Graph Estimation with Joint Additive Models

• Activity Number: 593
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Arend Voorman*+ and Ali Shojaie and Daniela Witten
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: graphical models ; lasso ; sparsity ; non-linearity

Abstract

In recent years, there has been considerable interest in estimating conditional independence graphs, especially in the high-dimensional setting. Most prior work in this area has assumed that the observations are drawn from a multivariate Gaussian distribution, or that conditional dependence relationionships among variables are linear. Unfortunately, if the assumption of Gaussianity is violated, then the resulting conditional independence estimates can be inaccurate. Here we present a semi-parametric method, Sparse Conditional Estimation with Joint Additive Models (SpaCE JAM), which allows for arbitrary additive conditional relationships among the features. We present an efficient algorithm for its computation, and prove that our estimator is consistent. We also extend our method to estimation of directed graphs with known causal ordering. Using simulated data, we show that SpaCE JAM enjoys superior performance to existing methods when there are nonlinear relationships among the features, and is comparable to methods that assume multivariate normality when there are linear relationships among the features. We also illustrate our method on a cell-signaling data set.