References:https://arxiv.org/abs/2206.02994
R package, Sieve. Perform nonparametric estimation by the method ofsieves (estimation using multivariate orthogonal series). This type ofestimators has been actively studied and applied in univariate featuresettings, but in multivariate cases it hasn’t received its deservedattention.
Installing a package from GitHub can be tricky. But I found 80% ofthe errors can be solved by restarting RStudio.
The current version can solve regression and classification problems.The algorithm gives the estimated condition mean (regression) andestimated conditional probability functions (classification). I willmake it able to handle time-to-event outcomes very soon.
The time and space expense both scale linearly in sample size and thenumber of basis functions specified by the users. Can directly handle10k x 100 (sample size x dimension of features) data scienceproblems.
Adaptive to the number of features/predictors truly associated withthe outcome. Can achieve the information lower bounds (minimax rate) ofestimation in many cases.
Generating the proper basis functions (something like multivariateFourier basis), put everything in a LASSO solver (thank you glmnet!).That’s it.
(Questions, suggestion, collaboration: shoot me an email: zty@uw.edu,Tianyu Zhang. Department of Biostatistics, University of Washington)