Nonlinear approximation via compositions

Efficient Decentralized Nonlinear Approximation via Selective Gossip

Recently, gossip algorithms have received much attention from the wireless sensor network community due to their simplicity, scalability and robustness. Motivated by applications such as compression and distributed transform coding, we propose a new gossip algorithm called Selective Gossip. Unlike the traditional randomized gossip which computes the average of scalar values, we run gossip algor...

Privacy-preserving linear and nonlinear approximation via linear programming

We propose a novel privacy-preserving random kernel approximation based on a data matrix A ∈ R 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 ∈ Rm corresponding to each of the m rows of A. Our approximation of y is a re...

Sparse Nonlinear Support Vector Machines via Stochastic Approximation

Nonlinear support vector machines (SVMs) are more broadly useful than linear SVMs, as they can find more accurate predictors when the data under consideration have curved intrinsic category boundaries. Nonlinear SVM formulations based on kernels are, however, often much more expensive and data-intensive to solve than linear SVMs, and the resulting classifiers can be expensive to apply. This pap...

Nonlinear approximation

This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come from linear spaces but rather from nonlinear manifolds. The central question to be studied is what, if any, are the advantages of nonlinear approximation over the simpler, more established, linear methods. T...

Nonlinear Methods of Approximation