Cross validation in LASSO and its acceleration

We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative discussion assuming that the number of observations is suffic...

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Veröffentlicht in:Journal of statistical mechanics Jg. 2016; H. 5
Hauptverfasser: Obuchi, Tomoyuki, Kabashima, Yoshiyuki
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IOP Publishing and SISSA 31.05.2016
ISSN:1742-5468
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Abstract We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative discussion assuming that the number of observations is sufficiently large, we provide simple formulas for approximately assessing two types of CV errors, which enable us to significantly reduce the necessary cost of computation. These formulas also provide a simple connection of the CV errors to the residual sums of squares between the reconstructed and the given measurements. Second, on the basis of this finding, we analytically evaluate the CV errors when the design matrix is given as a simple random matrix in the large size limit by using the replica method. Finally, these results are compared with those of numerical simulations on finite-size systems and are confirmed to be correct. We also apply the simple formulas of the first type of CV error to an actual dataset of the supernovae.
AbstractList We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative discussion assuming that the number of observations is sufficiently large, we provide simple formulas for approximately assessing two types of CV errors, which enable us to significantly reduce the necessary cost of computation. These formulas also provide a simple connection of the CV errors to the residual sums of squares between the reconstructed and the given measurements. Second, on the basis of this finding, we analytically evaluate the CV errors when the design matrix is given as a simple random matrix in the large size limit by using the replica method. Finally, these results are compared with those of numerical simulations on finite-size systems and are confirmed to be correct. We also apply the simple formulas of the first type of CV error to an actual dataset of the supernovae.
Author Obuchi, Tomoyuki
Kabashima, Yoshiyuki
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  givenname: Tomoyuki
  surname: Obuchi
  fullname: Obuchi, Tomoyuki
  email: obuchi@c.titech.ac.jp
  organization: Tokyo Institute of Technology Department of Mathematical and Computing Science, Yokohama, Kanagawa, 226-8502, Japan
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  givenname: Yoshiyuki
  surname: Kabashima
  fullname: Kabashima, Yoshiyuki
  email: kaba@c.titech.ac.jp
  organization: Tokyo Institute of Technology Department of Mathematical and Computing Science, Yokohama, Kanagawa, 226-8502, Japan
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Snippet We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator...
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Title Cross validation in LASSO and its acceleration
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