def derivMarginalLikelihood(params,trainingSet,PackParams,thisCovarClass,
useDerivs):
"""
NAME:
derivMarginalLikelihood
PURPOSE:
evaluate the derivative of the marginal (log) likelihood
INPUT:
params - ndarray consisting of
covarHyper - a set of covariance Hyperparameters
These can be unpacked by using the GPparams
trainingSet - trainingSet object
PackParams - parameters describing the GP (to unpack the parameters)
thisCovarClass - covariance class
OUTPUT:
derivative of the log of the marginal likelihood
HISTORY:
2010-07-25 - Written - Bovy (NYU)
"""
hyperParamsDict= unpack_params(params,PackParams)
covarFunc= PackParams.covarFunc(**hyperParamsDict)
N= trainingSet.nTraining
#Calculate Ky
Ky= _calc_ky(covarFunc,trainingSet,N)
try:
(Kyinv,Kylogdet)= fast_cholesky_invert(Ky,logdet=True)
except (numpy.linalg.linalg.LinAlgError,ValueError):
print "Warning: "
return -numpy.finfo(numpy.dtype(numpy.float64)).max
#All the derivatives return dictionaries with keys corresponding to the
#hyper-parameters
Kydothyper= _calc_kydot_hyper(covarFunc,trainingSet,N,hyperParamsDict)
alpha= numpy.dot(Kyinv,trainingSet.listy)
aat= numpy.outer(alpha,alpha)
Ldothyper= {}
for key in hyperParamsDict:
Ldothyper[key]= 0.5*numpy.trace(numpy.dot(Kyinv-aat,Kydothyper[key]))
#Now pack the derivatives, by cleverly re-using the packing routine
fakeCovar= thisCovarClass.covarFunc(**Ldothyper)
(derivs,derivspacking)= pack_params(fakeCovar,None,None)
#print "derivs", derivs
return derivs
def marginalLikelihood(params,trainingSet,PackParams,thisCovarClass,
thisMeanClass=None,
useDerivs=False):
"""
NAME:
marginalLikelihood
PURPOSE:
evaluate minus the marginal (log) likelihood
INPUT:
params - ndarray consisting of
covarHyper - a set of covariance Hyperparameters
These can be unpacked by using the PackParams
trainingSet - trainingSet object
PackParams - parameters describing the GP (to unpack the parameters)
thisCovarClass - covariance class (not used in this function)
thisMeanClass - same as previous two, but for the mean
function
OUTPUT:
log of the marginal likelihood
HISTORY:
2010-07-25 - Written - Bovy (NYU)
"""
hyperParamsDict= unpack_params(params,PackParams)
covarFunc= PackParams.covarFunc(**hyperParamsDict)
meanFunc= PackParams.meanFunc(**hyperParamsDict)
N= trainingSet.nTraining
#Calculate Ky
Ky= _calc_ky(covarFunc,trainingSet,N)
try:
(Kyinv,Kylogdet)= fast_cholesky_invert(Ky,logdet=True)
except (numpy.linalg.linalg.LinAlgError,ValueError):
if useDerivs:
print "Warning: parameter space includes non-positive definite regions; consider using useDerivs=False"
return numpy.finfo(numpy.dtype(numpy.float64)).max
datamean= _calc_mean(meanFunc,trainingSet,N)
chi2= numpy.dot((trainingSet.listy-datamean),
numpy.dot(Kyinv,(trainingSet.listy-datamean)))
return 0.5*(chi2+Kylogdet+N*_LOGTWOPI)