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author: | ||
- given: Neil D. | ||
family: Lawrence | ||
institution: University of Cambridge | ||
gscholar: r3SJcvoAAAAJ | ||
twitter: lawrennd | ||
orcid: 0000-0001-9258-1030 | ||
url: http://inverseprobability.com | ||
layout: lecture | ||
venue: Gaussian Process Summer School | ||
talkcss: https://inverseprobability.com/assets/css/talks.css | ||
postsdir: ../../../mlatcl/gpss/_lectures/ | ||
slidesdir: ../../../mlatcl/gpss/slides/ | ||
notesdir: ../../../mlatcl/gpss/_notes/ | ||
notebooksdir: ../../../mlatcl/gpss/_notebooks/ | ||
writediagramsdir: . | ||
scriptsdir: ../scripts/ | ||
diagramsdir: ./slides/diagrams/ | ||
potx: ../_includes/custom-reference.potx | ||
dotx: ../_includes/custom-reference.dotx | ||
transition: None | ||
baseurl: "gpss/" # the subpath of your site, e.g. /blog/ | ||
url: "https://mlatcl.github.io/" # the base hostname & protocol for your site | ||
ghub: | ||
- organization: lawrennd | ||
repository: talks | ||
branch: gh-pages | ||
directory: _gpss |
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--- | ||
title: Approximate Gaussian Processes | ||
featured_image: slides/diagrams/gp/sparse-demo-unconstrained-inducing-6-gp.svg | ||
week: 6 | ||
youtube: b635kuSqLww | ||
abstract: | ||
--- | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
\include{_gp/includes/approximate-gps.md} | ||
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\thanks | ||
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\references | ||
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--- | ||
title: Bayesian Learning of GP-LVM | ||
featured_image: slides/diagrams/gplvm/singlecell-bayes-gplvm.svg | ||
week: 10 | ||
abstract: | ||
--- | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
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\include{_gplvm/includes/bayes-gplvm-intro.md} | ||
\include{_gplvm/includes/variational-bayes-gplvm-long.md} | ||
\include{_gplvm/includes/mrd-gplvm.md} | ||
\include{_gplvm/includes/bayes-gplvm-tutorial.md} | ||
\include{_gplvm/includes/singlecell-bayes-gplvm.md} | ||
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\thanks | ||
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\references |
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#/bin/bash | ||
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FILES="" | ||
SKIP=true | ||
while read stub; do | ||
if $SKIP; then | ||
SKIP=false | ||
else | ||
maketalk $stub | ||
fi | ||
done < lectures.csv |
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--- | ||
title: Covariance Functions and Hyperparameter Optimization | ||
week: 3 | ||
featured_image: slides/diagrams/kern/sinc_covariance.gif | ||
abstract: > | ||
In this talk we review covariance functions and optimization of the GP log likelihoood. | ||
author: | ||
- given: Neil D. | ||
family: Lawrence | ||
affiliation: University of Cambridge | ||
transition: None | ||
--- | ||
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<!-- To compile --> | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
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\include{_gp/includes/gp-covariance-function-importance.md} | ||
\include{_gp/includes/gp-numerics-and-optimization.md} | ||
\include{_gp/includes/gp-optimize.md} | ||
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\include{_kern/includes/eq-covariance.md} | ||
\include{_kern/includes/computing-rbf-covariance.md} | ||
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\comment{Markov property} | ||
\include{_kern/includes/brownian-covariance.md} | ||
\include{_kern/includes/precision-matrices.md} | ||
\include{_kern/includes/ou-covariance.md} | ||
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\comment{Basis functions} | ||
\include{_kern/includes/basis-covariance.md} | ||
\include{_kern/includes/rbf-basis-covariance.md} | ||
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\comment{Fourier space} | ||
\include{_kern/includes/boechners-theorem.md} | ||
\include{_kern/includes/sinc-covariance.md} | ||
\include{_kern/includes/matern32-covariance.md} | ||
\include{_kern/includes/matern52-covariance.md} | ||
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\comment{Scale mixture} | ||
\include{_kern/includes/ratquad-covariance.md} | ||
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\comment{Polynomial} | ||
\include{_kern/includes/poly-covariance.md} | ||
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\comment{Periodic} | ||
\include{_kern/includes/periodic-covariance.md} | ||
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\comment{Infinite Neural Networks} | ||
