Graph estimation with joint additive models

In recent years, there has been considerable interest in estimating conditional independence graphs in the high-dimensional setting. Most prior work has assumed that the variables are multivariate Gaussian, or that the conditional means of the variables are linear. Unfortunately, if these assumptions are violated, then the resulting conditional independence estimates can be inaccurate. We present a semi-parametric method, SpaCE JAM, which allows the conditional means of the features to take on an arbitrary additive form. 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 non-linear relationships among the features, and is comparable to methods that assume multivariate normality when the conditional means are linear. We illustrate our method on a cell-signaling data set.
Comment: submitted to Biometrika. Method implementation available at http://cran.r-project.org/web/packages/spacejam/