<b>GaussianProcesses.jl</b>: A Nonparametric Bayes Package for the <i>Julia</i> Language

Fairbrother, Jamie; Nemeth, Christopher; Rischard, Maxime; Brea, Johanni

doi:10.18637/jss.v102.i01

“…The hyperparameters σ n , σ f , ℓ 1 , and ℓ 2 are estimated in J ulia [39] using the package developed by Fairbrother et al [55]. This package estimates the hyperparameters using maximum likelihood estimation [31, Chapter 5] using the package by Mogensen et al [56].…”

Section: Methodsmentioning

confidence: 99%

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

VandenHeuvel

¹

,

Drovandi

²

,

Simpson

³

2022

Preprint

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Parameter estimation for mathematical models of biological processes is often difficult and depends significantly on the quality and quantity of available data. We introduce an efficient framework using Gaussian processes to discover mechanisms underlying delay, migration, and proliferation in a cell invasion experiment. Gaussian processes are leveraged with bootstrapping to provide uncertainty quantification for the mechanisms that drive the invasion process. Our frame-work is efficient, parallelisable, and can be applied to other biological problems. We illustrate our methods using a canonical scratch assay experiment, demonstrating how simply we can explore different functional forms and develop and test hypotheses about underlying mechanisms, such as whether delay is present. All code and data to reproduce this work is available at https://github.com/DanielVandH/EquationLearning.jl.1Author summaryIn this work we introduce uncertainty quantification into equation learning methods, such as physics-informed and biologically-informed neural networks. Our framework is efficient and applicable to problems with unknown nonlinear mechanisms that we wish to learn from experiments where only sparse noisy data is available. We demonstrate our methods on a canonical scratch assay experiment from cell biology and show the underlying mechanisms can be learned, providing uncertainty intervals for functional forms and for solutions to partial differential equation models believed to describe the experiment.

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“…Plots.jl is used for visualizations in scientific publications from different fields, such as numerics [32,4,9,11,15,24], mathematics [14], biology [3,6], ecology [13] and geology [10,23] as well as for teaching purposes [8,22].…”

Section: Usagementioning

confidence: 99%

Plots.jl – A User Extendable Plotting API for the Julia Programming Language

Christ

¹

,

Schwabeneder

²

,

Rackauckas

³

et al. 2023

Journal of Open Research Software

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There are many excellent plotting libraries. Each excels at a specific use case: one is particularly suited for creating printable 2D figures for publication, another for generating interactive 3D graphics, while a third may have excellent LaTeX integration or be ideal for creating dashboards on the web. The aim of Plots.jl is to enable the user to use the same syntax to interact with a range of different plotting libraries, making it possible to change the library that does the actual plotting (the backend) without needing to touch the code that creates the content -and without having to learn multiple application programming interfaces (API). This is achieved by separating the specification of the plot from the implementation of the graphical backend. This plot specification is extendable by a recipe system that allows package authors and users to create new types of plots, as well as to specify how to plot any type of object (e.g. a statistical model, a map, a phylogenetic tree or the solution to a system of differential equations) without depending on the Plots.jl package. This design supports a modular ecosystem structure for plotting and yields a high code reuse potential across the entire Julia package ecosystem. Plots.jl is publicly available at https://github.com/JuliaPlots/Plots.jl.

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“…The hyperparameters σ n , σ f , ℓ 1 , and ℓ 2 are estimated in JULIA [40] using the Gaussian-Processes package developed by Fairbrother et al [55]. This package estimates the hyperparameters using maximum likelihood estimation [33,Chapter 5] using the Optim package by Mogensen et al [56].…”

Section: Fitting Gaussian Processesmentioning

confidence: 99%

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

VandenHeuvel

¹

,

Drovandi

²

,

Simpson

³

2022

View full text Add to dashboard Cite

Parameter estimation for mathematical models of biological processes is often difficult and depends significantly on the quality and quantity of available data. We introduce an efficient framework using Gaussian processes to discover mechanisms underlying delay, migration, and proliferation in a cell invasion experiment. Gaussian processes are leveraged with bootstrapping to provide uncertainty quantification for the mechanisms that drive the invasion process. Our framework is efficient, parallelisable, and can be applied to other biological problems. We illustrate our methods using a canonical scratch assay experiment, demonstrating how simply we can explore different functional forms and develop and test hypotheses about underlying mechanisms, such as whether delay is present. All code and data to reproduce this work are available at https://github.com/DanielVandH/EquationLearning.jl.

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GaussianProcesses.jl: A Nonparametric Bayes Package for the Julia Language

Cited by 15 publications

References 43 publications

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

Plots.jl – A User Extendable Plotting API for the Julia Programming Language

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

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