates in the cGGM part under a random design, and a new efficient backfitting procedure for estimating tuning parameters in the cGGM. The experimental results show that the proposed framework outperforms both parametric and nonparametric baselines.