\include{_kern/includes/mlp-covariance.md} | ||
\include{_kern/includes/relu-covariance.md} | ||
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\comment{Combining Covariances} | ||
\include{_kern/includes/add-covariance.md} | ||
\include{_kern/includes/prod-covariance.md} | ||
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\comment{Examples of Deploying Kernels} | ||
\include{_gp/includes/mauna-loa-gp.md} | ||
\include{_gp/includes/box-jenkins-airline-gp.md} | ||
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\comment{Spectral Mixture Kernel} | ||
\include{_kern/includes/spectral-mixture-kernel.md} | ||
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\thanks | ||
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\references | ||
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--- | ||
title: Deep Gaussian Processes I | ||
featured_image: slides/diagrams//deepgp/deep-nn-bottleneck2.svg | ||
week: 11 | ||
abstract: | ||
--- | ||
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\include{_gp/includes/mackay-bathwater.md} | ||
\include{_deepgp/includes/deep-nn-gp.md} | ||
\include{_ml/includes/deep-learning-overview.md} | ||
\include{_deepgp/includes/deep-theory.md} | ||
\include{_deepgp/includes/deep-gp-setup-code.md} | ||
\include{_deepgp/includes/olympic-marathon-deep-gp.md} | ||
\include{_deepgp/includes/della-gatta-deep-gp.md} | ||
\include{_deepgp/includes/step-function-deep-gp.md} | ||
\include{_deepgp/includes/motorcycle-helmet-deep-gp.md} | ||
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\thanks | ||
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\references | ||
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--- | ||
title: Deep Gaussian Processes II | ||
featured_image: slides/diagrams/deepgp/olympic-marathon-deep-gp-pinball.svg | ||
week: 12 | ||
abstract: | ||
--- | ||
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\include{_deepgp/includes/robot-wireless-deep-gp.md} | ||
\include{_deepgp/includes/deep-results.md} | ||
\include{_health/includes/deep-health-model.md} | ||
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\thanks | ||
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\references |
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--- | ||
title: Emulation | ||
week: 13 | ||
featured_image: slides/diagrams/uq/statistical-emulation001.svg | ||
abstract: In this session we introduce the notion of emulation and systems modeling with Gaussian processes. | ||
date: 2021-09-15 | ||
venue: Virtual GPSS | ||
author: | ||
- family: Lawrence | ||
given: Neil D. | ||
gscholar: r3SJcvoAAAAJ | ||
institute: University of Cambridge | ||
twitter: lawrennd | ||
orcid: 0000-0001-9258-1030 | ||
url: http://inverseprobability.com | ||
--- | ||
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\newslide{} | ||
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> We may regard the present state of the universe as the effect of its | ||
> past and the cause of its future. An intellect which at a certain | ||
> moment would know all forces that set nature in motion, and all | ||
> positions of all items of which nature is composed, ... | ||
\newslide{} | ||
> ... if this intellect | ||
> were also vast enough to submit these data to analysis, it would | ||
> embrace in a single formula the movements of the greatest bodies of | ||
> the universe and those of the tiniest atom; for such an intellect | ||
> nothing would be uncertain and the future just like the past would be | ||
> present before its eyes. | ||
> | ||
> --- Pierre Simon Laplace [@Laplace-essai14] | ||
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\include{_simulation/includes/game-of-life.md} | ||
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\speakernotes{Laplace's demon requires us to also know positions of all items and to submit the data to analysis.} | ||
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\newslide{} | ||
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\notes{We summarize this notion as} | ||
$$ | ||
\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction} | ||
$$ | ||
\notes{As we pointed out, there is an irony in Laplace's demon forming the cornerstone of a movement known as 'determinism', because Laplace wrote about this idea in an essay on probabilities. The more important quote in the essay was } | ||
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\include{_physics/includes/laplaces-gremlin.md} | ||
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\include{_simulation/includes/simulation-system.md} | ||
