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Privacy-preserving linear and nonlinear approximation via linear programming. (English) Zbl 1270.90029
Summary: We propose a novel privacy-preserving random kernel approximation based on a data matrix $$A\in \mathbb{R}^{m\times n}$$ whose rows are divided into privately owned blocks. Each block of rows belongs to a different entity that is unwilling to share its rows or make them public. We wish to obtain an accurate function approximation for a given $$y\in \mathbb{R}^m$$ corresponding to each of the $$m$$ rows of $$A$$. Our approximation of $$y$$ is a real function on $$\mathbb{R}^n$$ evaluated at each row of $$4$$ and is based on the concept of a reduced kernel $$K(A, B^{\prime})$$, where $$B^\prime$$ is the transpose of a completely random matrix $$B$$. The proposed linear-programming-based approximation, which is public but does not reveal the privately held data matrix $$A$$, has an accuracy comparable to that of an ordinary kernel approximation based on a publicly disclosed data matrix $$A$$.
MSC:
 90C05 Linear programming 90C90 Applications of mathematical programming
RSVM
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References:
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