Sparse generalized additive models (GAMs) are an extension of sparse generalized linear models which allow a model's prediction to vary non-linearly with an input variable. This enables the data analyst build more accurate models, especially when the linearity assumption is known to be a poor approximation of reality. Motivated by reluctant interaction modeling (Yu et al. 2019), we propose a multi-stage algorithm, called $\textit{reluctant additive modeling (RAM)}$, that can fit sparse generalized additive models at scale. It is guided by the principle that, if all else is equal, one should prefer a linear feature over a non-linear feature. Unlike existing methods for sparse GAMs, RAM can be extended easily to binary, count and survival data. We demonstrate the method's effectiveness on real and simulated examples.

We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the effect of each variable to be estimated as being either zero, linear, or a low-complexity curve, as determined by the data. We present a blockwise coordinate descent procedure for efficiently optimizing the penalized likelihood objective over a dense grid of the tuning parameter, producing a regularization path of additive models. We demonstrate the performance of our method on both real and simulated data examples, and compare it with existing techniques for additive model selection.