arXiv:2610. 08872v1 Announce Type: cross Abstract: We study community recovery in the sparse symmetric stochastic block model with $q$ communities, average degree $d$ and signal strength $\lambda$ through statistical decision theory and Fisher information, and obtain three characterizations of the Kesten-Stigum threshold $d\lambda^2=1$ and of the information-computation gap below it.
arXiv:2509. 15822v3 Announce Type: replace-cross Abstract: Predictions from statistical physics postulate that recovery of the communities in the Stochastic Block Model (SBM) with a fixed number $K$ of communities is possible in polynomial time above, and only above, the Kesten-Stigum (KS) threshold.
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
arXiv:2411.02835v3 Announce Type: replace-cross Abstract: The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborov\'a (2014), is a Hermitian matrix designed for applying spectral cluster...
arXiv:2610. 41802v1 Announce Type: cross Abstract: We show that outlier eigenvectors of the Bethe Hessian achieve weak recovery in the stochastic block model down to the Kesten-Stigum threshold, for every fixed common expected degree $d>1$.
arXiv:2610. 31612v1 Announce Type: new Abstract: We study learning a discrete distribution under person-level differential privacy in the batched setting.
We study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i.
arXiv:2609. 05318v1 Announce Type: new Abstract: Building on the pioneering paper of Kearns, Roth, and Ryu (SODA'26), we study information aggregation in a networked learning model.
arXiv:2607. 16676v1 Announce Type: cross Abstract: How deep does a graph neural network need to be on a sparse graph?
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.
arXiv:2609.26199v1 Announce Type: new Abstract: A large graph is often available only in part: a crawl stopped by its budget, a panel, a partial dump. When the sampled fraction $s$ is known by design...
The paper investigates high‑dimensional graph combinatorial hypothesis testing where a signal resides on the edges of an unknown subgraph. For Gaussian observations, it derives sharp statistical and computational thresholds for detecting the signal across various graph alternatives, using second‑moment bounds of likelihood ratios and low‑degree methods. The authors also establish a transfer principle linking exponential family models, identify new statistical‑computational gaps for structures like multiple planted cliques and hypercliques, and provide matching upper bounds under local regularity, thereby revealing universal threshold scales and connecting Gaussian and Erdős–Rényi settings.
arXiv:2610.32822v2 Announce Type: new Abstract: Sparse linear regression is a fundamental problem in high-dimensional statistics, and its private counterparts leave a large gap between the central an...