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

Ensemble Projection Pursuit for General Nonparametric Regression