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Multiple-Kernel Regression with Sparsity Constraints

S. Aziznejad, M. Unser

Proceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'19), Toulouse, French Republic, July 1-4, 2019, paper no. 103.

We consider the problem of learning a function from a sequence of its noisy samples in a continuous-domain hybrid search space. We adopt the generalized total-variation norm as a sparsity-promoting regularization term to make the problem well-posed. We prove that the solution of this problem admits a sparse kernel expansion with adaptive positions. We also show that the sparsity of the solution is upper-bounded by the number of data points. This allows for an enlargement of the search space and ensures the well-posedness of the problem.

AUTHOR="Aziznejad, S. and Unser, M.",
TITLE="Multiple-Kernel Regression with Sparsity Constraints",
BOOKTITLE="Proceedings of the Workshop on Signal Processing with
        Adaptive Sparse Structured Representations ({SPARS'19})",
address="Toulouse, French Republic",
month="July 1-4,",
note="paper no.\ 103")

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