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Fixed some bugs, added third derivative for log transformation, and did some doccing

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Alan Saul 2013-10-16 15:35:14 +01:00
parent 36c224d822
commit 6e28fdf4fd
6 changed files with 155 additions and 22 deletions
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17
GPy/likelihoods/noise_models/gaussian_noise.py
View file

@ -68,7 +68,7 @@ class Gaussian(NoiseDistribution):
def _predictive_variance_analytical(self,mu,sigma,predictive_mean=None):
return 1./(1./self.variance + 1./sigma**2)
def _mass(self, link_f, y):
def pdf_link(self, link_f, y, extra_data=None):
#FIXME: Careful now passing link_f in not gp (f)!
#return std_norm_pdf( (self.gp_link.transf(gp)-obs)/np.sqrt(self.variance) )
#Assumes no covariance, exp, sum, log for numerical stability
@ -76,21 +76,26 @@ class Gaussian(NoiseDistribution):
#return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance)))))
return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance)))))
def _mass(self, link_f, y, extra_data=None):
NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\
Please negate your function and use pdf in noise_model.py, if implementing a likelihood\
rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\
its derivatives")
def _nlog_mass(self, link_f, y, extra_data=None):
NotImplementedError("Deprecated, now doing chain in likelihood.py for link function evaluation\
NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\
Please negate your function and use logpdf in noise_model.py, if implementing a likelihood\
rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\
its derivatives")
def _dnlog_mass_dgp(self, link_f, y, extra_data=None):
NotImplementedError("Deprecated, now doing chain in likelihood.py for link function evaluation\
Please negate your function and use logpdf in noise_model.py, if implementing a likelihood\
NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\
Please negate your function and use dlogpdf_df in noise_model.py, if implementing a likelihood\
rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\
its derivatives")
def _d2nlog_mass_dgp2(self, link_f, y, extra_data=None):
NotImplementedError("Deprecated, now doing chain in likelihood.py for link function evaluation\
Please negate your function and use logpdf in noise_model.py, if implementing a likelihood\
NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\
Please negate your function and use d2logpdf_df2 in noise_model.py, if implementing a likelihood\
rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\
its derivatives")

7
GPy/likelihoods/noise_models/gp_transformations.py
View file

@ -80,6 +80,10 @@ class Probit(GPTransformation):
def d2transf_df2(self,f):
return -f * std_norm_pdf(f)
def d3transf_df3(self,f):
f2 = f**2
return -(1/(np.sqrt(2*np.pi)))*np.exp(-0.5*(f2))*(f2-1)
class Log(GPTransformation):
"""
.. math::
@ -96,6 +100,9 @@ class Log(GPTransformation):
def d2transf_df2(self,f):
return np.exp(f)
def d3transf_df3(self,f):
return np.exp(f)
class Log_ex_1(GPTransformation):
"""
.. math::

