Kernel regression is a well-established nonparametric method, in which the target value of a query point is estimated using a weighted average of the surrounding training examples. The weights are typically obtained by applying a distance-based kernel function, which presupposes the existence of a distance measure.This paper investigates the use of Genetic Programming for the evolution of task-...

The combination of Support Vector Machines with very high dimensional kernels, such as string or tree kernels, suffers from two major drawbacks: first, the implicit representation of feature spaces does not allow us to understand which features actually triggered the generalization; second, the resulting computational burden may in some cases render unfeasible to use large data sets for trainin...

This paper presents some aspects of implementing a User-Mode Linux with as few changes to the original Linux kernel as possible. To port a Linux kernel to a User-Mode environment, basically all parts of the kernel directly interacting with the hardware must be changed. To accomplish this, we need an environment which simulates some hardware parts. This includes simulation of interfaces to devic...

I have recently shown that the Bergman kernel associated to a finitely connected domain in the plane is given as an explicit rational combination of finitely many basic functions of one complex variable. In this paper, it is proved that all the basic functions and constants in the new formula for the Bergman kernel can be evaluated using one-dimensional integrals and simple linear algebra. In f...

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for other methods the spectral information can be used to estimate the excess risk. An important question remains on how close the sample eigenvalues/eigenvectors a...

A function on R with multiple local minima is approximated from below, via linear programming, by a linear combination of convex kernel functions using sample points from the given function. The resulting convex kernel underestimator is then minimized, using either a linear equation solver for a linear-quadratic kernel or by a Newton method for a Gaussian kernel, to obtain an approximation to a...

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.

When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into the classification method at hand. A common prior knowledge is that many datasets are on some kinds of manifolds. Distance-based classification methods can make use of this by a modified distance measure called geodesic distance. We introduce a new...

Kernel function k1 ▸ fix two objects xa and xb for which we want to compute similarity score ▸ assume we have answers to all comparisons d(xa, xj) ? < d(xa, xk) and d(xb, xj) ? < d(xb, xk), xj, xk ∈ D ▸ can rank objects in D with respect to their dissimilarity to xa and also with respect to their dissimilarity to xb ▸ computing Kendall’s τ between the two rankings as similarity score between xa...

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting – and prevalent in several fields of study – problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and gen...