Feature selection for functional PLS

Partial least squares methods are applied to statistical problems where data result from discretized functions rather than individual predictors. We apply the discrete wavelet transform by preconditioning the normal equations to solve the problem on the wavelet domain. The relative importance of the wavelet coefficients is then assessed by adaptively rescaling the solution in the transformed coordinates. The final solution is finally expressed in original terms by means of the inverse wavelet transform. The proposed method is well adapted for large scale problems. It is especially suited for data resulting from discretized functions related to modern instrumentation. The computational ease of the wavelet transform combined with the adaptive rescaling of the final solution allows obtaining sparse solutions in a computationally fast and efficient manner.

► We treat functional regression problems using PLS regression. ► We apply the discrete wavelet preconditioning. ► We flag the relevant coefficients by rescaling in the wavelet domain. ► We illustrate our proposal with two spectroscopic applications.