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speed ups for normal cdf

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This commit is contained in:
James Hensman 2015-04-09 15:42:02 +01:00
parent 337bf67559
commit 1e30ffd730
7 changed files with 38 additions and 96 deletions
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15
GPy/likelihoods/bernoulli.py
View file

@ -2,10 +2,10 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf
from ..util.univariate_Gaussian import std_norm_cdf, std_norm_pdf
import link_functions
from likelihood import Likelihood
from scipy import stats
class Bernoulli(Likelihood):
"""
@ -81,19 +81,18 @@ class Bernoulli(Likelihood):
if isinstance(self.gp_link, link_functions.Probit):
if gh_points is None:
gh_x, gh_w = np.polynomial.hermite.hermgauss(20)
gh_x, gh_w = self._gh_points()
else:
gh_x, gh_w = gh_points
from scipy import stats
shape = m.shape
m,v,Y = m.flatten(), v.flatten(), Y.flatten()
Ysign = np.where(Y==1,1,-1)
X = gh_x[None,:]*np.sqrt(2.*v[:,None]) + (m*Ysign)[:,None]
p = stats.norm.cdf(X)
p = std_norm_cdf(X)
p = np.clip(p, 1e-9, 1.-1e-9) # for numerical stability
N = stats.norm.pdf(X)
N = std_norm_pdf(X)
F = np.log(p).dot(gh_w)
NoverP = N/p
dF_dm = (NoverP*Ysign[:,None]).dot(gh_w)
@ -106,10 +105,10 @@ class Bernoulli(Likelihood):
def predictive_mean(self, mu, variance, Y_metadata=None):
if isinstance(self.gp_link, link_functions.Probit):
return stats.norm.cdf(mu/np.sqrt(1+variance))
return std_norm_cdf(mu/np.sqrt(1+variance))
elif isinstance(self.gp_link, link_functions.Heaviside):
return stats.norm.cdf(mu/np.sqrt(variance))
return std_norm_cdf(mu/np.sqrt(variance))
else:
raise NotImplementedError

12
GPy/likelihoods/likelihood.py
View file

@ -1,4 +1,4 @@
# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt)
# Copyright (c) 2012-2015 The GPy authors (see AUTHORS.txt)
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
@ -165,6 +165,13 @@ class Likelihood(Parameterized):
return z, mean, variance
#only compute gh points if required
__gh_points = None
def _gh_points(self):
if self.__gh_points is None:
self.__gh_points = np.polynomial.hermite.hermgauss(20)
return self.__gh_points
def variational_expectations(self, Y, m, v, gh_points=None, Y_metadata=None):
"""
Use Gauss-Hermite Quadrature to compute
@ -177,10 +184,9 @@ class Likelihood(Parameterized):
if no gh_points are passed, we construct them using defualt options
"""
#May be broken
if gh_points is None:
gh_x, gh_w = np.polynomial.hermite.hermgauss(20)
gh_x, gh_w = self._gh_points()
else:
gh_x, gh_w = gh_points

25
GPy/likelihoods/link_functions.py
View file

@ -1,10 +1,9 @@
# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt)
# Copyright (c) 2012-2015 The GPy authors (see AUTHORS.txt)
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from scipy import stats
from ..util.univariate_Gaussian import std_norm_cdf, std_norm_pdf
import scipy as sp
from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf,inv_std_norm_cdf
_exp_lim_val = np.finfo(np.float64).max
_lim_val = np.log(_exp_lim_val)
@ -64,13 +63,12 @@ class Identity(GPTransformation):
def d3transf_df3(self,f):
return np.zeros_like(f)
class Probit(GPTransformation):
"""
.. math::
g(f) = \\Phi^{-1} (mu)
"""
def transf(self,f):
return std_norm_cdf(f)
@ -79,13 +77,10 @@ class Probit(GPTransformation):
return std_norm_pdf(f)
def d2transf_df2(self,f):
#FIXME
return -f * std_norm_pdf(f)
def d3transf_df3(self,f):
#FIXME
f2 = f**2
return -(1/(np.sqrt(2*np.pi)))*np.exp(-0.5*(f2))*(1-f2)
return (np.square(f)-1.)*std_norm_pdf(f)
class Cloglog(GPTransformation):
@ -98,7 +93,7 @@ class Cloglog(GPTransformation):
or
f = \log (-\log(1-p))
"""
def transf(self,f):
return 1-np.exp(-np.exp(f))
@ -123,16 +118,16 @@ class Log(GPTransformation):
"""
def transf(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return np.exp(np.clip(f, -np.inf, _lim_val))
def dtransf_df(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return np.exp(np.clip(f, -np.inf, _lim_val))
def d2transf_df2(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return np.exp(np.clip(f, -np.inf, _lim_val))
def d3transf_df3(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return np.exp(np.clip(f, -np.inf, _lim_val))
class Log_ex_1(GPTransformation):
"""
@ -174,7 +169,7 @@ class Heaviside(GPTransformation):
.. math::
g(f) = I_{x \\in A}
g(f) = I_{x \\geq 0}
"""
def transf(self,f):