def bayes_factor(model_1: RawGPModelType,
model_2: RawGPModelType) -> float:
"""Compute the Bayes factor between two models.
https://en.wikipedia.org/wiki/Bayes_factor
:param model_1:
:param model_2:
:return:
"""
model_evidence_1 = np.exp(log_likelihood(model_1))
model_evidence_2 = np.exp(log_likelihood(model_2))
return model_evidence_1 / model_evidence_2
def log_likelihood_normalized(model: RawGPModelType) -> float:
"""Computes the normalized log likelihood.
:param model:
:return:
"""
return log_likelihood(model) / n_data(model)
def cov_parsimony_pressure(model: RawGPModelType,
model_scores: List[float],
model_sizes: List[int]) -> float:
"""Covariant parsimony pressure method of a model."""
model_size = n_params(model)
lml = log_likelihood(model)
return covariant_parsimony_pressure(fitness=lml, size=model_size, sizes=model_sizes, fitness_list=model_scores)
def pl2(model: RawGPModelType) -> float:
"""Compute the modified expected log-predictive likelihood (PL2) score of a model.
Ando & Tsay, 2009
:param model:
:return:
"""
n = n_data(model)
k = n_params(model)
nll = -log_likelihood(model)
return nll / n + k / (2 * n)
def AIC(model: RawGPModelType) -> float:
"""Akaike Information Criterion (AIC).
Calculate the AIC for a GPy `model` with maximum likelihood hyperparameters on a
given dataset.
https://en.wikipedia.org/wiki/Akaike_information_criterion
AIC = 2k - 2ln(L^)
"""
k = n_params(model)
return 2 * k - 2 * log_likelihood(model)
def BIC(model: RawGPModelType) -> float:
"""Bayesian Information Criterion (BIC).
Calculate the BIC for a Gaussian process model with maximum likelihood hyperparameters on a
given dataset.
https://en.wikipedia.org/wiki/Bayesian_information_criterion
BIC = ln(n)k - 2ln(L^)
"""
n = n_data(model)
k = n_params(model)
return np.log(n) * k - 2 * log_likelihood(model)