Efficient Learning of Sparse Differential Networks in Multi-Source Non-Paranormal Models

This paper introduces an efficient method for learning sparse structural changes-known as the differential network-between two classes of nonparanormal graphical models.We consider the practically important setting where datasets are heterogeneous and originate from multiple sources, yet share a common latent Gaussian covariance structure.Among existing approaches for estimating the differential network, one prominent method is based on minimizing a lasso-penalized D-trace loss function.However, current implementations of this approach suffer from high computational costs and approximation errors.To address these limitations, we propose a solution-path algorithm for the lassopenalized D-trace problem that builds on piecewise-linear path-following ideas and exploits the structure of the objective to efficiently compute exact solutions over a range of regularization parameters.Our method eliminates approximation error and substantially reduces computational cost.Further, we incorporate a data-integration mechanism to handle heterogeneous sources and derive non-asymptotic sample-complexity bounds that match those for homogeneous Statistica Sinica: Newly accepted Paper data-demonstrating flexibility with no statistical efficiency loss.On synthetic data, our method significantly outperforms state-of-the-art techniques in both speed and estimation accuracy.Finally, we applied the method to two real-world datasets.In ovarian cancer drug-resistance data, it identified key genetic markers.In breast cancer subtype data, it identified genes that differentiate luminal A and basal-like tumors.Many of these genes are supported by the biomedical literature, demonstrating the practical utility of the method.