pyGPGO.surrogates.GaussianProcess module

class pyGPGO.surrogates.GaussianProcess.GaussianProcess(covfunc, optimize=False, usegrads=False, mprior=0)[source]

Bases: object

Gaussian Process regressor class. Based on Rasmussen & Williams [1]_ algorithm 2.1.

Parameters:
  • covfunc (instance from a class of covfunc module) – Covariance function. An instance from a class in the covfunc module.
  • optimize (bool:) – Whether to perform covariance function hyperparameter optimization.
  • usegrads (bool) – Whether to use gradient information on hyperparameter optimization. Only used if optimize=True.
covfunc

Internal covariance function.

Type:object
optimize

User chosen optimization configuration.

Type:bool
usegrads

Gradient behavior

Type:bool
mprior

Explicit value for the mean function of the prior Gaussian Process.

Type:float

Notes

[1] Rasmussen, C. E., & Williams, C. K. I. (2004). Gaussian processes for machine learning. International journal of neural systems (Vol. 14). http://doi.org/10.1142/S0129065704001899

__init__(covfunc, optimize=False, usegrads=False, mprior=0)[source]

Gaussian Process regressor class. Based on Rasmussen & Williams [1]_ algorithm 2.1.

Parameters:
  • covfunc (instance from a class of covfunc module) – Covariance function. An instance from a class in the covfunc module.
  • optimize (bool:) – Whether to perform covariance function hyperparameter optimization.
  • usegrads (bool) – Whether to use gradient information on hyperparameter optimization. Only used if optimize=True.
covfunc

Internal covariance function.

Type:object
optimize

User chosen optimization configuration.

Type:bool
usegrads

Gradient behavior

Type:bool
mprior

Explicit value for the mean function of the prior Gaussian Process.

Type:float

Notes

[1] Rasmussen, C. E., & Williams, C. K. I. (2004). Gaussian processes for machine learning. International journal of neural systems (Vol. 14). http://doi.org/10.1142/S0129065704001899

_grad(param_vector, param_key)[source]

Returns gradient for each hyperparameter, evaluated at a given point.

Parameters:
  • param_vector (list) – List of values corresponding to hyperparameters to query.
  • param_key (list) – List of hyperparameter strings corresponding to param_vector.
Returns:

Gradient for each evaluated hyperparameter.
Return type:

np.ndarray
_lmlik(param_vector, param_key)[source]

Returns marginal negative log-likelihood for given covariance hyperparameters.

Parameters:
  • param_vector (list) – List of values corresponding to hyperparameters to query.
  • param_key (list) – List of hyperparameter strings corresponding to param_vector.
Returns:

Negative log-marginal likelihood for chosen hyperparameters.
Return type:

float
fit(X, y)[source]

Fits a Gaussian Process regressor

Parameters:
  • X (np.ndarray, shape=(nsamples, nfeatures)) – Training instances to fit the GP.
  • y (np.ndarray, shape=(nsamples,)) – Corresponding continuous target values to X.
getcovparams()[source]

Returns current covariance function hyperparameters

Returns:Dictionary containing covariance function hyperparameters
Return type:dict
optHyp(param_key, param_bounds, grads=None, n_trials=5)[source]

Optimizes the negative marginal log-likelihood for given hyperparameters and bounds. This is an empirical Bayes approach (or Type II maximum-likelihood).

Parameters:
  • param_key (list) – List of hyperparameters to optimize.
  • param_bounds (list) – List containing tuples defining bounds for each hyperparameter to optimize over.
param_grad(k_param)[source]

Returns gradient over hyperparameters. It is recommended to use self._grad instead.

Parameters:k_param (dict) – Dictionary with keys being hyperparameters and values their queried values.
Returns:Gradient corresponding to each hyperparameters. Order given by k_param.keys()
Return type:np.ndarray
predict(Xstar, return_std=False)[source]

Returns mean and covariances for the posterior Gaussian Process.

Parameters:
  • Xstar (np.ndarray, shape=((nsamples, nfeatures))) – Testing instances to predict.
  • return_std (bool) – Whether to return the standard deviation of the posterior process. Otherwise, it returns the whole covariance matrix of the posterior process.
Returns:

  • np.ndarray – Mean of the posterior process for testing instances.
  • np.ndarray – Covariance of the posterior process for testing instances.
update(xnew, ynew)[source]

Updates the internal model with xnew and ynew instances.

Parameters:
  • xnew (np.ndarray, shape=((m, nfeatures))) – New training instances to update the model with.
  • ynew (np.ndarray, shape=((m,))) – New training targets to update the model with.