We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated features. For fast sparse logistic regression, our computational speed-up over other best-subset search techniques owes to linear and quadratic surrogate cuts for the logistic loss that allow us to efficiently screen features for elimination, as well as use of a priority queue that favors a more uniform exploration of features. As an alternative to the logistic loss, we propose the exponential loss, which permits an analytical solution to the line search at each iteration. Our algorithms are generally 2 to 5 times faster than previous approaches. They produce interpretable models that have accuracy comparable to black box models on challenging datasets.

We introduce L0Learn: an open-source package for sparse regression and classification using L0 regularization. L0Learn implements scalable, approximate algorithms, based on coordinate descent and local combinatorial optimization. The package is built using C++ and has a user-friendly R interface. Our experiments indicate that L0Learn can scale to problems with millions of features, achieving competitive run times with state-of-the-art sparse learning packages. L0Learn is available on both CRAN and GitHub.