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.