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Merge branch 'master' of github.com:SheffieldML/GPy

Browse source 
Conflicts:
	GPy/examples/__init__.py
This commit is contained in:
Ricardo Andrade 2013-03-11 14:10:37 +00:00
commit 7c3c2fc9c0
46 changed files with 829 additions and 559 deletions
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7
GPy/__init__.py
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@ -9,3 +9,10 @@ import util
import examples
from core import priors
import likelihoods
import testing
from numpy.testing import Tester
from nose.tools import nottest
@nottest
def tests():
Tester(testing).test(verbose=10)

1
GPy/examples/__init__.py
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@ -5,3 +5,4 @@ import classification
import regression
import dimensionality_reduction
import non_gaussian
import tutorials

56
GPy/examples/tuto_GP_regression.py
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@ -1,56 +0,0 @@
# The detailed explanations of the commands used in this file can be found in the tutorial section
import pylab as pb
pb.ion()
import numpy as np
import GPy
X = np.random.uniform(-3.,3.,(20,1))
Y = np.sin(X) + np.random.randn(20,1)*0.05
kernel = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
m = GPy.models.GP_regression(X,Y,kernel)
print m
m.plot()
m.constrain_positive('')
m.unconstrain('') # Required to remove the previous constrains
m.constrain_positive('rbf_variance')
m.constrain_bounded('lengthscale',1.,10. )
m.constrain_fixed('noise',0.0025)
m.optimize()
m.optimize_restarts(Nrestarts = 10)
###########################
# 2-dimensional example #
###########################
import pylab as pb
pb.ion()
import numpy as np
import GPy
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(50,2))
Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05
# define kernel
ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
# create simple GP model
m = GPy.models.GP_regression(X,Y,ker)
# contrain all parameters to be positive
m.constrain_positive('')
# optimize and plot
pb.figure()
m.optimize('tnc', max_f_eval = 1000)
m.plot()
print(m)

139
GPy/examples/tuto_kernel_overview.py
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@ -1,139 +0,0 @@
# The detailed explanations of the commands used in this file can be found in the tutorial section
import pylab as pb
import numpy as np
import GPy
pb.ion()
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=2.)
ker3 = GPy.kern.rbf(1, .5, .5)
print ker2
ker1.plot()
ker2.plot()
ker3.plot()
k1 = GPy.kern.rbf(1,1.,2.)
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
# Product of kernels
k_prod = k1.prod(k2)
k_prodorth = k1.prod_orthogonal(k2)
# Sum of kernels
k_add = k1.add(k2)
k_addorth = k1.add_orthogonal(k2)
pb.figure(figsize=(8,8))
pb.subplot(2,2,1)
k_prod.plot()
pb.title('prod')
pb.subplot(2,2,2)
k_prodorth.plot()
pb.title('prod_orthogonal')
pb.subplot(2,2,3)
k_add.plot()
pb.title('add')
pb.subplot(2,2,4)
k_addorth.plot()
pb.title('add_orthogonal')
pb.subplots_adjust(wspace=0.3, hspace=0.3)
k1 = GPy.kern.rbf(1,1.,2)
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
k = k1 * k2 # equivalent to k = k1.prod(k2)
print k
# Simulate sample paths
X = np.linspace(-5,5,501)[:,None]
Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
# plot
pb.figure(figsize=(10,4))
pb.subplot(1,2,1)
k.plot()
pb.subplot(1,2,2)
pb.plot(X,Y.T)
pb.ylabel("Sample path")
pb.subplots_adjust(wspace=0.3)
k = (k1+k2)*(k1+k2)
print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.Matern32(1)
k3 = GPy.kern.white(1)
k = k1 + k2 + k3
print k
k.constrain_positive('var')
k.constrain_fixed(np.array([1]),1.75)
k.tie_param('len')
k.unconstrain('white')
k.constrain_bounded('white',lower=1e-5,upper=.5)
print k
k_cst = GPy.kern.bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
Kanova = (k_cst + k_mat).prod_orthogonal(k_cst + k_mat)
print Kanova
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(40,2))
Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
# Create GP regression model
m = GPy.models.GP_regression(X,Y,Kanova)
pb.figure(figsize=(5,5))
m.plot()
pb.figure(figsize=(20,3))
pb.subplots_adjust(wspace=0.5)
pb.subplot(1,5,1)
m.plot()
pb.subplot(1,5,2)
pb.ylabel("= ",rotation='horizontal',fontsize='30')
pb.subplot(1,5,3)
m.plot(which_functions=[False,True,False,False])
pb.ylabel("cst +",rotation='horizontal',fontsize='30')
pb.subplot(1,5,4)
m.plot(which_functions=[False,False,True,False])
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
pb.subplot(1,5,5)
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
m.plot(which_functions=[False,False,False,True])
import pylab as pb
import numpy as np
import GPy
pb.ion()
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.rbf(1, .5, .25)
ker1.plot()
ker2.plot()
ker3.plot()
#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
pb.figure(figsize=(16,12))
pb.subplots_adjust(wspace=.5, hspace=.5)
for i, kern in enumerate(kernels):
pb.subplot(3,4,i+1)
kern.plot(x=7.5,plot_limits=[0.00001,15.])
pb.title(kernel_names[i]+ '\n')
# actual plot for the noise
i = 11
X = np.linspace(0.,15.,201)
WN = 0*X
WN[100] = 1.
pb.subplot(3,4,i+1)
pb.plot(X,WN,'b')

