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- W2294175020 abstract "LASSO is known to have a problem of excessive shrinkage at a sparse representation. To analyze this problem in detail, in this paper, we consider a positive scaling for soft-thresholding estimators that are LASSO estimators in an orthogonal regression problem. We especially consider a non-parametric orthogonal regression problem which includes wavelet denosing. We first gave a risk (generalization error) of LARS (least angle regression) based soft-thresholding with a single scaling parameter. We then showed that an optimal scaling value that minimizes the risk under a sparseness condition is 1 + O ( log n / n ) , where n is the number of samples. The important point is that the optimal value of scaling is larger than one. This implies that expanding soft-thresholding estimator shows a better generalization performance compared to a naive soft-thresholding. This also implies that a risk of LARS-based soft-thresholding with the optimal scaling is smaller than without scaling. We then showed their difference is O ( log n / n ) . This also shows an effectiveness of the introduction of scaling. Through simple numerical experiments, we found that LARS-based soft-thresholding with scaling can improve both of sparsity and generalization performance compared to a naive soft-thresholding." @default.
- W2294175020 created "2016-06-24" @default.
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- W2294175020 date "2016-06-01" @default.
- W2294175020 modified "2023-09-26" @default.
- W2294175020 title "On scaling of soft-thresholding estimator" @default.
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- W2294175020 doi "https://doi.org/10.1016/j.neucom.2016.02.043" @default.
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