Projection pursuit regression (PPR) is described in Hastie et al.'s The Elements of Statistical Learning in the chapter on neural networks. The algorithm was introduced by Friedman and Stuetzle (1981). It seems to be equivalent to fitting a neural network with one hidden layer, but where the hidden-node activation functions are non-parametric functions to be estimated. There is a function ppr in R for fitting PPR models, but I can find very little discussion of this method on the internet. Much of the scientific literature where PPR is mentioned dates from the 1990s and earlier. Is it fair to say that PPR is now obsolete, or are there situations where it has unique advantages over more commonly used methods such as neural networks?
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$\begingroup$ Your conclusion wrt PPRs obsolesence is consistent with my recollection of the method. After F&S came Rand's Sally Morton and her thesis which gave it wide publicity but subsequent objections pointed out its limitations and by the end of the 90s further development was derailed, even by Morton. $\endgroup$– user78229Commented Jul 24, 2023 at 11:05
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$\begingroup$ @MikeHunter Hi Mike. Can you recall some of the objections to PPR? $\endgroup$– EstacionarioCommented Jul 24, 2023 at 12:40
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$\begingroup$ Not in specifics but there were reviews published wrt criticisms of PPR in the years following Morton's Rand publication. Want me to dig them up for you? $\endgroup$– user78229Commented Jul 24, 2023 at 14:42
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$\begingroup$ @MikeHunter Yes, thanks, that would be helpful! $\endgroup$– EstacionarioCommented Jul 25, 2023 at 8:50
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1$\begingroup$ pnas.org/doi/10.1073/pnas.1801177115 "Although PPA has been found to perform better than PCA in most cases, there is some important notes to make on when PPA does not work. PPA does not work well when the class sizes are no equal." towardsdatascience.com/… "The main limitation of manual projection pursuit is the amount of time it takes to exhaustively explore a given space." davis.wpi.edu/~matt/courses/nland/node4.html $\endgroup$– user78229Commented Jul 25, 2023 at 13:46
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