Related papers: The Completion of Covariance Kernels
Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…
We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the…
Enhancing classical machine learning (ML) algorithms through quantum kernels is a rapidly growing research topic in quantum machine learning (QML). A key challenge in using kernels -- both classical and quantum -- is that ML workflows…
This is a continuation of the study of the theory of quantum stochastic dilation of completely positive semigroups on a von Neumann or $C^*$ algebra, here with unbounded generators. The additional assumption of symmetry with respect to a…
The classical sequential growth model for causal sets provides a template for the dynamics in the deep quantum regime. This growth dynamics is intrinsically temporal and causal, with each new element being added to the existing causal set…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…
The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…