We develop a super-fast kernel density estimation algorithm (FastKDE) and based on this a fast kernel independent component analysis algorithm (KDICA). FastKDE calculates the kernel density estimator exactly and its computation only requires sorting n numbers plus roughly 2n evaluations of the exponential function, where n is the sample size. KDICA converges as quickly as parametric ICA algorit...

Kernel principal component analysis has been introduced as a method of extracting a set of orthonormal nonlinear features from multivariate data, and many impressive applications are being reported within the literature. This article presents the view that the eigenvalue decomposition of a kernel matrix can also provide the discrete expansion coefficients required for a nonparametric orthogonal...

Given an i.i.d. sample drawn from a density f on the real line, the problem of testing whether f is in a given class of densities is considered. Testing procedures constructed on the basis of minimizing the L1-distance between a kernel density estimate and any density in the hypothesized class are investigated. General non-asymptotic bounds are derived for the power of the test. It is shown tha...

Main techniques of probability density estimation on Riemannian manifolds are reviewed in the hyperbolic case. For computational reasons we chose to focus on the kernel density estimation and we provide the expression of Pelletier estimator on hyperbolic space. The method is applied to density estimation of re ection coe cients from radar observations.

A Greek weight associated to a parameterized random variable Z(λ) is a random variable π such that ∇λE[φ(Z(λ))] =E[φ(Z(λ))π] for any function φ. The importance of the set of Greek weights for the purpose of Monte Carlo simulations has been highlighted in the recent literature. Our main concern in this paper is to devise methods which produce the optimal weight, which is well known to be given b...

We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed bandwidth as well as for various variable bandwidths, e.g. the nearest neighbor bandwidth. An elementary p...

We analyze a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical M -estimation. The KDE based on a Gaussian kernel is interpreted as a sample mean in the associated reproducing kernel Hilbert space (RKHS). This mean is esti...

The kernel method has become a useful trick and has been widely applied to various learning models to extend their nonlinear approximation and classification capabilities. Such extensions have also recently occurred to the Self-Organising Map (SOM). In this paper, two recently proposed kernel SOMs are reviewed, together with their link to an energy function. The Self-Organising Mixture Network ...

In this paper, a class of estimators of the center of symmetry based on the empirical characteristic function is examined. In the spirit of the Hodges-Lehmann estimator, the resulting procedures are shown to be a function of the pairwise averages. The proposed procedures are also shown to have an equivalent representation as the minimizers of certain distances between two corresponding kernel d...

High density clusters can be characterized by the connected components of a level set L(λ) = {x : p(x) > λ} of the underlying probability density function p generating the data, at some appropriate level λ ≥ 0. The complete hierarchical clustering can be characterized by a cluster tree T = ⋃ λ L(λ). In this paper, we study the behavior of a density level set estimate L̂(λ) and cluster tree estim...