arXiv subjects

Hynek Lavička

Publications and source records attributed to Hynek Lavička.

4 recordsLinked to original sources

arXiv2026

On the Practical Estimation and Interpretation of Rényi Transfer Entropy

Rényi transfer entropy (RTE) is a generalization of classical transfer entropy that replaces Shannon's entropy with Rényi's information measure. This, in turn, introduces a new tunable parameter $α$, which accounts for sensitivity to low- or high-probability events. Although RTE shows strong potential for analyzing causal relations in complex, non-Gaussian systems, its practical use is limited, primarily due to challenges related to its accurate estimation and interpretation. These difficulties are especially pronounced when working with finite, high-dimensional, or heterogeneous datasets. In this paper, we systematically study the performance of a k-nearest neighbor estimator for both Rényi entropy (RE) and RTE using various synthetic data sets with clear cause-and-effect relationships inherent to their construction. We test the estimator across a broad range of parameters, including sample size, dimensionality, memory length, and Rényi order $α$. In particular, we apply the estimator to a set of simulated processes with increasing structural complexity, ranging from linear dynamics to nonlinear systems with multi-source couplings. To address interpretational challenges arising from potentially negative RE and RTE values, we introduce three reliability conditions and formulate practical guidelines for tuning the estimator parameters. We show that when the reliability conditions are met and the parameters are calibrated accordingly, the resulting effective RTE estimates accurately capture directional information flow across a broad range of scenarios. Results obtained show that the explanatory power of RTE depends sensitively on the choice of the Rényi parameter $α$. This highlights the usefulness of the RTE framework for identifying the drivers of extreme behavior in complex systems.

nlin.PS↗

arXiv2022

Causal inference in time series in terms of Rényi transfer entropy

Uncovering causal interdependencies from observational data is one of the great challenges of nonlinear time series analysis. In this paper, we discuss this topic with the help of information-theoretic concept known as Rényi information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi transfer entropy. We show that by choosing Rényi $α$ parameter appropriately we can control information that is transferred only between selected parts of underlying distributions. This, in turn, provides particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of "black swan" events such as spikes or sudden jumps are of a key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend this results to heavy-tailed $α$-Gaussian variables. These results allow to establish connection between autoregressive and Rényi entropy based information-theoretic approaches to data-driven causal inference. To aid our intuition we employ Leonenko et al. entropy estimator and analyze Rényi information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi transfer entropy not only allowed us to detect a threshold of synchronization but it also provided a non-trivial insight into the structure of a transient regime that exists between region of chaotic correlations and synchronization threshold. In addition, from Rényi transfer entropy we could reliably infer the direction of coupling - and hence causality, only for coupling strengths smaller that the onset value of transient regime, i.e. when two Rössler systems were coupled, but have not yet entered a synchronization.

cs.IT↗

arXiv2017

Transitions between superstatistical regimes: validity, breakdown and applications

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.

q-fin.ST↗

arXiv2016

Fluctuation analysis of high frequency electric power load in the Czech Republic

We analyze the electric power load in the Czech Republic (CR) which exhibits a seasonality as well as other oscillations typical for European countries. Moreover, we detect 1/f noise property of electrical power load with extra additional peaks that allows to separate it into a deterministic and stochastic part. We then focus on the analysis of the stochastic part using improved Multi-fractal Detrended Fluctuation Analysis method (MFDFA) to investigate power load datasets with a minute resolution. Extracting the noise part of the signal by using Fourier transform allows us to apply this method to obtain the fluctuation function and to estimate the generalized Hurst exponent together with the correlated Hurst exponent, its improvement for the non-Gaussian datasets. The results exhibit a strong presence of persistent behaviour and the dataset is characterized by a non-Gaussian skewed distribution. There are also indications for the presence of the probability distribution that has heavier tail than the Gaussian distribution.

physics.soc-ph↗