LOO

Methods for the LOO (leave-one-out) module in hetgpy

LOO_preds(model, ids=None)[source]

Provide leave one out predictions, e.g., for model testing and diagnostics. This is used in the method plot available on GP and TP models.

Parameters:

  • model (homGP or hetGP) – hetGPy model to evaluate. TPs not considered at this point.

  • ids (vector of indices of the unique design point considered (defaults to all))

Return type:

dict with mean and variance predictions at x_i assuming this point has not been evaluated

Notes

For TP models, psi is considered fixed

References

O. Dubrule (1983), Cross validation of Kriging in a unique neighborhood, Mathematical Geology 15, 687–699. cr cr F. Bachoc (2013), Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes

Examples

>>> from hetgpy import homGP
>>> from hetgpy.LOO import LOO_preds
>>> from hetgpy.find_reps import find_reps
>>> from hetgpy.example_data import mcycle
>>> import numpy as np
>>> m = mcycle()
>>> X, Z = m['times'], m['accel']
>>> model = homGP()
>>> model.mle(X = X, Z = Z, lower = [0.1], upper = [10],
>>>          covtype = "Matern5_2", known = dict(beta0 = 0))
>>> LOO_p = LOO_preds(model)
>>> d = find_reps(X,Z)
>>> LOO_ref = np.zeros(shape=(d['X0'].shape[0],2))
>>> rows = np.arange(d['X0'].shape[0])
>>> for i in rows:
>>>     idxs = np.delete(rows,i)
>>>     model_i = homGP()
>>>     model_i.mle(X = dict(X0 = d['X0'][idxs,:], Z0 = d['Z0'][idxs],
>>>                 mult = d['mult'][idxs]),
>>>                 Z = np.concatenate([d['Zlist'][j] for j in idxs]),
>>>                        lower = [0.1], upper = [50], covtype = "Matern5_2",
>>>                        known = dict(theta = model.theta, g = model.g,
>>>                                    beta0 = 0))
>>>     model_i.nu_hat = model.nu_hat
>>>     p_i = model_i.predict(d['X0'][i:i+1,:])
>>>     LOO_ref[i,:] = np.array([p_i['mean'], p_i['sd2']]).squeeze()
>>> print(np.ptp(LOO_ref[:,0] - LOO_p['mean']))
>>> print(np.ptp(LOO_ref[:,1] - LOO_p['sd2']))
>>> model.plot()