A dynamic modeling approach for anomaly detection using stochastic differential equations

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

doi:10.1016/j.dsp.2016.03.006

Cited by 6 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is set as G(z, 0) = Q(z, 0) being the analytic solution [Eq. (10)] or can be supplied as a list of known samples associated to latent variable values. To observe a significant change in the statistics and challenge the training, we choose the dimensionless SDE parameters as ν = 1, σ = 0.7, x 0 = 4, and t 0 = −0.2 such that we evolve a narrow normal distribution with strongly shifted mean into a broad normal distribution at µ = 0.…”

Section: Qqm-based Generative Modellingmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

Paine,

Elfving,

Kyriienko

2021

Preprint

View full text Add to dashboard Cite

We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an underlying probability distribution and extract samples as DQC expectation values. Using quantile mechanics we propagate the system in time, thereby allowing for time-series generation. We test the method by simulating the Ornstein-Uhlenbeck process and sampling at times different from the initial point, as required in financial analysis and dataset augmentation. Additionally, we analyse continuous quantum generative adversarial networks (qGANs), and show that they represent quantile functions with a modified (reordered) shape that impedes their efficient time-propagation. Our results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE-based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.

show abstract

Section: Qqm-based Generative Modellingmentioning

confidence: 99%

“…In biology SDEs help in the studies of population dynamics [7] and epidemiology [8,9]. They can also help to detect anomalies [10]. SDEs are widely used in financial calculus [11], a fundamental component of all mechanisms of pricing financial derivatives and description of market dynamics.…”

Section: Introductionmentioning

confidence: 99%

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

Paine,

Elfving,

Kyriienko

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…[ 8,9 ] They can also help to detect anomalies. [ 10 ] SDEs are widely used in financial calculus, [ 11 ] a fundamental component of all mechanisms of pricing financial derivatives and description of market dynamics. Potential applications of SDEs in finance lie in predicting stock prices, currency exchange rates and more.…”

Section: Introductionmentioning

confidence: 99%

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time‐Series

Paine

Elfving²,

Kyriienko

2023

Adv Quantum Tech

View full text Add to dashboard Cite

A quantum algorithm is proposed for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, the quantile function is represented for an underlying probability distribution and samples extracted as DQC expectation values. Using quantile mechanics the system is propagated in time, thereby allowing for time‐series generation. The method is tested by simulating the Ornstein‐Uhlenbeck process and sampling at times different from the initial point, as required in financial analysis and dataset augmentation. Additionally, continuous quantum generative adversarial networks (qGANs) are analyzed, and the authors show that they represent quantile functions with a modified (reordered) shape that impedes their efficient time‐propagation. The results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE‐based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.

show abstract

“…Upcoming anomalies in asset operations cause a change in system dynamics, and induce deviation from its estimated density function. Statistical tests are used to evaluate if a newly recorded data point is significantly different to be deemed anomalous (Rajabzadeh et al, 2016;Kang, 2018).…”

Section: Introductionmentioning

confidence: 99%

Anomaly detection in a fleet of industrial assets with hierarchical statistical modeling

Dhada

Girolami

Parlikad

2020

DCE

View full text Add to dashboard Cite

Anomaly detection in asset condition data is critical for reliable industrial asset operations. But statistical anomaly classifiers require certain amount of normal operations training data before acceptable accuracy can be achieved. The necessary training data are often not available in the early periods of assets operations. This problem is addressed in this paper using a hierarchical model for the asset fleet that systematically identifies similar assets, and enables collaborative learning within the clusters of similar assets. The general behavior of the similar assets are represented using higher level models, from which the parameters are sampled describing the individual asset operations. Hierarchical models enable the individuals from a population, comprising of statistically coherent subpopulations, to collaboratively learn from one another. Results obtained with the hierarchical model show a marked improvement in anomaly detection for assets having low amount of data, compared to independent modeling or having a model common to the entire fleet.

show abstract

A dynamic modeling approach for anomaly detection using stochastic differential equations

Cited by 6 publications

References 18 publications

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time‐Series

Anomaly detection in a fleet of industrial assets with hierarchical statistical modeling

Contact Info

Product

Resources

About