High-Dimensional Sparse Graph Estimation by Integrating DTW-D Into Bayesian Gaussian Graphical Models

Abstract

Graphical models provide an effective way to reveal complicated associations in data and especially to learn the structures among large numbers of variables with respect to few observations in a high-dimensional space. In this paper, a novel graphical algorithm that integrates the dynamic time warping (DTW)-D measure into the birth–death Markov Chain Monte Carlo (BDMCMC) methodology (DTWD-BDMCMC) is proposed for modeling the intrinsic correlations buried in data. The DTW-D, which is the ratio of DTW over the Euclidean distance (ED), is targeted to calibrate the warping observation sequences. The approach of the BDMCMC is a Bayesian framework used for structure learning in sparse graphical models. In detail, a modified DTW-D distance matrix is first developed to construct a weighted covariance instead of the traditional covariance calculated with the ED. We then build on Bayesian Gaussian models with the weighted covariance with the aim to be robust against problems of sequence distortion. Moreover, the weighted covariance is used as limited prior information to facilitate an initial graphical structure, on which we finally employ the BDMCMC for the determination of the reconstructed Gaussian graphical model. This initialization is beneficial to improve the convergence of the BDMCMC sampling. We implement our method on broad simulated data to test its ability to deal with different kinds of graphical structures. This paper demonstrates the effectiveness of the proposed method in comparison with its rivals, as it is competitively applied to Gaussian graphical models and copula Gaussian graphical models. In addition, we apply our method to explore real-network attacks and genetic expression data.