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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.


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