"Extremely efficient procedures for fitting the entire lasso or elastic-net
regularization path for linear regression, logistic and multinomial
regression models.
The algorithm uses cyclical coordinate descent in a pathwise fashion, as
described in the paper:
[1] Regularized Paths for Generalized Linear Models via Coordinate
Descent<http://www-stat.stanford.edu/%7Ehastie/Papers/glmnet.pdf>(Journal
of Statistical Software 33(1), 2010) and the paper:
Pathwise coordinate
optimization,<http://www-stat.stanford.edu/%7Etibs/ftp/fuse.pdf>The
Annals of Applied Statistics. Volume 1, Number 2 (2007), 302-332"
source: http://www-stat.stanford.edu/~tibs/glmnet-matlab/
The R glmnet package is only a wrapper to the original Fortran
implementation, there is also a outdated python wrapper "glmnet-python". By
glmnet linear regression I mean the algorithm used in
the glmnet implementation and described in [1] including the tricks you
mentioned.
> The current content of cd_fast.pyx is a partial implementation of
> those (only squared error regression loss without active set).
>
Yes, the current implementation uses "Naive Updates" as it is called in
[1], I'm using Covariance Updates that are cheaper from a O-notation
perspective. The drawback is that this can only be exploited if some values
are efficiently cached, that's where the problems are at the moment.
I hope this makes some sense.
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