Adaptive Noisy Data Augmentation for Regularized Construction of Undirected Graphical Models

We develop the AdaPtive Noise Augmentation (PANDA) technique to regularize the estimation of undirected graphical models. PANDA iteratively optimizes the objective function given adaptively augmented data to achieve regularization on model parameters. The augmented noisy data is designed to deliver various regularization effects on single graph estimation as well as simultaneous construction of multiple graphs, including but not limited to
$l_{\gamma}$
for
$\gamma\in[0,2]$
, elastic net, SCAD, group lasso, and adaptive lasso in single graph estimations; and the joint group lasso and the joint fused ridge regularizations for multiple graph estimation. PANDA can be seamlessly implemented in practice in software that implements generalized linear models and users do not have to employ ad-hoc optimizers to minimize regularized loss functions for graph construction. We show the non-inferiority of PANDA in various types of graph estimation in simulated data, benchmarked against some common graph estimation methods. We also apply PANDA to an autism spectrum disorder dataset to construct a graph with mixed node types and to a lung cancer microarray data set to simultaneously construct four protein networks, demonstrating the effectiveness of PANDA in constructing practically interpretable and meaningful graphical models.