• Corpus ID: 44072170

Distributed Cartesian Power Graph Segmentation for Graphon Estimation

@article{Wei2018DistributedCP,
  title={Distributed Cartesian Power Graph Segmentation for Graphon Estimation},
  author={Shitong Wei and Oscar Hernan Madrid Padilla and James Sharpnack},
  journal={ArXiv},
  year={2018},
  volume={abs/1805.09978}
}
We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for any connected graph, under subGaussian noise, the PGFL achieves the same mean-square error rate as 2D total variation denoising for signals of bounded variation. We study the use… 

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References

SHOWING 1-10 OF 36 REFERENCES

The DFS Fused Lasso: Linear-Time Denoising over General Graphs

It is proved that for any signal, its total variation over the induced chain graph induced by running depth-first search (DFS) over the nodes of the graph is no more than twice its total variations over the original graph.

Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

This paper proposes a computationally efficient procedure to estimate a graphon from a set of observed networks generated from it based on a stochastic blockmodel approximation (SBA) of the graphon, and shows that the estimation error vanishes as the size of thegraph approaches infinity.

Sparsistency of the Edge Lasso over Graphs

This paper investigates sparsistency of fused lasso for general graph structures, i.e. its ability to correctly recover the exact support of piece-wise constant graphstructured patterns asymptotically (for largescale graphs) and refers to it as Edge Lasso on the (structured) normal means setting.

Detecting Activations over Graphs using Spanning Tree Wavelet Bases

This work considers the detection of activations over graphs under Gaussian noise, and introduces the spanning tree wavelet basis over graphs, a localized basis that reflects the topology of the graph, and proves that for any spanning tree, this approach can distinguish null from alternative in a low signal-to-noise regime.

Trend Filtering on Graphs

A family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences, are introduced, which generalizes the idea of trend filtering, used for univariate nonparametric regression, to graphs.

An iterative step-function estimator for graphons

This work proposes an iterative step-function estimator (ISFE) that, given an initial partition, iteratively clusters nodes based on their edge densities with respect to the previous iteration's partition.

Discrete signal processing on graphs: Graph fourier transform

This framework extends traditional discrete signal processing theory to structured datasets by viewing them as signals represented by graphs, so that signal coefficients are indexed by graph nodes and relations between them are represented by weighted graph edges.

Deep Convolutional Networks on Graph-Structured Data

This paper develops an extension of Spectral Networks which incorporates a Graph Estimation procedure, that is test on large-scale classification problems, matching or improving over Dropout Networks with far less parameters to estimate.

A Consistent Histogram Estimator for Exchangeable Graph Models

A histogram estimator of a graphon that is provably consistent and numerically efficient is proposed, based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of agraph, then smooths the sorted graph using total variation minimization.

Estimating network edge probabilities by neighborhood smoothing

This work proposes a novel computationally efficient method, based on neighborhood smoothing to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires.