A crucial technique for scaling kernel methods to very large data sets reaching or exceeding millions of instances is based on low-rank approximation of kernel matrices. We introduce a new family of algorithms based on mixtures of Nyström approximations, ensemble Nyström algorithms, that yield more accurate low-rank approximations than the standard Nyström method. We give a detailed study of va...

This paper considers a Monte-Carlo Nystrom method for solving integral equations of the second kind, whereby values $(z(y_i))_{1\leq i\leq N}$ solution $z$ at set $N$ random and independent points $(y_i)_{1\leq are approximated by $(z_{N,i})_{1\leq discrete $N$-dimensional linear system obtained replacing with empirical average over samples N}$. Under unique assumption that equation admits $z(y...

A method is presented for solving the momentum-space Schrödinger equation with a linear potential. The Lande-subtracted momentum-space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved ...

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of s landmark points sampled by their ridge leverage scores, requiring just O(ns) kernel evaluations and O(ns) additional r...

In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally ...

An embedded diagonally implicit Range-Kutta Nystrom (RKN) method is constructed for the integration of initial value problems for second order ordinary differential equations possessing oscillatory solutions. This embedded method is derived using a three stage diagonally implicit Runge-Kutta Nystrom method of order four within which a third order three stage diagonally implicit Runge-Kutta Nyst...

The Nyström method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect of this method is the distribution according to which columns are sampled from the original matrix. In this work, we present an analysis of different sampling techniques for the Nyström method. Our analysis includes both empirical and the...

s: Giardina T.D., Baldwin J, Sittig DF, Singh H, Patient Perceptions of Test Result Notification Via the Patient Portal. Access, Analysis, Action. Public Health Informatics Conference, Atlanta, GA, August 19-25, 2016. Nystrom D.T., Giardina T.D., Baldwin J, Sittig D.F., Singh H., Exploring the Patient Perspective on Access, Interpretation, and Use of Test Results from Patient Portals. AMIA 2016...

The GMM (generalized min-max) kernel was recently proposed [5] as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM kernel to linear kernel. We call this approach as “GMM-GCWS”. In the machine learning l...

Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystro...