Lasso

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Lasso.jl is a pure Julia implementation of the glmnet coordinate descent algorithm for fitting linear and generalized linear Lasso and Elastic Net models, as described in:

Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1. http://www.jstatsoft.org/v33/i01/

Lasso.jl also includes an implementation of the O(n) fused Lasso implementation described in:

Johnson, N. A. (2013). A dynamic programming algorithm for the fused lasso and L0-segmentation. Journal of Computational and Graphical Statistics, 22(2), 246–260. doi:10.1080/10618600.2012.681238

As well as an implementation of polynomial trend filtering based on:

Ramdas, A., & Tibshirani, R. J. (2014). Fast and flexible ADMM algorithms for trend filtering. arXiv Preprint arXiv:1406.2082. Retrieved from http://arxiv.org/abs/1406.2082

Also implements the Gamma Lasso, a concave regularization path glmnet variant: Taddy, M. (2017) One-Step Estimator Paths for Concave Regularization Journal of Computational and Graphical Statistics, 26:3, 525-536 http://dx.doi.org/10.1080/10618600.2016.1211532

Quick start

To fit a Lasso path with default parameters:

fit(LassoPath, X, y, dist, link)

dist is any distribution supported by GLM.jl and link defaults to the canonical link for that distribution.

To fit a fused Lasso model:

fit(FusedLasso, y, λ)

To fit a polynomial trend filtering model:

fit(TrendFilter, y, order, λ)

To fit a Gamma Lasso path:

fit(GammaLassoPath, X, y, dist, link; γ=1.0)

It supports the same parameters as fit(LassoPath...), plus γ which controls the concavity of the regularization path. γ=0.0 is the Lasso. Higher values tend to result in sparser coefficient estimates.

More documentation is available at .

TODO

• User-specified weights are untested
• Maybe integrate LARS.jl

See also

• LassoPlot.jl, a package for plotting regularization paths.
• GLMNet.jl, a wrapper for the glmnet Fortran code.
• LARS.jl, an implementation of least angle regression for fitting entire linear (but not generalized linear) Lasso and Elastic Net coordinate paths.