Correlation detection in trees for partial graph alignment

• URL: http://arxiv.org/abs/2107.07623v1
• Date: Thu, 15 Jul 2021 22:02:27 GMT
• Title: Correlation detection in trees for partial graph alignment
• Authors: Luca Ganassali, Laurent Massouli\'e, Marc Lelarge
• Abstract summary: We consider alignment of graphs, which consists in finding a mapping between the nodes of two graphs which preserves most of the edges. Our approach is to compare local structures in the two graphs, matching two nodes if their neighborhoods are 'close enough' for correlated graphs. This problem can be rephrased in terms of testing whether a pair of branching trees is drawn from either a product distribution, or a correlated distribution.
• Score: 3.5880535198436156
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider alignment of sparse graphs, which consists in finding a mapping between the nodes of two graphs which preserves most of the edges. Our approach is to compare local structures in the two graphs, matching two nodes if their neighborhoods are 'close enough': for correlated Erd\H{o}s-R\'enyi random graphs, this problem can be locally rephrased in terms of testing whether a pair of branching trees is drawn from either a product distribution, or a correlated distribution. We design an optimal test for this problem which gives rise to a message-passing algorithm for graph alignment, which provably returns in polynomial time a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. With an average degree $\lambda = O(1)$ in the graphs, and a correlation parameter $s \in [0,1]$, this result holds with $\lambda s$ large enough, and $1-s$ small enough, completing the recent state-of-the-art diagram. Tighter conditions for determining whether partial graph alignment (or correlation detection in trees) is feasible in polynomial time are given in terms of Kullback-Leibler divergences.

Related papers

• Graph Fourier MMD for Signals on Graphs [67.68356461123219]
  We propose a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation. We showcase it on graph benchmark datasets as well as on single cell RNA-sequencing data analysis.
  arXiv  Detail & Related papers  (2023-06-05T00:01:17Z)
• Matching Correlated Inhomogeneous Random Graphs using the $k$-core Estimator [5.685589351789462]
  We study the so-called emph$k$-core estimator, which outputs a correspondence that induces a large, common subgraph of both graphs. We specialize our general framework to derive new results on exact and partial recovery in correlated block models, correlated Chung-Lu geometric graphs, and correlated random graphs.
  arXiv  Detail & Related papers  (2023-02-10T18:21:35Z)
• Random graph matching at Otter's threshold via counting chandeliers [16.512416293014493]
  We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each. This is the first graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs.
  arXiv  Detail & Related papers  (2022-09-25T20:00:28Z)
• 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)
• Collaborative likelihood-ratio estimation over graphs [55.98760097296213]
  Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF) We develop this idea in a concrete non-parametric method that we call Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF) We derive convergence rates for our collaborative approach that highlights the role played by variables such as the number of available observations per node, the size of the graph, and how accurately the graph structure encodes the similarity between tasks.
  arXiv  Detail & Related papers  (2022-05-28T15:37:03Z)
• Approximating the Log-Partition Function [16.59989033959959]
  We provide an approach to quantify the approximation ratio through the property of the underlying graph structure. We provide a near lineartime variant that achieves an approximation ratio equal to the inverse of square-root of minimal effective resistance of the graph.
  arXiv  Detail & Related papers  (2021-02-19T22:57:32Z)
• 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)
• Factorizable Graph Convolutional Networks [90.59836684458905]
  We introduce a novel graph convolutional network (GCN) that explicitly disentangles intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2020-10-12T03:01:40Z)
• 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)
• Wasserstein-based Graph Alignment [56.84964475441094]
  We cast a new formulation for the one-to-many graph alignment problem, which aims at matching a node in the smaller graph with one or more nodes in the larger graph. We show that our method leads to significant improvements with respect to the state-of-the-art algorithms for each of these tasks.
  arXiv  Detail & Related papers  (2020-03-12T22:31:59Z)

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.