Joint estimation of multiple high-dimensional Gaussian copula graphical models

Brain connectivity alteration detection via matrix-variate differential network model

Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activities. Growing evidence now suggests that the brain connectivity network experiences alterations with the presence of numerous neurological disorders, thus differential brain network analysis may provide new insights into disease pathologies. The data from neurophysiological measurement are often multidimensional and in a matrix form, posing a challenge in brain connectivity analysis. Existing graphical model estimation methods either assume a vector normal distribution that in essence requires the columns of the matrix data to be independent or fail to address the estimation of differential networks across different populations. To tackle these issues, we propose an innovative matrix-variate differential network (MVDN) model. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix and use an alternating direction method of multipliers algorithm for the optimization problem. Theoretical and simulation studies demonstrate that MVDN significantly outperforms other state-of-the-art methods in dynamic differential network analysis. We illustrate with a functional connectivity analysis of an attention deficit hyperactivity disorder dataset. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies.

A new insight into underlying disease mechanism through semi-parametric latent differential network model

BACKGROUND

In genomic studies, to investigate how the structure of a genetic network differs between two experiment conditions is a very interesting but challenging problem, especially in high-dimensional setting. Existing literatures mostly focus on differential network modelling for continuous data. However, in real application, we may encounter discrete data or mixed data, which urges us to propose a unified differential network modelling for various data types.

RESULTS

We propose a unified latent Gaussian copula differential network model which provides deeper understanding of the unknown mechanism than that among the observed variables. Adaptive rank-based estimation approaches are proposed with the assumption that the true differential network is sparse. The adaptive estimation approaches do not require precision matrices to be sparse, and thus can allow the individual networks to contain hub nodes. Theoretical analysis shows that the proposed methods achieve the same parametric convergence rate for both the difference of the precision matrices estimation and differential structure recovery, which means that the extra modeling flexibility comes at almost no cost of statistical efficiency. Besides theoretical analysis, thorough numerical simulations are conducted to compare the empirical performance of the proposed methods with some other state-of-the-art methods. The result shows that the proposed methods work quite well for various data types. The proposed method is then applied on gene expression data associated with lung cancer to illustrate its empirical usefulness.

CONCLUSIONS

The proposed latent variable differential network models allows for various data-types and thus are more flexible, which also provide deeper understanding of the unknown mechanism than that among the observed variables. Theoretical analysis, numerical simulation and real application all demonstrate the great advantages of the latent differential network modelling and thus are highly recommended.