Related papers: Point processes in a metric space

We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…

Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…

We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the…

We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…

With the continued digitization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when…

This paper defines pointwise clustering metrics, a collection of metrics for characterizing the similarity of two clusterings. These metrics have several interesting properties which make them attractive for practical applications. They can…

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…

Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we…

We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…

In this paper we characterize the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. The extremal sums behave completely different by compared to…

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…

Machine learning models are routinely integrated into process mining pipelines to carry out tasks like data transformation, noise reduction, anomaly detection, classification, and prediction. Often, the design of such models is based on…

Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among…

A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…

The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -- there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present…

We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…

Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…

We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…