API¶
Main Class¶
- class gptide.gpscipy.GPtideScipy(xd, xm, sd, cov_func, cov_params, **kwargs)¶
Gaussian Process regression class
Uses scipy to do the heavy lifting
- Parameters
- xd: numpy.ndarray [N, D]
Input data locations
- xm: numpy.ndarray [M, D]
Output/target point locations
- sd: float
Data noise parameter
- cov_func: callable function
Function used to compute the covariance matrices
- cov_params: tuple
Parameters passed to cov_func
- Other Parameters
- P: int (default=1)
number of output dimensions
- cov_kwargs: dictionary, optional
keyword arguments passed to cov_func
- mean_func: callable function
Returns the mean function
- mean_params: tuple
parameters passed to the mean function
- mean_kwargs: dict
kwargs passed to the mean function
- Attributes
- mean_func
Methods
__call__(yd)Predict the GP posterior mean given data
conditional(yd[, samples])Sample from the conidtional distribution
Compute the log of the marginal likelihood
prior([samples, noise])Sample from the prior distribution
update_xm(xm)Update the output locations and the covariance kernel
- __call__(yd)¶
Predict the GP posterior mean given data
- Parameters
- yd: numpy.ndarray [N,1]
Observed data
- Returns
- numpy.ndarray
Prediction
- __init__(xd, xm, sd, cov_func, cov_params, **kwargs)¶
Initialise GP object and evaluate mean and covatiance functions.
- conditional(yd, samples=1)¶
Sample from the conidtional distribution
- Parameters
- yd: numpy.ndarray [N,1]
Observed data
- samples: int, optional (default=1)
number of samples
- Returns
- conditional_sample: numpy.ndarray [N,samples]
output array
- log_marg_likelihood(yd)¶
Compute the log of the marginal likelihood
- prior(samples=1, noise=0.0)¶
Sample from the prior distribution
- Parameters
- samples: int, optional (default=1)
number of samples
- Returns
- prior_sample: numpy.ndarray [N,samples]
array of output samples
- update_xm(xm)¶
Update the output locations and the covariance kernel
Parent Class¶
Classes for Gaussian Process regression
- class gptide.gp.GPtide(xd, xm, sd, cov_func, cov_params, **kwargs)¶
Gaussian Process base class
Intended as a placeholder for classes built with other libraries (scipy, jax)
- Attributes
- mean_func
Methods
__call__(yd)Placeholder
conditional(yd[, samples])Placeholder
Placeholder
prior([samples])Placeholder
update_xm(xm)Update the output locations and the covariance kernel
- conditional(yd, samples=1)¶
Placeholder
- log_marg_likelihood(yd)¶
Placeholder
- prior(samples=1)¶
Placeholder
- update_xm(xm)¶
Update the output locations and the covariance kernel
Covariance functions¶
Covariance functions for optimal interpolation
- gptide.cov.cosine(x, xpr, l)¶
Cosine base function
- gptide.cov.expquad(x, xpr, l)¶
Exponential quadration base function
- gptide.cov.matern12(x, xpr, l)¶
Matern 3/2 base function
- gptide.cov.matern32(x, xpr, l)¶
Matern 3/2 base function
- gptide.cov.matern52(x, xpr, l)¶
Matern 5/2 base function
- gptide.cov.matern_general(dx, eta, nu, l)¶
General Matern base function
- gptide.cov.matern_spectra(f, eta, nu, l, n=1)¶
Helper routine to compute the power spectral density of a general Matern function
- gptide.cov.periodic(x, xpr, l, p)¶
Periodic base function
Inference¶
MCMC parameter estimation using emcee
- gptide.mcmc.mcmc(xd, yd, covfunc, cov_priors, noise_prior, meanfunc=None, mean_priors=[], mean_kwargs={}, GPclass=<class 'gptide.gpscipy.GPtideScipy'>, gp_kwargs={}, nwalkers=200, nwarmup=200, niter=20, nprior=500, parallel=False, verbose=False)¶
Main MCMC function
Run MCMC using emcee.EnsembleSampler and return posterior samples, log probability of your MCMC chain, samples from your priors and the actual emcee.EnsembleSampler [for testing].
- Parameters
- xd: numpy.ndarray [N, D]
Input data locations / predictor variable(s)
- yd: numpy.ndarray [N,1]
Observed data
- covfunc: function
Covariance function
- cov_priors: list of scipy.stats.rv_continuous objects
List containing prior probability distribution for each parameter of the covfunc
- noise_priors: scipy.stats.rv_continuous object
Prior for I.I.D. noise
- Returns
- samples:
MCMC chains after burn in
- log_prob:
Log posterior probability for each sample in the MCMC chain after burn in
- p0:
Samples from the prior distributions
- sampler: emcee.EnsembleSampler
The actual emcee.EnsembleSampler used
- Other Parameters
- meanfunc: function [None]
Mean function
- mean_priors: list of scipy.stats.rv_continuous objects
List containing prior probability distribution for each parameter of the meanfunc
- mean_kwargs: dict
Key word arguments for the mean function
- GPclass: gptide.gp.GPtide class [GPtideScipy]
The GP class used to estimate the log marginal likelihood
- gp_kwargs: dict
Key word arguments for the GPclass initialisation
- nwalkers: int
see emcee.EnsembleSampler
- nwarmup: int
see emcee.EnsembleSampler
- niter: int
see emcee.EnsembleSampler.run_mcmc
- nprior: int
number of samples from the prior distributions to output
- parallel: bool [False]
Set to true to run parallel
- verbose: bool [False]
Set to true for more output
- gptide.mle.mle(xd, yd, covfunc, covparams_ic, noise_ic, meanfunc=None, meanparams_ic=[], mean_kwargs={}, GPclass=<class 'gptide.gpscipy.GPtideScipy'>, gp_kwargs={}, priors=None, method='L-BFGS-B', bounds=None, options=None, callback=None, verbose=False)¶
Main MLE function
Optimise the GP kernel parameters by minimising the negative log marginal likelihood/probability using scipy.optimize.minimize. If priors are specified the log marginal probability is optimised, otherwise the log marginal likelihood is minimised.
- Parameters
- xd: numpy.ndarray [N, D]
Input data locations / predictor variable(s)
- yd: numpy.ndarray [N,1]
Observed data
- covfunc: function
Covariance function
- covparams_ic: numeric
Initial guess for the covariance function parameters
- noise_ic: scipy.stats.rv_continuous object
Initial guess for the I.I.D. noise
- Other Parameters
- meanfunc: function [None]
Mean function
- meanparams_ic: scipy.stats.rv_continuous object
Initial guess for the mean function parameters
- mean_kwargs: dict
Key word arguments for the mean function
- GPclass: gptide.gp.GPtide class [GPtideScipy]
The GP class used to estimate the log marginal likelihood
- gp_kwargs: dict
Key word arguments for the GPclass initialisation
- priors:
List containing prior probability distribution for each parameter of the noise, covfunc and meanfunc. If specified the log marginal probability is optimised, otherwise the log marginal likelihood is minimised.
- verbose: bool [False]
Set to true for more output
- method: str [‘L-BFGS-B’]
see scipy.optimize.minimize
- bounds: sequence or Bounds, optional [None]
see scipy.optimize.minimize
- options: dict, optional [None]
see scipy.optimize.minimize
- callback: callable, optional [None]
see scipy.optimize.minimize