Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve

Schretter, Colas; He, Zhijian; Gerber, Mathieu; Chopin, Nicolás; Niederreiter, Harald

doi:10.1007/978-3-319-33507-0_28

Cited by 6 publications

(5 citation statements)

References 16 publications

(22 reference statements)

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“…As shown in Gerber and Chopin () and Schretter et al . (), transformations through the Hilbert space filling curve and its inverse preserve a notion of distance between probability measures. The Hilbert curve

H : false[0, 1 false] \to {[0, 1]}^{d_{y}}

is a Hölder continuous mapping from [0,1] into

{false[0, 1 false]}^{d_{y}}

.…”

Section: Wasserstein Approximate Bayesian Computationmentioning

confidence: 99%

“…We propose a new distance generalizing this idea when d y > 1, by sorting samples according to their projection via the Hilbert space-filling curve. As shown in Gerber and Chopin (2015) and Schretter et al (2016), transformations through the Hilbert space-filling curve and its inverse preserve a notion of distance between probability measures. The Hilbert curve H : [0, 1] → [0, 1] dy is a Hölder continuous mapping from [0, 1] into [0, 1] dy .…”

Section: Hilbert Distancementioning

confidence: 99%

See 1 more Smart Citation

Approximate Bayesian Computation with the Wasserstein Distance

Bernton

Jacob

Gerber

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

104

145

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Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model.

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H : false[0, 1 false] \to {[0, 1]}^{d_{y}}

is a Hölder continuous mapping from [0,1] into

{false[0, 1 false]}^{d_{y}}

.…”

Section: Wasserstein Approximate Bayesian Computationmentioning

confidence: 99%

Section: Hilbert Distancementioning

confidence: 99%

Approximate Bayesian Computation with the Wasserstein Distance

Bernton

Jacob

Gerber

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

104

145

View full text Add to dashboard Cite

show abstract

“…We take, e.g., the [0.25, 0.5, 0.75] quantiles from * as bias values, to be used in computing PPV. We use a low-discrepancy sequence to assign quantiles to different kernel/dilation combinations [35].…”

Section: Biasmentioning

confidence: 99%

MiniRocket

Dempster

Schmidt

Webb

2021

Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery &Amp; Data Mining

197

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Rocket achieves state-of-the-art accuracy for time series classification with a fraction of the computational expense of most existing methods by transforming input time series using random convolutional kernels, and using the transformed features to train a linear classifier. We reformulate Rocket into a new method, MiniRocket. MiniRocket is up to 75 times faster than Rocket on larger datasets, and almost deterministic (and optionally, fully deterministic), while maintaining essentially the same accuracy. Using this method, it is possible to train and test a classifier on all of 109 datasets from the UCR archive to state-of-the-art accuracy in under 10 minutes. MiniRocket is significantly faster than any other method of comparable accuracy (including Rocket), and significantly more accurate than any other method of remotely similar computational expense. CCS CONCEPTS• Computing methodologies → Machine learning; • Information systems → Data mining.

show abstract

“…We take, e.g., the [0.25, 0.5, 0.75] quantiles from W d * X as bias values, to be used in computing PPV. We use a low-discrepancy sequence to assign quantiles to different kernel/dilation combinations [35].…”

Section: Biasmentioning

confidence: 99%

MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification

Dempster,

Schmidt,

Webb

2020

Preprint

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Until recently, the most accurate methods for time series classification were limited by high computational complexity. Rocket achieves stateof-the-art accuracy with a fraction of the computational expense of most existing methods by transforming input time series using random convolutional kernels, and using the transformed features to train a linear classifier. We reformulate Rocket into a new method, MiniRocket, making it up to 75 times faster on larger datasets, and making it almost deterministic (and optionally, with additional computational expense, fully deterministic), while maintaining essentially the same accuracy. Using this method, it is possible to train and test a classifier on all of 109 datasets from the UCR archive to state-of-the-art accuracy in less than 10 minutes. MiniRocket is significantly faster than any other method of comparable accuracy (including Rocket), and significantly more accurate than any other method of even roughly-similar computational expense. As such, we suggest that MiniRocket should now be considered and used as the default variant of Rocket.

show abstract

Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve

Cited by 6 publications

References 16 publications

Approximate Bayesian Computation with the Wasserstein Distance

Approximate Bayesian Computation with the Wasserstein Distance

MiniRocket

MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification

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