Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Polonik, Wolfgang"'
We derive Gaussian approximation bounds for random forest predictions based on a set of training points given by a Poisson process, under fairly mild regularity assumptions on the data generating process. Our approach is based on the key observation
Externí odkaz:
http://arxiv.org/abs/2403.09960
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true regression functi
Externí odkaz:
http://arxiv.org/abs/2402.14985
We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is bounded f
Externí odkaz:
http://arxiv.org/abs/2311.00140
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the add-one cos
Externí odkaz:
http://arxiv.org/abs/2210.10744
Autor:
Chandler, Gabriel, Polonik, Wolfgang
This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an extension of the depth quantile functions (DQF) approach. The DQF approa
Externí odkaz:
http://arxiv.org/abs/2201.06682
Autor:
Hacquard, Olympio, Balasubramanian, Krishnakumar, Blanchard, Gilles, Levrard, Clément, Polonik, Wolfgang
Publikováno v:
JMLR, 2022
We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami operator
Externí odkaz:
http://arxiv.org/abs/2110.13749
Autor:
Qiao, Wanli, Polonik, Wolfgang
The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose two novel algorithms, and provide theoretical guarantees for their con
Externí odkaz:
http://arxiv.org/abs/2104.12314
In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observati
Externí odkaz:
http://arxiv.org/abs/2103.14668
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the E
Externí odkaz:
http://arxiv.org/abs/2005.07557
The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. Existing limit theorems for topological statistics prove difficult to use in practice
Externí odkaz:
http://arxiv.org/abs/2005.01417