The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.
By Chuansen Peng, Yifan Xia, Jinshan Zhong, Xiaojing Shen
arXiv:2608. 13418v1 Announce Type: cross Abstract: Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution.
By Yikai Xu, Zhao Chen, Jian Huang
Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution. To this end, we propose Wasserstein Filtering (WF), a novel sample selection framework that discards a fraction of suspicious samples and estimates the target distribution using the empirical measure of the remaining data.
arXiv:2509. 09371v2 Announce Type: replace-cross Abstract: Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions.
By Zitao Wang, Nian Si, Molei Liu
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
By Charles Dufour, Ulysse Naepels, Leonardo V. Santoro
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni
The paper examines whether deep ensembles effectively capture uncertainty in message‑passing graph neural networks. Across eight diverse datasets, ensembles only marginally outperform single models, mainly by reducing optimization noise rather than improving uncertainty estimates. The authors identify an epistemic collapse—independently trained networks converge to similar predictions—due to the smoothing bias of message passing, and provide a theoretical bound linking this collapse to graph topology and Dirichlet energy.
By Pedro C. Vieira, Viacheslav Borovitskiy, Pedro Ribeiro
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
By Linglingzhi Zhu, Yunqin Zhu, Yao Xie
arXiv:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
By Eduardo Fernandes Montesuma, Yassir Bendou, Mike Gartrell
arXiv:2602. 04272v2 Announce Type: replace-cross Abstract: The Importance-Weighted Evidence Lower Bound (IW-ELBO) has emerged as an effective objective for variational inference (VI), tightening the standard ELBO and mitigating the mode-seeking behaviour.
By Peiwen Jiang, Takuo Matsubara, Minh-Ngoc Tran
arXiv:2506.17874v3 Announce Type: replace-cross
Abstract: In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image clas...
By Jiaming Hu, Yeping Jin, Debarghya Mukherjee, Ioannis Ch. Paschalidis
LapDDPM is a conditional Graph Diffusion Probabilistic Model that generates high‑fidelity, biologically plausible single‑cell RNA sequencing data. It incorporates graph‑based inductive biases and a spectral adversarial perturbation mechanism to enforce robustness against structural noise, effectively acting as a Distributionally Robust Optimization framework. The model extends to spatial transcriptomics and multi‑modal data, and experimental results on datasets such as PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome show it outperforms state‑of‑the‑art baselines in distribution matching, manifold preservation, and downstream utility.
By Lorenzo Bini, Stephane Marchand-Maillet