Related papers: Theory of approximation and continuity of random p…
Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…
The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes…
We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on…
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
The main result of this paper is a functional limit theorem for the sine-process. In particular, we study the limit distribution, in the space of trajectories, for the number of particles in a growing interval. The sine-process has the…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
Abundant literature has been published on approximation methods for the forward initial margin. The most popular ones being the family of regression methods. This paper describes the mathematical foundations on which these regression…
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity -- what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don't admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given…