Minimax Rates for STIT and Poisson Hyperplane Random Forests

09/22/2021
by   Eliza O'Reilly, et al.
0

In [12], Mourtada, Gaïffas and Scornet showed that, under proper tuning of the complexity parameters, random trees and forests built from the Mondrian process in ℝ^d achieve the minimax rate for β-Hölder continuous functions, and random forests achieve the minimax rate for (1+β)-Hölder functions in arbitrary dimension, where β∈ (0,1]. In this work, we show that a much larger class of random forests built from random partitions of ℝ^d also achieve these minimax rates. This class includes STIT random forests, the most general class of random forests built from a self-similar and stationary partition of ℝ^d by hyperplane cuts possible, as well as forests derived from Poisson hyperplane tessellations. Our proof technique relies on classical results as well as recent advances on stationary random tessellations in stochastic geometry.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/15/2018

Minimax optimal rates for Mondrian trees and forests

Introduced by Breiman (2001), Random Forests are widely used as classifi...
research
02/12/2018

Random Hinge Forest for Differentiable Learning

We propose random hinge forests, a simple, efficient, and novel variant ...
research
11/08/2017

Universal consistency and minimax rates for online Mondrian Forests

We establish the consistency of an algorithm of Mondrian Forests, a rand...
research
11/11/2019

Simplifying Random Forests: On the Trade-off between Interpretability and Accuracy

We analyze the trade-off between model complexity and accuracy for rando...
research
02/07/2012

Information Forests

We describe Information Forests, an approach to classification that gene...
research
08/06/2020

Modeling of time series using random forests: theoretical developments

In this paper we study asymptotic properties of random forests within th...
research
02/17/2020

Transmission and navigation on disordered lattice networks, directed spanning forests and scaling limits

Stochastic networks based on random point sets as nodes have attracted c...

Please sign up or login with your details

Forgot password? Click here to reset