Related papers: Trends in recurrence analysis of dynamical systems
Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving many event types and observations have become prevalent with…
Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
Recent artificial intelligence (AI) technologies show remarkable evolution in various academic fields and industries. However, in the real world, dynamic data lead to principal challenges for deploying AI models. An unexpected data change…
The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
The aim of the present study is to detect abrupt trend changes in the mean of a multidimensional sequential signal. Directly inspired by papers of Fernhead and Liu ([4] and [5]), this work describes the signal in a hierarchical manner : the…
In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for…
This paper studies the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time…
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
We review recent developments in detecting and estimating multiple change-points in time series models with exogenous and endogenous regressors, panel data models, and factor models. This review differs from others in multiple ways: (1) it…
Our languages are in constant flux driven by external factors such as cultural, societal and technological changes, as well as by only partially understood internal motivations. Words acquire new meanings and lose old senses, new words are…
Recent progress in recommender system research has shown the importance of including temporal representations to improve interpretability and performance. Here, we incorporate temporal representations in continuous time via recurrent point…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
Across many data domains, co-occurrence statistics about the joint appearance of objects are powerfully informative. By transforming unsupervised learning problems into decompositions of co-occurrence statistics, spectral algorithms provide…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…