71 citations · 180 across the 7 of their papers we have counts for
7 papers
Finding Singular Features
Christopher Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the -dimensi…
Nonparametric Inference For Density Modes
Christopher Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and…
Nonparametric ridge estimation
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It…
Manifold estimation and singular deconvolution under Hausdorff loss
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold esti…
Minimax Manifold Estimation
Christopher Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
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. We assume that the…
The Geometry of Nonparametric Filament Estimation
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We consider the problem of estimating filamentary structure from planar point process data. We make some connections with computational geometry and we develop nonparametric method…
On the path density of a gradient field
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
We consider the problem of reliably finding filaments in point clouds. Realistic data sets often have numerous filaments of various sizes and shapes. Statistical techniques exist f…