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Mathematical Research at the University of Cambridge


MARS is a popular method for nonparametric regression proposed by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural LASSO variant of the MARS method. Our method is based on least squares estimation over a convex class of functions obtained by considering infinite-dimensional linear combinations of functions in the MARS basis and putting a variation based complexity constraint. Our method is naturally connected to nonparametric function estimation methods under smoothness constraints. Under natural design assumptions, we prove that our estimator achieves a rate of convergence that depends only logarithmically on dimension and thus avoids the usual curse of dimensionality to some extent. This is joint work with Dohyeong Ki and Billy Fang.

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Oct 29th 2021
16:00 to 17:00



Aditya Guntuboyina (UC Berkeley)