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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)
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)
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)
We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a lattice. To tackle this issue, a neighborhood selection procedure has been recently introduced. 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 fields (GMRFs)(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)
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)
We consider the problem of estimating the conditional mean of a real Gaussian variable Y = p i=1 θ i X i + ǫ where the vector of the covariates (X i) 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(More)