Related papers: Equivalent symmetric kernels of determinantal poin…

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.

We study Palm measures of determinantal point processes with $J$-Hermitian correlation kernels. A point process $\mathbb{P}$ on the punctured real line $\mathbb{R}^* = \mathbb{R}_{+} \sqcup \mathbb{R}_{-}$ is said to be $\textit{balanced…

We construct a canonical embedding of the space $L^2$ over a determinantal point process to the fermionic Fock space. Equivalently, we show that a determinantal process is the spectral measure for some explicit commutative group of Gaussian…

We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are…

We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the…

Symmetric kernel matrices are a well-researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly…

We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…

Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…

The purpose of this article is to develop a theory behind the occurrence of "path-integral" kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants…

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large…

Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…

This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…

We study some random interlaced configurations considering the eigenvalues of the main minors of Hermitian random matrices of the classical complex Lie algebras. We claim that these random configurations are determinantal and give their…

At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance,…

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…

A Bayes point machine is a single classifier that approximates the majority decision of an ensemble of classifiers. This paper observes that kernel interpolation is a Bayes point machine for Gaussian process classification. This observation…

We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the H\"older continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…