Lasso and elastic nets by orthants
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We propose a new method for computing the lasso path, using the fact that the Manhattan norm of the coefficient vector is linear over every orthant of the parameter space. We use simple calculus and present an algorithm in which the lasso path is series of orthant moves. Our proposal gives the same results as standard literature, with the advantage of neat interpretation of results and explicit lasso formulæ. We extend this proposal to elastic nets and obtain explicit, exact formulæ for the elastic net path, and with a simple change, our lasso algorithm can be used for elastic nets. We present computational examples and provide simple R prototype code.
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