Related papers: Random dynamical systems, entropies and informatio…
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…
Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
The rapid growth and diversity in service offerings and the ensuing complexity of information technology ecosystems present numerous management challenges (both operational and strategic). Instrumentation and measurement technology is, by…
This two-part paper presents a new approach to predictive analysis for social processes. Part I identifies a class of social processes, called positive externality processes, which are both important and difficult to predict, and introduces…
In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the…
Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…
Capturing both the structural and temporal aspects of interactions is crucial for many real world datasets like contact between individuals. Using the link stream formalism to capture the dynamic of the systems, we tackle the issue of…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Artificial intelligence models and methods commonly lack causal interpretability. Despite the advancements in interpretable machine learning (IML) methods, they frequently assign importance to features which lack causal influence on the…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…
Information theoretic quantities are extremely useful in discovering relationships between two or more data sets. One popular method---particularly for continuous systems---for estimating these quantities is the nearest neighbour…
This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…