1. What are the contributions in "Variable selection in wavelet regression models" ?
By performing variable selection in the wavelet domain the authors show that it is possible to identify important variables as being part of shortor large-scale features.. In this article the authors demonstrate three types of variable selection methods applied to the wavelet domain: selection of optimal combination of scales, thresholding based on mutual information and truncation of weight vectors in the partial least squares ( PLS ) regression algorithm.. Therefore, the suggested method is to extract information about the selected variables that otherwise would have been inaccessible.. This information can be used to suggest whether the underlying features may be dominated by narrow ( selective ) peaks ( indicated by variables in short wavelet scale regions ) or by broader regions ( indicated by variables in long wavelet scale regions ).
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![Fig. 6. (A) The b-coefficient vector from the PLS model with the best scale combination using the scales [1 3 5 6 7] for Data set 2 is shown. The RMS prediction is 9.3%; (B) the result after performing PLS variable selection by truncating w-vector coefficients on Data set 2. Prediction RMS here is 7.9% with 44 variables; (C) mutual information variable selection on Data set 2 where the MI model is chosen on the basis on the best model in the calibration set; (D) mutual information variable selection on Data set 2 where the MI model is forced to use only the first 44 variables (to make it comparable with results in (B)).](/figures/fig-6-a-the-b-coefficient-vector-from-the-pls-model-with-the-26gzmu8b.png)

