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Found 21 papers, 7 papers with code
Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs
We study the convergence of message passing graph neural networks on random graph models to their continuous counterpart as the number of nodes tends to infinity.
A Faster Sampler for Discrete Determinantal Point Processes
Finally, an interesting by-product of the analysis is that a realisation from a DPP is typically contained in a subset of size O(m log m) formed using leverage score i. i. d.
Variance Reduction for Inverse Trace Estimation via Random Spanning Forests
The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems.
Variance reduction in stochastic methods for large-scale regularised least-squares problems
Large dimensional least-squares and regularised least-squares problems are expensive to solve.
Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs
This article unveils a new relation between the Nishimori temperature parametrizing a distribution P and the Bethe free energy on random Erdos-Renyi graphs with edge weights distributed according to P. Estimating the Nishimori temperature being a task of major importance in Bayesian inference problems, as a practical corollary of this new relation, a numerical method is proposed to accurately estimate the Nishimori temperature from the eigenvalues of the Bethe Hessian matrix of the weighted graph.
Fast Graph Kernel with Optical Random Features
If this method can still be prohibitively costly for usual random features, we then incorporate optical random features that can be computed in constant time.
Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian
This article considers the problem of community detection in sparse dynamical graphs in which the community structure evolves over time.
A unified framework for spectral clustering in sparse graphs
This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities.
Optimal Laplacian regularization for sparse spectral community detection
Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks.
Approximating Spectral Clustering via Sampling: a Review
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph.
Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs
Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs.
Determinantal Point Processes for Coresets
We apply our results to both the k-means and the linear regression problems, and give extensive empirical evidence that the small additional computational cost of DPP sampling comes with superior performance over its iid counterpart.
Asymptotic Equivalence of Fixed-size and Varying-size Determinantal Point Processes
In this work we show that as the size of the ground set grows, $k$-DPPs and DPPs become equivalent, meaning that their inclusion probabilities converge.
Optimized Algorithms to Sample Determinantal Point Processes
The standard sampling algorithm is separated in three phases: 1/~eigendecomposition of $\mathbf{L}$, 2/~an eigenvector sampling phase where $\mathbf{L}$'s eigenvectors are sampled independently via a Bernoulli variable parametrized by their associated eigenvalue, 3/~a Gram-Schmidt-type orthogonalisation procedure of the sampled eigenvectors.
Design of graph filters and filterbanks
The aim of this chapter is to review general concepts for the introduction of filters and representations of graph signals.
Signal Processing Information Theory Social and Information Networks Information Theory
Échantillonnage de signaux sur graphes via des processus déterminantaux
We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes.
Graph sampling with determinantal processes
For large graphs, ie, in cases where the graph's spectrum is not accessible, we investigate, both theoretically and empirically, a sub-optimal but much faster DPP based on loop-erased random walks on the graph.
Compressive K-means
We demonstrate empirically that CKM performs similarly to Lloyd-Max, for a sketch size proportional to the number of cen-troids times the ambient dimension, and independent of the size of the original dataset.
Compressive Spectral Clustering
Spectral clustering has become a popular technique due to its high performance in many contexts.
Random sampling of bandlimited signals on graphs
On the contrary, the second strategy is adaptive but yields optimal results.
Accelerated Spectral Clustering Using Graph Filtering Of Random Signals
We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm.
Social and Information Networks Numerical Analysis
