Abstract: We consider n-by-n matrices whose (i, j)-th entry is f(XT i Xj), where X1, . . . ,Xn are i.i.d. standard Gaussian random vectors in Rp, and f is a real-valued function. The eigenvalue distribution of these random kernel matrices is studied at the “large p, large n” regime. It is shown that, when p, n → ∞ and p/n = γ which is a constant, and f is properly scaled so that V ar(f(XT i Xj)...

Computing with functions on SO(3) is a task found in various areas of application. When it comes to approximation kernel based methods are a suitable tool to handle these functions. In this paper we present an algorithm which allows us to evaluate linear combinations of functions on SO(3) as well as an truly fast algorithm to sum up radial functions on SO(3). These approaches based on non-equis...

One of the central problems in the study of Support vector machine (SVM) is kernel selection, that’s based essentially on the problem of choosing a kernel function for a particular task and dataset. By contradiction to other machine learning algorithms, SVM focuses on maximizing the generalisation ability, which depends on the empirical risk and the complexity of the machine. In the following p...

The kernel density estimator (KDE) based on a radial positive-semidefinite kernel may be viewed as a sample mean in a reproducing kernel Hilbert space. This mean can be viewed as the solution of a least squares problem in that space. Replacing the squared loss with a robust loss yields a robust kernel density estimator (RKDE). Previous work has shown that RKDEs are weighted kernel density estim...

We present an in-depth examination of the effectiveness of radial basis function kernel (beyond Gaussian) estimators based on orthogonal random feature maps. We show that orthogonal estimators outperform state-of-the-art mechanisms that use iid sampling under weak conditions for tails of the associated Fourier distributions. We prove that for the case of many dimensions, the superiority of the ...

We report results from molecular dynamics studies concerning the microscopic structure and dynamics of the ternary, bulk metallic glass-forming Cu60Ti20Zr20 alloy. In detail we consider the partial radial distribution functions, nearest-neighbor numbers, specific heat, simulated glass temperature, diffusion coefficients, and incoherent intermediate scattering function (ISF). The applied atomic ...

Keywords: Approximate solutions to integral equations Radial and kernel-based networks Gaussian kernels Model complexity Analysis of algorithms a b s t r a c t Approximate solutions to inhomogeneous Fredholm integral equations of the second kind by radial and kernel networks are investigated. Upper bounds are derived on errors in approximation of solutions of these equations by networks with in...

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong linear properties. This negative result hints that radial kernel are perhaps not suitable over geo...

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong linear properties. This negative result hints that radial kernel are perhaps not suitable over geo...

Computing with functions on the rotation group is a task found in various areas of application. When it comes to approximation kernel based methods are a suitable tool to handle these functions. In this paper we present an algorithm which allows us to evaluate linear combinations of functions on the rotation group as well as an truly fast algorithm to sum up radial functions on the rotation gro...