A path algorithm for the Fused Lasso Signal Approximator

10/03/2009

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by   Holger Hoefling, et al.

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The Lasso is a very well known penalized regression model, which adds an L_1 penalty with parameter λ_1 on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L_1 penalty with parameter λ_2 on the difference of neighboring coefficients, assuming there is a natural ordering. In this paper, we develop a fast path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ_1 and λ_2. In the supplement, we also give an algorithm for the general Fused Lasso for the case with predictor matrix ∈R^n × p with rank()=p.