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We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erdös-Rényi graph with probability p0. Under the (composite) alternative, there is a… (More)

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. Taking the stochastic block model as an approximation, we construct… (More)

- Christophe Giraud, Sylvie Huet, Nicolas Verzelen
- Statistical applications in genetics and…
- 2012

Applications on inference of biological networks have raised a strong interest in the problem of graph estimation in high-dimensional Gaussian graphical models. To handle this problem, we propose a two-stage procedure which first builds a family of candidate graphs from the data, and then selects one graph among this family according to a dedicated… (More)

We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of successful detection as both the sample size n and the dimension p tend to the infinity. Testing procedures that achieve… (More)

- Nicolas Verzelen
- Computational Statistics & Data Analysis
- 2010

We study the non-parametric covariance estimation of a stationary Gaussian field X observed on a lattice. To tackle this issue, we have introduced a model selection procedure in a previous paper [Ver09]. This procedure amounts to selecting a neighborhood m̂ by a penalization method and estimating the covariance of X in the space of Gaussian Markov random… (More)

- Noel Cressie, Nicolas Verzelen
- Computational Statistics & Data Analysis
- 2008

We consider the problem of detecting a tight community in a sparse random network. This is formalized as testing for the existence of a dense random subgraph in a random graph. Under the null hypothesis, the graph is a realization of an Erdös-Rényi graph on N vertices and with connection probability p0; under the alternative, there is an unknown subgraph on… (More)

Let (Y, (Xi)1≤i≤p) be a real zero mean Gaussian vector and V be a subset of {1, . . . , p}. Suppose we are given n i.i.d. replications of this vector. We propose a new test for testing that Y is independent of (Xi)i∈{1,...p}\V conditionally to (Xi)i∈V against the general alternative that it is not. This procedure does not depend on any prior information on… (More)

- Nicolas Verzelen
- 2009

We consider the problem of estimating the conditional mean of a real Gaussian variable Y = ∑p i=1 θiXi+ ǫ where the vector of the covariates (Xi)1≤i≤p follows a joint Gaussian distribution. This issue often occurs when one aims at estimating the graph or the distribution of a Gaussian graphical model. We introduce a general model selection procedure which… (More)

- Nicolas Verzelen
- 2009

This is a technical appendix to “Adaptive estimation of stationary Gaussian fields” [6]. We present several proofs that have been skipped in the main paper. These proofs are organised as in Section 8 of [6]. AMS 2000 subject classifications: Primary 62H11; secondary 62M40.