Welcome to kingpin’s documentation!

kingpin 🎳

👀 Treed Gaussian process algorithm

Install 💥

pip install kingpin-tgp

Demo

kingpin example/motorcyle.txt

Features

• Flexible allowing you to build GP models using any GP library you like 📦

• Treed GPs to handle non-stationary data 🌟

Theory

We implement a treed Gaussian process (TGP) algorithm [1] in Python. A TGP automatically partitions the input space and trains a GP in each partition. This allows us to model non-stationary data, heteroscedastic noise and divide and conquer large datasets. The GP hyperparameters and the number and locations of divisions are marginalised using recursive-jump MCMC.

Example

First we import the kingpin package

import kingpin as kp

We use numpy to create a dataset

import numpy as np

x = np.linspace(0, 10, 101)
y = 100. * np.ones_like(x)
y[x > 5.05] = 300.
y[x > 7.55] = 100.
noise = np.ones_like(x)

and choose prediction points

p = np.linspace(x.min(), x.max(), 201)

Now we are ready to make our TGP model. We use the from_data constructor. This means that hyperparameter and tree modelling choices are based on peeking at the data

tgp = kp.TGP.from_data(x, y, noise, p)

Alternatively, all aspects of the model can be chosen by hand. Now we run RJ-MCMC to marginalise the hyperparameters and tree structure

tgp.walk(n_threads=1, n_iter=1000, n_burn=500)

Finally, we cam take a look at results

tgp.plot()
tgp.mean
tgp.cov

and diagnostics

tgp.acceptance
tgp.arviz_summary()

More examples

• More examples
  • Motorcyle data
  • Step-functions

BibTeX

@article{tgp,
	title        = {{Bayesian Treed Gaussian Process Models With an Application to Computer Modeling}},
	author       = {Robert B Gramacy and Herbert K. H Lee},
	year         = 2008,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor & Francis},
	volume       = 103,
	number       = 483,
	pages        = {1119--1130},
	doi          = {10.1198/016214508000000689},
}

API

• Treed-GP classes
  • RJMCMC
    • RJMCMC.step()
    • RJMCMC.walk()
  • TGP
    • TGP.acceptance
    • TGP.arviz_summary()
    • TGP.cov
    • TGP.from_data()
    • TGP.mean
    • TGP.savefig()
    • TGP.savetxt()
    • TGP.show()
    • TGP.stdev
    • TGP.to_arviz()
    • TGP.walk()
• Building GP models
  • Model
  • Celerite2
  • Normal
  • Uniform
  • Independent
• Types
  • ArrayLike
  • TreePrior
  • Prior
  • Proposal
  • TruncatedProposal

References

[1]

Robert B Gramacy and Herbert K. H Lee. Bayesian Treed Gaussian Process Models With an Application to Computer Modeling. Journal of the American Statistical Association, 103(483):1119–1130, 2008. doi:10.1198/016214508000000689.