Regularization Paths for Generalized Linear Models via Coordinate Descent.

TLDR

We develop fast algorithms for estimating generalized linear models with convex penalties. The algorithms use cyclical coordinate descent along a regularization path to fit linear, logistic, and multinomial regression models with ℓ1, ℓ2, or elastic‑net penalties, and scale to large, sparse datasets. Comparative timing experiments show the new algorithms are considerably faster than competing methods.

Abstract

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multinomial regression problems while the penalties include ℓ(1) (the lasso), ℓ(2) (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.