Approximate kernel regression in Stata using random Fourier features

Nonlinear regression has wide application, including adjusting for confounders and secular trends in observational studies, modeling dose- and exposure-response relationships, predicting risk, and characterizing treatment effect heterogeneity. Kernel methods facilitate flexible nonparametric regression, but the computation time and memory of classical approaches scale quadratically in the number of observations. In this talk, I will describe the makerff command for approximating kernel regression using trigonometric basis functions called random Fourier features. With this approximation, time and memory scale linearly in the number of observations for a given number of features. The command generates these features from a covariate varlist; kernel regression can then be approximated by ridge-penalized regression for continuous, binary, count, and time-to-event outcomes. I will present examples in which the command is used to approximate kernel logistic regression for risk prediction, and kernel Cox regression with g-computation and bootstrap inference for marginal effect estimation.