\include{_data-science/includes/experiment-analyze-design.md} | ||
\include{_uq/includes/emulation.md} | ||
\notes{\include{_gp/includes/gpy-emulation.md}} | ||
\include{_software/includes/emukit-software.md} | ||
\include{_uq/includes/emukit-vision.md} | ||
\include{_uq/includes/emukit-playground.md} | ||
\notes{\include{_uq/includes/emukit-tutorial.md}} | ||
\notes{\include{_uq/includes/emukit-sensitivity-analysis.md}} | ||
\notes{\include{_uq/includes/catapult-sensitivity-analysis.md}} | ||
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\thanks | ||
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\references | ||
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--- | ||
title: Gaussian Distributions to Processes | ||
abstract: > | ||
In this sesson we go from the Gaussian distribution to the Gaussian process and in doing so we move from a finite system to an infinite system. | ||
featured_image: slides/diagrams/gp/two_point_sample008.svg | ||
week: 2 | ||
--- | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
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\newslide{Two Dimensional Gaussian Distribution} | ||
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\include{_ml/includes/two-d-gaussian.md} | ||
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\newslide{Multivariate Gaussian Properties} | ||
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\include{_ml/includes/multivariate-gaussian-properties-summary.md} | ||
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\newslide{Linear Gaussian Models} | ||
\slides{ | ||
Gaussian processes are initially of interest because | ||
1. linear Gaussian models are easier to deal with | ||
2. Even the parameters *within* the process can be handled, by considering a particular limit. | ||
} | ||
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\include{_ml/includes/multivariate-gaussian-properties.md} | ||
\include{_ml/includes/linear-model-overview.md} | ||
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\newslide{Distributions over Functions} | ||
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\include{_gp/includes/gp-intro-very-short.md} | ||
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\include{_gp/includes/gpdistfunc.md} | ||
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\include{_kern/includes/computing-rbf-covariance.md} | ||
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\include{_kern/includes/poly-covariance.md} | ||
\include{_kern/includes/rbf-basis-covariance.md} | ||
\include{_gp/includes/infinite-basis.md} | ||
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\thanks | ||
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\references |
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--- | ||
title: Latent Force Models | ||
week: 9 | ||
abstract: | ||
--- | ||
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\thanks | ||
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\references | ||
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lectureId | ||
uncertainty-and-modelling | ||
gaussian-distributions-to-processes | ||
covariance-functions | ||
optimizing-parameters | ||
multi-output-gps | ||
approximate-gps | ||
non-gaussian-likelihoods | ||
unsupervised-learning-with-gps | ||
latent-force-models | ||
bayesian-learning-gplvm | ||
deep-gps-I | ||
deep-gps-II | ||
emulation |
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BASE=emulation | ||
include ../make-talk-flags.mk | ||
include ../make-talk.mk |
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--- | ||
title: Multi-output Gaussian Processes | ||
featured_image: slides/diagrams//kern/kronecker_KI.svg | ||
week: 5 | ||
youtube: MkkeBmEZ8LE | ||
abstract: > | ||
In this lecture we review multi-output Gaussian processes. Introducing them initially through a Kalman filter representation of a GP. | ||
--- | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
\include{_gp/includes/multi-output-gaussian-process.md} | ||
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\thanks | ||
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\references | ||
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--- | ||
title: Non Gaussian Likelihoods | ||
week: 7 | ||
abstract: | ||
--- | ||
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\include{_gpss/includes/gpss-notebook-setup.md} | ||
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\include{_gp/includes/non-gaussian-gps.md} | ||
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\thanks | ||
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\references |
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