Related papers: Measuring dependencies between variables of a dyna…

Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…

We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…

This paper briefly elaborates on a development in (applied) fuzzy logic that has taken place in the last couple of decades, namely, the complementation or even replacement of the traditional knowledge-based approach to fuzzy rule-based…

Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting…

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…

In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…

This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of…

Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…

Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…

Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…

We consider analysis of dependent functional data that are correlated because of a longitudinal-based design: each subject is observed at repeated time visits and for each visit we record a functional variable. We propose a novel…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

In a typical supervised machine learning setting, the predictions on all test instances are based on a common subset of features discovered during model training. However, using a different subset of features that is most informative for…

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…

A model-free measure of coupling between dynamical variables is built from time series embedding principle. The approach described does not require a mathematical form for the dynamics to be assumed. The approach also does not require…