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Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…

The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…

In a novel approach to quantum dynamics, we apply the tools of recurrence network analysis to the dynamics of the quantum mechanical expectation values of observables. We construct and analyse $\epsilon$-recurrence networks from the…

Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…

Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review…

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…

One of the important tasks of the Reliability Estimation is Analysis of the Fault Tree. A problem of Fault Trees analysis is considered one of the most complex ones, since structure of such trees is characterized by a considerable number of…

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…

Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…

Link prediction is a popular research area with important applications in a variety of disciplines, including biology, social science, security, and medicine. The fundamental requirement of link prediction is the accurate and effective…

The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…

While generative models have become increasingly prevalent across various domains, fundamental concerns regarding their reliability persist. A crucial yet understudied aspect of these models is the uncertainty quantification surrounding…

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be…

We investigate the risk of overestimating the performance gain when applying neural network based receivers in systems with pseudo random bit sequences or with limited memory depths, resulting in repeated short patterns. We show that with…

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…

Risk evaluation is a forecast, and its validity must be backtested. Probability distribution forecasts are used in this work and allow for more powerful validations compared to point forecasts. Our aim is to use bivariate copulas in order…

Widespread deployment of societal-scale machine learning systems necessitates a thorough understanding of the resulting long-term effects these systems have on their environment, including loss of trustworthiness, bias amplification, and…

In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…