Gumbel central limit theorem for max-min and min-max

Eliazar, Iddo; Metzler, Ralf; Reuveni, Shlomi

doi:10.1103/physreve.100.020104

Cited by 10 publications

(4 citation statements)

References 49 publications

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“…For example, climate changes were found to be reflected in the appearance of extreme (record-breaking) temperatures [1,2], rainfall [3,4], and possibly other extreme weather conditions [5]. Statistics of records are also important in the context of earthquakes [6], in studies of stock pricing in economics [7,8], sports [9,10], and in the theory of random matrices [11][12][13] to name but a few (see, e.g. [14,15] for a more detailed overview).…”

Section: Introductionmentioning

confidence: 99%

Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Hartich

Godec

2019

J. Phys. A: Math. Theor.

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Extreme value functionals of stochastic processes are inverse functionals of the first passage time -a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for analyzing extreme value statistics of ergodic reversible Markov processes in confining potentials on the hand of the underlying relaxation eigenspectra. We derive a chain of inequalities, which bounds the long-time asymptotics of first passage densities, and thereby extrema, from above and from below. The bounds involve a time integral of the transition probability density describing the relaxation towards equilibrium. We apply our general results to the analysis of extreme value statistics at long times in the case of Ornstein-Uhlenbeck process and a 3-dimensional Brownian motion confined to a sphere, also known as Bessel process. We find that even on time-scales that are shorter than the equilibration time, the large deviation limit characterizing long-time asymptotics can approximate the statistics of extreme values remarkably well. Our findings provide a novel perspective on the study of extrema beyond the established limit theorems for sequences of independent random variables and for asymmetric diffusion processes beyond a constant drift.

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Section: Introductionmentioning

confidence: 99%

Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Hartich

Godec

2019

J. Phys. A: Math. Theor.

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“…Every other value is then transformed into a floating point number between these two bounding integers. Mathematically [48], this is achieved via the Equation ( 3).…”

Section: Data Normalisationmentioning

confidence: 99%

Generation of Synthetic CPTs with Access to Limited Geotechnical Data for Offshore Sites

et al. 2023

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The initial design phase for offshore wind farms does not require complete geotechnical mapping and individual cone penetration testing (CPT) for each expected turbine location. Instead, background information from open source studies and previous historic records for geology and seismic data are typically used at this early stage to develop a preliminary ground model. This study focuses specifically on the interpolation and extrapolation of cone penetration test (CPT) data. A detailed methodology is presented for the process of using a limited number of CPTs to characterise the geotechnical behavior of an offshore site using artificial neural networks. In the presented study, the optimised neural network achieved a predictive error of 0.067 . Accuracy is greatest at depths of less than 10m. The pitfalls of using machine learning for geospatial interpolation are explained and discussed.

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“…In the proposed system, Min-Max Scaling has been employed as a normalization technique for numerical features [22]. This process transforms the numerical features so that they all fall within the same scale, typically ranging from 0 to 1.…”

Section: Data Transformationmentioning

confidence: 99%

Intelligent Intrusion Detection Based on Multi-Model Federated Learning for Software Defined Network

Al-Ameer,

Bhaya

2023

IJSSE

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To address the challenges posed by traditional network architectures, the Software-Defined Network (SDN) architecture was introduced. However, SDNs are not immune to many security threats (e.g. Dos, Backdoors). In this paper, we present an advanced intrusion detection system that leverages federated learning (FL) and deep learning (DL) techniques to check whether attacks occur or not on SDN. FL has been employed as a collaborative learning technique, enabling various data planes to conduct local training on their respective client datasets. Following local training on each data plane, the local model parameters are securely transmitted to the controller server. At the controller server, these local training parameters are aggregated to construct a global model. The resulting aggregation outcome is then shared back with each local model to update them, enhancing their ability to detect attacks. Three datasets were used to evaluate the efficacy of the suggested method: UNSW-NB15, NF-UQ-NIDS-v2, and CICIDS2017. The obtained results demonstrate a strong performance in anomaly detection, with an accuracy value reach to 95.68%.

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Gumbel central limit theorem for max-min and min-max

Cited by 10 publications

References 49 publications

Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Generation of Synthetic CPTs with Access to Limited Geotechnical Data for Offshore Sites

Intelligent Intrusion Detection Based on Multi-Model Federated Learning for Software Defined Network

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