Yaxuan Bai, Xiaofan Lu, Linan Zhang, Function approximations via $\ell_{1} -\ell_{2}$ optimization
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DOI: 10.23952/jano.6.2024.3.05
Volume 6, Issue 3, 1 December 2024, Pages 371-389
Abstract. In recent years, the difference-of-convex (DC) optimization has been successfully applied to real-world problems, including signal recovery and image processing. In this paper, we apply a special case of DC optimization, optimization, to the application of function approximation. Using the sparsity-promoting property of optimization, we aim to extract an approximation of an unknown function with parsimonious terms from random features. Using concentration inequalities of random variables, we derive a probabilistic error bound for a certain class of functions. From approximation experiments on both synthetic and real datasets, we demonstrate that the proposed optimization outperforms the benchmark algorithm in the aspect of approximation accuracy and robustness to randomness.
How to Cite this Article:
Y. Bai, X. Lu, L. Zhang, Function approximations via optimization, J. Appl. Numer. Optim. 6 (2024), 371-389.
