Related papers: Rotation Invariant Angular Descriptor Via A Bandli…

Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…

This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…

Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…

We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs)…

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the $d$-dimensional Euclidean space. Both the…

We establish some new bounds on the log-covering numbers of (anisotropic) Gaussian reproducing kernel Hilbert spaces. Unlike previous results in this direction we focus on small explicit constants and their dependency on crucial parameters…

We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…