EPFL | Biomedical Imaging Group | Multikernel Regression

Multikernel Regression with Sparsity Constraint

S. Aziznejad, M. Unser

SIAM Journal on Mathematics of Data Science, vol. 3, no. 1, pp. 201-224, 2021.

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 multikernel 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 ℓ₁ penalty on the kernel coefficients. Finally, we illustrate numerically the outcome of our theory.

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AUTHOR="Aziznejad, S. and Unser, M.",
TITLE="Multikernel Regression with Sparsity Constraint",
JOURNAL="{SIAM} Journal on Mathematics of Data Science",
YEAR="2021",
volume="3",
number="1",
pages="201--224",
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