Trend filtering for functional regression

We propose a penalized approach for scalar on function regression. The method combines ideas from the trend filtering literature and regularization, allowing great flexibility and adaptivity to different degree of smoothness. The method leverages on a proper transformation of the functional predictor based on derivative operators of a certain degree. This allows to define an equivalent generalized lasso problem, that has some similarity to the spline basis approach, but removes the constraints on the locations of the basis. The perfomances of the methods are shown via experimental results.