Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.Comment: 19 pages, 4 figure

Interpolation of discount factors

This paper deals with the problem of interpolation of discount factors between time buckets. The problem occurs when price and interest rate data of a market segment are assigned to discrete time buckets. A simple criterion is developed in order to identify arbitrage-free robust interpolation methods. Methods closely examined include linear, exponential and weighted exponential interpolation. Weighted exponential interpolation, a method still preferred by some banks and also offered by commercial software vendors, creates several problems and therefore makes simple exponential interpolation a more logical choice. Linear interpolation provides a good approximation of exponential interpolation for a sufficiently dense time grid. --

Modal interpolation program, L215 (INTERP). Volume 1: Engineering and usage

The usage of the Modal Interpolation Program L215 (INTERP) is described. The program uses modal data to form sets of arrays containing interpolation coefficients. The interpolation arrays can then be used to determine displacements at various aerodynamic surface and surface slopes that are parallel and perpendicular to the freestream direction. Five different interpolation methods are available. A description of the data manipulation and the interpolation methods is presented

Re-encoding reformulation and application to Welch-Berlekamp algorithm

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm