AdaPtive Noisy Data Augmentation (PANDA) for Simultaneous Construction of Multiple Graph Models

TL;DR

This paper introduces PANDA, an extension of data augmentation techniques for jointly estimating multiple graphical models with different node types, improving accuracy and efficiency in both Gaussian and non-Gaussian contexts.

Contribution

It develops a unified framework with two types of noise augmentation for simultaneous graph estimation, incorporating structural and numerical similarity regularizations.

Findings

PANDA performs comparably to existing methods for Gaussian models.

It significantly outperforms naive approaches for non-Gaussian models.

Applied to lung cancer data, PANDA successfully constructs multiple protein networks.

Abstract

We extend the data augmentation technique PANDA by Li et al. (2018) that regularizes single graph estimation to jointly learning multiple graphical models with various node types in a unified framework. We design two types of noise to augment the observed data: the first type regularizes the estimation of each graph while the second type promotes either the structural similarity, referred as the \joint group lasso regularization, or the numerical similarity, referred as the joint fused ridge regularization, among the edges in the same position across graphs. The computation in PANDA is straightforward and only involves obtaining maximum likelihood estimator in generalized linear models in an iterative manner. The simulation studies demonstrate PANDA is non-inferior to existing joint estimation approaches for Gaussian graphical models, and significantly improves over the naive differencing approach for non-Gaussian graphical models. We apply PANDA to a real-life lung cancer microarray data to simultaneously construct four protein networks.