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New Kernels For Density and Regression Estimation via Randomized Histograms

Title:

New Kernels For Density and Regression Estimation via Randomized Histograms

Ruhi, Ruhi ORCID: https://orcid.org/0000-0001-7181-3816 (2018) New Kernels For Density and Regression Estimation via Randomized Histograms. Masters thesis, Concordia University.

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Abstract

In early 20’s, the first person to notice the link between Random Forests (RF)and Kernel Methods, Leo Breiman(Breiman, 2000), pointed out that RandomForests grown using independent and identically distributed random variables in the tree construction is equivalent to kernels acting on true distribution. Later, Scornet (Scornet, 2016b) defined Kernel-based Random Forest (KeRF) estimates and gave explicit expression for the kernels based on Centered RF and Uniform RF. In this paper, we will study the general expression for the connection function(kernel function) of an RF when splits/cuts are performed according to uniform distribution and also according to any general distribution. We also establish the consistency of KeRF estimates in both cases and their asymptotic normality.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Ruhi, Ruhi
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:28 August 2018
Thesis Supervisor(s):Sen, Arusharka
ID Code:984577
Deposited By: Ruhi Ruhi
Deposited On:16 Nov 2018 16:09
Last Modified:16 Nov 2018 16:09
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