Detection threshold for correlated Erd\H{o}s-R\'enyi graphs via densest subgraphs

• URL: http://arxiv.org/abs/2203.14573v1
• Date: Mon, 28 Mar 2022 08:32:43 GMT
• Title: Detection threshold for correlated Erd\H{o}s-R\'enyi graphs via densest subgraphs
• Authors: Jian Ding, Hang Du
• Abstract summary: We solve the problem of detecting edge correlation between two ErdHos-R'enyi random graphs on $n$ unlabeled nodes. A key novelty in our work is an interesting connection between the detection problem and the densest subgraph of an ErdHos-R'enyi graph.
• Score: 9.12788494573002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of detecting edge correlation between two Erd\H{o}s-R\'enyi random graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are sampled independently; under the alternative, the two graphs are independently sub-sampled from a parent graph which is Erd\H{o}s-R\'enyi $\mathbf{G}(n, p)$ (so that their marginal distributions are the same as the null). We establish a sharp information-theoretic threshold when $p = n^{-\alpha+o(1)}$ for $\alpha\in (0, 1]$ which sharpens a constant factor in a recent work by Wu, Xu and Yu. A key novelty in our work is an interesting connection between the detection problem and the densest subgraph of an Erd\H{o}s-R\'enyi graph.

Related papers

• Collaborative non-parametric two-sample testing [55.98760097296213]
  The goal is to identify nodes where the null hypothesis $p_v = q_v$ should be rejected. We propose the non-parametric collaborative two-sample testing (CTST) framework that efficiently leverages the graph structure. Our methodology integrates elements from f-divergence estimation, Kernel Methods, and Multitask Learning.
  arXiv  Detail & Related papers  (2024-02-08T14:43:56Z)
• Detection of Dense Subhypergraphs by Low-Degree Polynomials [72.4451045270967]
  Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem. We consider detecting the presence of a planted $Gr(ngamma, n-alpha)$ subhypergraph in a $Gr(n, n-beta) hypergraph. Our results are already new in the graph case $r=2$, as we consider the subtle log-density regime where hardness based on average-case reductions is not known.
  arXiv  Detail & Related papers  (2023-04-17T10:38:08Z)
• Statistical limits of correlation detection in trees [0.7826806223782055]
  This paper addresses the problem of testing whether two observed trees $(t,t')$ are sampled independently or from a joint distribution under which they are correlated. Motivated by graph alignment, we investigate the conditions of existence of one-sided tests. We find that no such test exists for $s leq sqrtalpha$, and that such a test exists whenever $s > sqrtalpha$, for $lambda$ large enough.
  arXiv  Detail & Related papers  (2022-09-27T22:26:53Z)
• Causal Bandits for Linear Structural Equation Models [58.2875460517691]
  This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model. It is assumed that the graph's structure is known and has $N$ nodes. Two algorithms are proposed for the frequentist (UCB-based) and Bayesian settings.
  arXiv  Detail & Related papers  (2022-08-26T16:21:31Z)
• Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignment [51.74913666829224]
  We show that for datasets with strong inherent anti-correlations, a suitable graph contains both positive and negative edge weights. We propose a linear-time signed graph sampling method centered on the concept of balanced signed graphs. Experimental results show that our signed graph sampling method outperformed existing fast sampling schemes noticeably on various datasets.
  arXiv  Detail & Related papers  (2022-08-18T09:19:01Z)
• Matching recovery threshold for correlated random graphs [9.12788494573002]
  For two correlated graphs which are independently sub-sampled from a common ErdHos-R'enyi graph $mathbfG(n, p)$, we wish to recover their emphlatent matching from the observation of these two graphs emphwithout labels. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.
  arXiv  Detail & Related papers  (2022-05-29T13:04:20Z)
• Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation [61.39364567221311]
  Graph-level anomaly detection (GAD) describes the problem of detecting graphs that are abnormal in their structure and/or the features of their nodes. One of the challenges in GAD is to devise graph representations that enable the detection of both locally- and globally-anomalous graphs. We introduce a novel deep anomaly detection approach for GAD that learns rich global and local normal pattern information by joint random distillation of graph and node representations.
  arXiv  Detail & Related papers  (2021-12-19T05:04:53Z)
• Settling the Sharp Reconstruction Thresholds of Random Graph Matching [19.54246087326288]
  We study the problem of recovering the hidden correspondence between two edge-correlated random graphs. For dense graphs with $p=n-o(1)$, we prove that there exists a sharp threshold. For sparse ErdHos-R'enyi graphs with $p=n-Theta(1)$, we show that the all-or-nothing phenomenon no longer holds.
  arXiv  Detail & Related papers  (2021-01-29T21:49:50Z)
• Adversarial Linear Contextual Bandits with Graph-Structured Side Observations [80.95090605985042]
  A learning agent repeatedly chooses from a set of $K$ actions after being presented with a $d$-dimensional context vector. The agent incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures. Two efficient algorithms are developed based on textttEXP3.
  arXiv  Detail & Related papers  (2020-12-10T15:40:07Z)
• Testing correlation of unlabeled random graphs [18.08210501570919]
  We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated. Under the alternative, the two graphs are edge-correlated under some latent node correspondence, but have the same marginal distributions as the null.
  arXiv  Detail & Related papers  (2020-08-23T19:19:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.