122
GPy/likelihoods/noise_models/noise_distributions.py
View file

@ -399,16 +399,82 @@ class NoiseDistribution(object):
"""
return sp.optimize.fmin_ncg(self._nlog_joint_predictive_scaled,x0=(mu,self.gp_link.transf(mu)),fprime=self._gradient_nlog_joint_predictive,fhess=self._hessian_nlog_joint_predictive,args=(mu,sigma),disp=False)
def logpdf(self, f, y, extra_data=None):
def pdf_link(self, link_f, y, extra_data=None):
raise NotImplementedError
def logpdf_link(self, link_f, y, extra_data=None):
raise NotImplementedError
def dlogpdf_dlink(self, link_f, y, extra_data=None):
raise NotImplementedError
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
raise NotImplementedError
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
raise NotImplementedError
def dlogpdf_link_dtheta(self, link_f, y, extra_data=None):
raise NotImplementedError
def dlogpdf_dlink_dtheta(self, link_f, y, extra_data=None):
raise NotImplementedError
def d2logpdf_dlink2_dtheta(self, link_f, y, extra_data=None):
raise NotImplementedError
def pdf(self, f, y, extra_data=None):
"""
Evaluates the link function link(f) then computes the log likelihood using it
Evaluates the link function link(f) then computes the likelihood (pdf) using it
.. math:
p(y|\\lambda(f))
:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: likelihood evaluated for this point
:rtype: float
"""
link_f = self.gp_link.transf(f)
return self.logpdf_link(f, y, extra_data=extra_data)
return self.pdf_link(link_f, y, extra_data=extra_data)
def logpdf(self, f, y, extra_data=None):
"""
Evaluates the link function link(f) then computes the log likelihood (log pdf) using it
.. math:
\\log p(y|\\lambda(f))
:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: log likelihood evaluated for this point
:rtype: float
"""
link_f = self.gp_link.transf(f)
return self.logpdf_link(link_f, y, extra_data=extra_data)
def dlogpdf_df(self, f, y, extra_data=None):
"""
TODO: Doc strings
Evaluates the link function link(f) then computes the derivative of log likelihood using it
Uses the Faa di Bruno's formula for the chain rule
.. math::
\\frac{d\\log p(y|\\lambda(f))}{df} = \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d\\lambda(f)}{df}
:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: derivative of log likelihood evaluated for this point
:rtype: float
"""
link_f = self.gp_link.transf(f)
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data)
@ -417,7 +483,19 @@ class NoiseDistribution(object):
def d2logpdf_df2(self, f, y, extra_data=None):
"""
TODO: Doc strings
Evaluates the link function link(f) then computes the second derivative of log likelihood using it
Uses the Faa di Bruno's formula for the chain rule
.. math::
\\frac{d^{2}\\log p(y|\\lambda(f))}{df^{2}} = \\frac{d^{2}\\log p(y|\\lambda(f))}{d^{2}\\lambda(f)}\\left(\\frac{d\\lambda(f)}{df}\\right)^{2} + \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d^{2}\\lambda(f)}{df^{2}}
:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: second derivative of log likelihood evaluated for this point
:rtype: float
"""
link_f = self.gp_link.transf(f)
d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, extra_data=extra_data)
@ -428,7 +506,19 @@ class NoiseDistribution(object):
def d3logpdf_df3(self, f, y, extra_data=None):
"""
TODO: Doc strings
Evaluates the link function link(f) then computes the third derivative of log likelihood using it
Uses the Faa di Bruno's formula for the chain rule
.. math::
\\frac{d^{3}\\log p(y|\\lambda(f))}{df^{3}} = \\frac{d^{3}\\log p(y|\\lambda(f)}{d\\lambda(f)^{3}}\\left(\\frac{d\\lambda(f)}{df}\\right)^{3} + 3\\frac{d^{2}\\log p(y|\\lambda(f)}{d\\lambda(f)^{2}}\\frac{d\\lambda(f)}{df}\\frac{d^{2}\\lambda(f)}{df^{2}} + \\frac{d\\log p(y|\\lambda(f)}{d\\lambda(f)}\\frac{d^{3}\\lambda(f)}{df^{3}}
:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: third derivative of log likelihood evaluated for this point
:rtype: float
"""
link_f = self.gp_link.transf(f)
d3logpdf_dlink3 = self.d3logpdf_dlink3(link_f, y, extra_data=extra_data)
@ -440,23 +530,33 @@ class NoiseDistribution(object):
return chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3)
def dlogpdf_dtheta(self, f, y, extra_data=None):
"""
TODO: Doc strings
"""
link_f = self.gp_link.transf(f)
return self.dlogpdf_link_dtheta(link_f, y, extra_data=extra_data)
def dlogpdf_df_dtheta(self, f, y, extra_data=None):
"""
TODO: Doc strings
"""
link_f = self.gp_link.transf(f)
dlink_df = self.gp_link.dtransf_df(f)
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data)
return chain_1(dlogpdf_dlink_dtheta, dlink_df)
def d2logpdf_df2_dtheta(self, f, y, extra_data=None):
"""
TODO: Doc strings
"""
link_f = self.gp_link.transf(f)
dlink_df = self.gp_link.dtransf_df(f)
d2link_df2 = self.gp_link.d2transf_df2(f) #FIXME: I THINK ITS THIS
d2link_df2 = self.gp_link.d2transf_df2(f)
d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(link_f, y, extra_data=extra_data)
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data)
return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2)
#FIXME: Why isn't this chain_1?
#return chain_1(d2logpdf_dlink2_dtheta, d2link_df2)
return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2)
def _laplace_gradients(self, f, y, extra_data=None):
#link_f = self.gp_link.transf(f)
@ -508,14 +608,10 @@ class NoiseDistribution(object):
q3 = np.vstack(q3)
return pred_mean, pred_var, q1, q3
def samples(self, gp):
"""
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
"""
pass
raise NotImplementedError

