Multi-Kernel Regression with Sparsity Constraint
Machine Learning
2020-12-18 v4 Machine Learning
Abstract
In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised learning in a continuous-domain hybrid search space with gTV regularization. We show that the solution admits a multi-kernel expansion with adaptive positions. In this representation, the number of active kernels is upper-bounded by the number of data points while the gTV regularization imposes an penalty on the kernel coefficients. Finally, we illustrate numerically the outcome of our theory.
Cite
@article{arxiv.1811.00836,
title = {Multi-Kernel Regression with Sparsity Constraint},
author = {Shayan Aziznejad and Michael Unser},
journal= {arXiv preprint arXiv:1811.00836},
year = {2020}
}