Related papers: Generalizations of Mat\'ern's hard-core point proc…
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling density, with the gradient of an arbitrary density of interest…
We derive the (matrix-valued) Feynman rules of the mass perturbation theory and use it for the resummation of the $n$-point functions with the help of the Dyson-Schwinger equations. We use these results for a short review of the complete…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
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 Probability Hypothesis Density (PHD) filter, which is used for multi-target tracking based on sensor measurements, relies on the propagation of the first-order moment, or intensity function, of a point process. This algorithm assumes…
We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…
First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…
The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$)…
Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
Regulation of material softness has both theoretical and practical significances due to irreplaceable applications of soft matter in rather diverse areas. This article is dedicated to draft a theoretical category on interpreting the…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
A popular and flexible time series model for counts is the generalized integer autoregressive process of order $p$, GINAR($p$). These Markov processes are defined using thinning operators evaluated on past values of the process along with a…