Rodeo: Sparse, greedy nonparametric regression

TL;DR

Rodeo is a greedy, nonparametric regression method that adaptively selects relevant variables and bandwidths, effectively reducing dimensionality and achieving near-optimal convergence rates.

Contribution

It introduces a novel greedy approach for simultaneous variable and bandwidth selection in nonparametric regression, avoiding the curse of dimensionality.

Findings

Achieves near optimal minimax rates in relevant variables

Avoids curse of dimensionality under certain conditions

Easy to implement and computationally efficient

Abstract

We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method--called rodeo (regularization of derivative expectation operator)--conducts a sequence of hypothesis tests to threshold derivatives, and is easy to implement. Under certain assumptions on the regression function and sampling density, it is shown that the rodeo applied to local linear smoothing avoids the curse of dimensionality, achieving near optimal minimax rates of convergence in the number of relevant variables, as if these variables were isolated in advance.