arXiv:2606. 31230v1 Announce Type: new Abstract: We study the task of learning the structure of a $d$-sparse Gaussian graphical model on $n$ variables from a single trajectory of Glauber dynamics.
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
arXiv:2608. 19914v1 Announce Type: new Abstract: Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks.
arXiv:2411. 03163v4 Announce Type: replace-cross Abstract: In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models.
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.
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.
arXiv:2606. 24011v1 Announce Type: cross Abstract: A crucial assumption in graph signal processing (GSP) is the existence of an underlying graph that captures the pairwise similarities between nodes, allowing filters to be designed based on this graph for tasks such as denoising.
arXiv:2606. 31063v1 Announce Type: cross Abstract: Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids.
arXiv:2606. 07151v1 Announce Type: new Abstract: Traditional change point detection in dynamic networks assumes abrupt transitions between stationary states, overlooking scenarios of continuous evolution which arise in most real-world applications, such as social networks or physical systems.
arXiv:2607. 28706v1 Announce Type: cross Abstract: We study the convergence properties of the random-sweep Gibbs sampler for Gaussian graphical models with a thin-membrane prior.
The paper introduces the Generalized Graph Variational Autoencoder (GGVA), which replaces the Kullback–Leibler divergence in the standard variational graph autoencoder with any member of the Rényi–Tsallis family of order $q$. The authors show that for $q<1$ the Tsallis divergence is bounded, whereas the KL and Rényi divergences are unbounded, and that this boundedness can significantly increase the amount of posterior information retained—up to 49× more than the VGAE on several benchmark graphs. Experiments demonstrate that the GGVA’s retained information improves node classification performance, though it does not improve link‑prediction accuracy and only delays, rather than prevents, posterior collapse.
The paper introduces a data‑adaptive test statistic for evaluating conditional independence in the graph structure of stationary Gaussian time series, addressing both short‑memory and long‑memory regimes. It provides a finite‑sample Berry–Esseen type Gaussian approximation and validates the testing procedure via block bootstrap, even in ultra‑high‑dimensional settings. The authors also propose a consistency‑enhancing correction, achieving asymptotic consistency in size and power, and demonstrate the method on fMRI data to explore brain functional connectivity.
arXiv:2511.22435v2 Announce Type: replace Abstract: Invariant learning on graphs aims to build predictors that rely on causal substructures rather than on environment-specific shortcuts. Current meth...