Interactive Visualisation of Gaussian processes

This is an interactive extension of a visualisation I developed for an invited talk at the FAI seminar series at University College London. Try out the live demo!

Standing on the shoulders of...

This webapp is built using Svelte, D3.js, and ml-matrix. Equations are rendered by KaTeX. Thanks to Ryan Davis for the CollapsibleCard.

There are several ways to make smooth animations across different samples. One way is to take random samples (independently or from HMC trajectories) and smoothly interpolate between them; here, using Catmull–Rom splines. Another way is to construct great circles in the sample space, which goes back to Philipp Hennig's technical note Animating samples from Gaussian distributions. How to compute the isocontour ellipses of a bivariate Gaussian distribution is explained by Chuong B. Do in this note.

Other visualisations

There are plenty of other Gaussian process visualisations out there; here are some I came across so far (if you know of others you like, please let me know, I'm happy to extend the list!):

Interactive tutorial: A Visual Exploration of Gaussian Processes (distill.pub) by Jochen Görtler, Rebecca Kehlbeck, Oliver Deussen (source, using D3.js, ml-matrix)
Interactive tutorial: A Practical Guide to Gaussian Processes by Marc Peter Deisenroth, Yicheng Luo, Mark van der Wilk
Demo by Johan Wågberg (source, using D3.js, Numeric.js)
Demo by Tomi Peltola (source, using React, D3.js, Numeric.js)
Demo by Nicolas Durrande (source, using R and Shiny)
Demo by Chi Feng (source, using dat.gui, jQuery)

Comments, bugs, feature suggestions

If you encounter any issues or have ideas for what might make this visualisation even better, please get in touch or open an issue in this repository. :)

Svelte development

Get started

Install the dependencies...

# cd into this directory
npm install

...then start Rollup:

npm run dev

Navigate to localhost:5000. You should see your app running. Edit a component file in src, save it, and reload the page to see your changes.

By default, the server will only respond to requests from localhost. To allow connections from other computers, edit the sirv commands in package.json to include the option --host 0.0.0.0.

If you're using Visual Studio Code we recommend installing the official extension Svelte for VS Code. If you are using other editors you may need to install a plugin in order to get syntax highlighting and intellisense.

Contributing

Using TypeScript

This repository is set up to use TypeScript. Run the checks with

npx svelte-check

(Note: if you run svelte-check from a subdirectory, e.g. src/, it will not find the included type hints in custom_typings/.)

Using Prettier

This repository is set up to use Prettier. Before committing code, run

npx prettier -w src

Building and running in production mode

To create an optimised version of the app:

npm run build

You can run the newly built app with npm run start. This uses sirv, which is included in your package.json's dependencies so that the app will work when you deploy to platforms like Heroku.

Single-page app mode

By default, sirv will only respond to requests that match files in public. This is to maximise compatibility with static fileservers, allowing you to deploy your app anywhere.

If you're building a single-page app (SPA) with multiple routes, sirv needs to be able to respond to requests for any path. You can make it so by editing the "start" command in package.json:

"start": "sirv public --single"

Deploying to the web

With Vercel

Install vercel if you haven't already:

npm install -g vercel

Then, from within your project folder:

cd public
vercel deploy --name my-project

With surge

Install surge if you haven't already:

npm install -g surge