We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R-D given a noisy sample from the manifold. Under certain conditions, we show that the optimal rate of convergence is n(-2/(2+d)). Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded
International audienceIn this paper we consider the problem of optimality in manifold reconstruction...
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We sh...
In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-dimensio...
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimensi...
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimensi...
International audienceWe focus on the problem of manifold estimation: given a set of observations sa...
We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under sev...
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dime...
54 pages, 11 figuresInternational audienceMany algorithms in machine learning and computational geom...
21 pagesThe purpose of this paper is to study the problem of estimating a compactly supported densit...
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the d...
The hypothesis that high dimensional data tends to lie in the vicinity of a low di-mensional manifol...
We derive non-asymptotic minimax bounds for the Hausdorff estimation of $d$-dimensional submanifolds...
International audienceIn this paper, we address the problem of regression estimation in the context ...
Certains jeux de données présentent des caractéristiques géométriques et topologiques non triviales ...
International audienceIn this paper we consider the problem of optimality in manifold reconstruction...
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We sh...
In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-dimensio...
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimensi...
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimensi...
International audienceWe focus on the problem of manifold estimation: given a set of observations sa...
We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under sev...
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dime...
54 pages, 11 figuresInternational audienceMany algorithms in machine learning and computational geom...
21 pagesThe purpose of this paper is to study the problem of estimating a compactly supported densit...
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the d...
The hypothesis that high dimensional data tends to lie in the vicinity of a low di-mensional manifol...
We derive non-asymptotic minimax bounds for the Hausdorff estimation of $d$-dimensional submanifolds...
International audienceIn this paper, we address the problem of regression estimation in the context ...
Certains jeux de données présentent des caractéristiques géométriques et topologiques non triviales ...
International audienceIn this paper we consider the problem of optimality in manifold reconstruction...
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We sh...
In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-dimensio...