The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Previous work [1] has show...

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...

Imitation learning refers to the problem where an agent learns a policy that mimics the demonstration provided by the expert, without any information on the cost function of the environment. Classical approaches to imitation learning usually rely on a restrictive class of cost functions that best explains the expert’s demonstration, exemplified by linear functions of pre-defined features on sta...

Given sets of observations of training and test data, we consider the problem of re-weighting the training data such that its distribution more closely matches that of the test data. We achieve this goal by matching covariate distributions between training and test sets in a high dimensional feature space (specifically, a reproducing kernel Hilbert space). This approach does not require distrib...

The problem of estimating the marginal density of a linear process by kernel methods is considered. Under general conditions, kernel density estimators are shown to be asymptotically normal. Their limiting covariance matrix is computed. We also find the optimal bandwidth in the sense that it asymptotically minimizes the mean square error of the estimators. The assumptions involved are easily ve...

The kernel bandwidth of the classical Mean-Shift tracking algorithm is fixed, and it usually results in tracking failure when the target’s size changes. A kernel bandwidth adaptive Mean-Shift tracking algorithm is presented with frame difference method to solve the question in this paper. According to the targets’ size obtained from the inter-frame difference method, the bandwidth matrix of ker...

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the ...

Abstract: In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared error based bandwidth estimators are introduced and their performance is illustrated via Monte Carlo simulation. The least-squares cross-validation me...

In this study, morphological characteristics as well as ten of Simple Sequence Repeat (SSRs) loci were used to analyze the genetic diversity and relationships among 12 natural populations of Persian walnut (Juglans regia L.) in northern and western regions of Iran. The results showed that there was a high level of genetic diversity among the walnuts, both in terms of their SSRs loci as well as ...