  The projection pursuit regression (PPR) has played an important role in the
development of statistics and machine learning. However, when compared to other
established methods like random forests (RF) and support vector machines (SVM),
PPR has yet to showcase a similar level of accuracy as a statistical learning
technique. In this paper, we revisit the estimation of PPR and propose an
\textit{optimal} greedy algorithm and an ensemble approach via "feature
bagging", hereafter referred to as ePPR, aiming to improve the efficacy.
Compared to RF, ePPR has two main advantages. Firstly, its theoretical
consistency can be proved for more general regression functions as long as they
are $L^2$ integrable, and higher consistency rates can be achieved. Secondly,
ePPR does not split the samples, and thus each term of PPR is estimated using
the whole data, making the minimization more efficient and guaranteeing the
smoothness of the estimator. Extensive comparisons based on real data sets show
that ePPR is more efficient in regression and classification than RF and other
competitors. The efficacy of ePPR, a variant of Artificial Neural Networks
(ANN), demonstrates that with suitable statistical tuning, ANN can equal or
even exceed RF in dealing with small to medium-sized datasets. This revelation
challenges the widespread belief that ANN's superiority over RF is limited to
processing extensive sample sizes.
