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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)

- Nicolas Verzelen
- 2012

Consider the standard Gaussian linear regression model Y = Xθ 0 + ǫ, where Y ∈ R n is a response vector and X ∈ R n×p is a design matrix. Numerous work have been devoted to building efficient estimators of θ 0 when p is much larger than n. In such a situation, a classical approach amounts to assume that θ 0 is approximately sparse. This paper studies the… (More)

- Ery Arias-Castro, Nicolas Verzelen, Yuri I. Ingster
- 2013

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 un-weighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erdös-Rényi graph with probability p 0. Under the (composite) alternative, there is a… (More)

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 p 0 ; under the alternative, there is an unknown subgraph… (More)

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 m by a penalization method and estimating the covariance of X in the space of Gaussian Markov random… (More)

- Nicolas Verzelen
- 2009

This is a technical appendix to " Adaptive estimation of stationary Gaus-sian fields " [6]. We present several proofs that have been skipped in the main paper. These proofs are organised as in Section 8 of [6].

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional Principal Component Analysis. Interestingly, the procedures are completely data-driven and do not require any prior… (More)

Let (Y, (X i) 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 (X i) i∈{1,...p}\V conditionally to (X i) i∈V against the general alternative that it is not. This procedure does not depend on any prior information… (More)