
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
We prove a central limit theorem for the components of the eigenvectors ...
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Optimal Bayesian Estimation for Random Dot Product Graphs
We propose a Bayesian approach, called the posterior spectral embedding,...
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Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs
In this work we show that, using the eigendecomposition of the adjacenc...
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Outofsample extension of graph adjacency spectral embedding
Many popular dimensionality reduction procedures have outofsample exte...
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Graph Encoder Embedding
In this paper we propose a lightning fast graph embedding method called ...
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Robust relative error estimation
Relative error estimation has been recently used in regression analysis....
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Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality
What does the informational complexity of dynamical networked systems te...
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Efficient Estimation for Random Dot Product Graphs via a Onestep Procedure
We propose a onestep procedure to efficiently estimate the latent positions in random dot product graphs. Unlike the classical spectralbased methods such as the adjacency and Laplacian spectral embedding, the proposed onestep procedure takes both the lowrank structure of the expected value of the adjacency matrix and the Bernoulli likelihood information of the sampling model into account simultaneously. We show that for each individual vertex, the corresponding row of the onestep estimator converges to a multivariate normal distribution after proper scaling and centering up to an orthogonal transformation, with an efficient covariance matrix, provided that the initial estimator satisfies the socalled approximate linearization property. The onestep estimator improves the commonlyadopted spectral embedding methods in the following sense: Globally for all vertices, it yields a smaller asymptotic sum of squarederror, and locally for each individual vertex, the asymptotic covariance matrix of the corresponding row of the onestep estimator is smaller than those of the spectral embedding in spectra. The usefulness of the proposed onestep procedure is demonstrated via numerical examples and the analysis of a realworld Wikipedia graph dataset.
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