On regularized polynomial functional regression
This work addresses regression problems in functional data analysis, offering incremental theoretical and practical advances.
The paper tackles polynomial functional regression by establishing a novel finite sample bound that incorporates smoothness, capacity, and regularization, extending results from linear functional regression. It provides numerical evidence that higher-order polynomial terms improve performance.
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity conditions, and regularization techniques. In doing so, it extends and generalizes several findings from the context of linear functional regression as well. We also provide numerical evidence that using higher order polynomial terms can lead to an improved performance.