MS-WDRO Fuses Heterogeneous Graph Data for Better Learning.

Inferring network topology from graph signals is a fundamental problem with applications spanning neuroscience, sensor networks, and social media. A common challenge arises when target-domain data is scarce, while abundant, but heterogeneous, source-domain data exists. Simply averaging these diverse sources often degrades performance by collapsing distinct geometries into a biased consensus. This research proposes MS-WDRO (Multi-Source Wasserstein Distributionally Robust Graph Learning), a framework that leverages the Wasserstein metric's distribution-preserving properties to effectively fuse heterogeneous sources. It computes a weighted Wasserstein barycenter, which acts as a geometrically principled nominal distribution, and then constructs an ambiguity ball around it to account for residual uncertainty. Minimizing the worst-case risk within this framework yields a tractable regularized Laplacian estimator, solved efficiently using an ADMM scheme. The method provides strong non-asymptotic guarantees, including concentration bounds and an out-of-sample excess risk bound. Furthermore, the solver is unrolled into a differentiable architecture, allowing for end-to-end training and data-adaptive calibration of hyperparameters. Experiments demonstrate MS-WDRO's consistent outperformance of baselines in graph recovery and diagnostic utility, particularly in data-scarce regimes.