Reviews: Wavelet regression and additive models for irregularly spaced data

This paper proposes regression methods using wavelets, which does not require irregularly spaced data or the number of observation to be a power of 2. The key idea is to interpolate the raw data to fitted values on the regular grid and run regression algorithm with l1-penalty, i.e., proximal gradient descent. It is natural to generalize additive models for a potentially large number of covariates. The authors analyze (minimax) convergence rates of the proposed methods over Besov spaces. In experiments, they benchmark their methods under some synthetic functions and report that they perform better than competitors. The necessary assumptions of traditional wavelets regressions (equi-spaced and a power of 2 data) restricts to apply them into practical applications.