Privacy-preserving linear and nonlinear approximation via linear programming.

*(English)*Zbl 1270.90029Summary: 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 \(A\).

##### Keywords:

privacy-preserving approximation; random kernels; support vector machines; linear programming##### Software:

RSVM
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\textit{G. M. Fung} and \textit{O. L. Mangasarian}, Optim. Methods Softw. 28, No. 1, 207--216 (2013; Zbl 1270.90029)

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##### References:

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