  In this paper we propose using the principle of boosting to reduce the bias
of a random forest prediction in the regression setting. From the original
random forest fit we extract the residuals and then fit another random forest
to these residuals. We call the sum of these two random forests a
\textit{one-step boosted forest}. We show with simulated and real data that the
one-step boosted forest has a reduced bias compared to the original random
forest. The paper also provides a variance estimate of the one-step boosted
forest by an extension of the infinitesimal Jackknife estimator. Using this
variance estimate we can construct prediction intervals for the boosted forest
and we show that they have good coverage probabilities. Combining the bias
reduction and the variance estimate we show that the one-step boosted forest
has a significant reduction in predictive mean squared error and thus an
improvement in predictive performance. When applied on datasets from the UCI
database, one-step boosted forest performs better than random forest and
gradient boosting machine algorithms. Theoretically we can also extend such a
boosting process to more than one step and the same principles outlined in this
paper can be used to find variance estimates for such predictors. Such boosting
will reduce bias even further but it risks over-fitting and also increases the
computational burden.
