Let $r\geq3$ be fixed, and let $\mathbf{G}_n$ be the set of all simple graphs with vertex set $[n]=\{1,\ldots,n\}$. We consider an exponential random graph model which gives higher probability to $G \...
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
The paper investigates the entropy of random graphs produced by piecewise Hölder continuous graphons. It establishes a convergence rate for the normalized entropy as graph size increases and outlines the main proof ideas, with full details in the appendix. Using this result, the authors derive explicit quantitative entropy bounds for both the stochastic block model and the random geometric graph model, moving beyond previous asymptotic statements.
arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
arXiv:2607. 17469v1 Announce Type: cross Abstract: A randomized algorithm may terminate almost surely even though exceptional random tapes make it run forever.
arXiv:2606. 23715v1 Announce Type: cross Abstract: A Markov Logic Network (MLN) is a probabilistic relational model used in Statistical Relational Artificial Intelligence for defining a probability distribution on the set of possible worlds with domain $D$ for an arbitrary finite domain $D$.
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
arXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spect...
We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$,...
arXiv:2601. 03946v3 Announce Type: replace-cross Abstract: We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries.
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:2609.10529v1 Announce Type: cross Abstract: We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and...