Bias reduction for non-asymptotic inference on the true regression function using random forests

Develop bias-reduction methodology for the k-PNN random-forest estimator that enables construction of non-asymptotically valid confidence intervals for the true regression function value r0(x0), including suitable data-driven bias correction and variance estimation that align with the established Gaussian approximations.

Background

The Gaussian approximation results in the paper imply non-asymptotic confidence intervals for the expected random-forest prediction, but not directly for the true regression function r0(x0) because the bias is non-negligible relative to the standard deviation.

The authors provide bias bounds that demonstrate this non-negligibility and note that effective bias reduction is crucial to obtain valid confidence intervals for r0(x0). While prior work has addressed bias in different random-forest variants (e.g., subsampling/bagging), a non-asymptotic bias-reduction approach compatible with their framework is still lacking.