no code implementations • 15 Mar 2024 • Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian, Wolfgang Polonik
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.
no code implementations • 22 Feb 2024 • Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true regression function lies in an $L_2$-fractional Sobolev space with order $s\in (0, 1)$.
no code implementations • 31 Oct 2023 • Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
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 from above and below.
no code implementations • 19 Oct 2022 • Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
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.
no code implementations • 26 Oct 2021 • Olympio Hacquard, Krishnakumar Balasubramanian, Gilles Blanchard, Clément Levrard, Wolfgang Polonik
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 of the manifold, that are regularized with topological penalties.
no code implementations • 26 Apr 2021 • Wanli Qiao, Wolfgang Polonik
The extraction of filamentary structure from a point cloud is discussed.
no code implementations • 29 Nov 2016 • Rushil Anirudh, Jayaraman J. Thiagarajan, Irene Kim, Wolfgang Polonik
We present an approach to model time series data from resting state fMRI for autism spectrum disorder (ASD) severity classification.