7
GPy/testing/laplace_tests.py
View file

@ -4,6 +4,7 @@ import GPy
from GPy.models import GradientChecker
import functools
import inspect
from GPy.likelihoods.noise_models import gp_transformations
def dparam_partial(inst_func, *args):
"""
@ -77,7 +78,7 @@ class LaplaceTests(unittest.TestCase):
self.var = np.random.rand(1)
self.stu_t = GPy.likelihoods.student_t(deg_free=5, sigma2=self.var)
self.gauss = GPy.likelihoods.gaussian(variance=self.var, D=self.D, N=self.N)
self.gauss = GPy.likelihoods.gaussian(gp_transformations.Log(), variance=self.var, D=self.D, N=self.N)
#Make a bigger step as lower bound can be quite curved
self.step = 1e-3
@ -92,7 +93,7 @@ class LaplaceTests(unittest.TestCase):
def test_mass_logpdf(self):
print "\n{}".format(inspect.stack()[0][3])
np.testing.assert_almost_equal(
np.log(self.gauss._mass(self.f.copy(), self.Y.copy())),
np.log(self.gauss.pdf(self.f.copy(), self.Y.copy())),
self.gauss.logpdf(self.f.copy(), self.Y.copy()))
@ -149,7 +150,7 @@ class LaplaceTests(unittest.TestCase):
""" dGauss_dlink's """
def test_gaussian_dlogpdf_dlink(self):
print "\n{}".format(inspect.stack()[0][3])
logpdf = functools.partial(self.gauss.logpdf, y=self.Y)
logpdf = functools.partial(self.gauss.logpdf_link, y=self.Y)
dlogpdf_dlink = functools.partial(self.gauss.dlogpdf_dlink, y=self.Y)
grad = GradientChecker(logpdf, dlogpdf_dlink, self.f.copy(), 'g')
grad.randomize()

8
doc/GPy.testing.rst
View file

@ -76,6 +76,14 @@ GPy.testing.mrd_tests module
:undoc-members:
:show-inheritance:
GPy.testing.noise_distributions module
--------------------------------------
.. automodule:: GPy.testing.noise_distributions
:members:
:undoc-members:
:show-inheritance:
GPy.testing.prior_tests module
------------------------------

16
doc/GPy.util.rst
View file

@ -27,6 +27,14 @@ GPy.util.classification module
:undoc-members:
:show-inheritance:
GPy.util.config module
----------------------
.. automodule:: GPy.util.config
:members:
:undoc-members:
:show-inheritance:
GPy.util.datasets module
------------------------
@ -91,6 +99,14 @@ GPy.util.multioutput module
:undoc-members:
:show-inheritance:
GPy.util.netpbmfile module
--------------------------
.. automodule:: GPy.util.netpbmfile
:members:
:undoc-members:
:show-inheritance:
GPy.util.plot module
--------------------