Abstract

This paper introduces an efficient method for learning sparse struc

tural 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 incorpo-

rate a data‑integration mechanism to handle heterogeneous sources and derive

non‑asymptotic sample‑complexity bounds that match those for homogeneous

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.

Key words and phrases: Differential network analysis, Graphical models, non- paranormal models, precision matrix estimation, structure learning

Information

Preprint No.SS-2025-0275
Manuscript IDSS-2025-0275
Complete AuthorsMojtaba Nikahd, Seyed Abolfazl Motahari
Corresponding AuthorsSeyed Abolfazl Motahari
Emailsmotahari@sharif.edu

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Supplementary Materials

Extended experimental evaluations and rigorous proofs for all theoretical

results are detailed in the online supplement.

Supplementary materials are available for download.