We focus on an optimization algorithm for a normal-likelihood-based group Lasso in multivariate linear regression. A negative multivariate normallog-likelihoodfunction with a block-norm penalty is used as the object...
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ISBN:
(纸本)9789811627651;9789811627644
We focus on an optimization algorithm for a normal-likelihood-based group Lasso in multivariate linear regression. A negative multivariate normallog-likelihoodfunction with a block-norm penalty is used as the objective function. A solution for the minimization problem of a quadratic form with a norm penalty is given without using the Karush-Kuhn-Tucker condition. In special cases, the minimization problem can be solved without solving simultaneous equations of the first derivatives. We derive update equations of a coordinate descent algorithm for minimizing the objective function. Further, by using the result of the special case, we also derive update equations of an iterative thresholding algorithm for minimizing the objective function.
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