Related papers: Hypercomplex Generalizations of Gaussian-type Meas…
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…
Localization and dilation procedures are discussed for infinite dimensional $\alpha$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).
We introduce an entirely new class of high-order methods for computational fluid dynamics (CFD) based on the Gaussian Process (GP) family of stochastic functions. Our approach is to use kernel-based GP prediction methods to…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
We mainly consider two metrics: a Gromov hyperbolic metric and a scale invariant Cassinian metric. We compare these two metrics and obtain their relationship with certain well-known hyperbolic-type metrics, leading to several inclusion…
We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…
We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to…
Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…
Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of…
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…
Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…