201
GPy/examples/tutorials.py Normal file
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@ -0,0 +1,201 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
"""
Code of Tutorials
"""
def tuto_GP_regression():
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
import pylab as pb
pb.ion()
import numpy as np
import GPy
X = np.random.uniform(-3.,3.,(20,1))
Y = np.sin(X) + np.random.randn(20,1)*0.05
kernel = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
m = GPy.models.GP_regression(X,Y,kernel)
print m
m.plot()
m.constrain_positive('')
m.unconstrain('') # Required to remove the previous constrains
m.constrain_positive('rbf_variance')
m.constrain_bounded('lengthscale',1.,10. )
m.constrain_fixed('noise',0.0025)
m.optimize()
m.optimize_restarts(Nrestarts = 10)
###########################
# 2-dimensional example #
###########################
import pylab as pb
pb.ion()
import numpy as np
import GPy
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(50,2))
Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05
# define kernel
ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
# create simple GP model
m = GPy.models.GP_regression(X,Y,ker)
# contrain all parameters to be positive
m.constrain_positive('')
# optimize and plot
pb.figure()
m.optimize('tnc', max_f_eval = 1000)
m.plot()
print(m)
def tuto_kernel_overview():
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
import pylab as pb
import numpy as np
import GPy
pb.ion()
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=2.)
ker3 = GPy.kern.rbf(1, .5, .5)
print ker2
ker1.plot()
ker2.plot()
ker3.plot()
k1 = GPy.kern.rbf(1,1.,2.)
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
# Product of kernels
k_prod = k1.prod(k2)
k_prodorth = k1.prod_orthogonal(k2)
# Sum of kernels
k_add = k1.add(k2)
k_addorth = k1.add_orthogonal(k2)
pb.figure(figsize=(8,8))
pb.subplot(2,2,1)
k_prod.plot()
pb.title('prod')
pb.subplot(2,2,2)
k_prodorth.plot()
pb.title('prod_orthogonal')
pb.subplot(2,2,3)
k_add.plot()
pb.title('add')
pb.subplot(2,2,4)
k_addorth.plot()
pb.title('add_orthogonal')
pb.subplots_adjust(wspace=0.3, hspace=0.3)
k1 = GPy.kern.rbf(1,1.,2)
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
k = k1 * k2 # equivalent to k = k1.prod(k2)
print k
# Simulate sample paths
X = np.linspace(-5,5,501)[:,None]
Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
# plot
pb.figure(figsize=(10,4))
pb.subplot(1,2,1)
k.plot()
pb.subplot(1,2,2)
pb.plot(X,Y.T)
pb.ylabel("Sample path")
pb.subplots_adjust(wspace=0.3)
k = (k1+k2)*(k1+k2)
print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.Matern32(1)
k3 = GPy.kern.white(1)
k = k1 + k2 + k3
print k
k.constrain_positive('var')
k.constrain_fixed(np.array([1]),1.75)
k.tie_param('len')
k.unconstrain('white')
k.constrain_bounded('white',lower=1e-5,upper=.5)
print k
k_cst = GPy.kern.bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
Kanova = (k_cst + k_mat).prod_orthogonal(k_cst + k_mat)
print Kanova
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(40,2))
Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
# Create GP regression model
m = GPy.models.GP_regression(X,Y,Kanova)
pb.figure(figsize=(5,5))
m.plot()
pb.figure(figsize=(20,3))
pb.subplots_adjust(wspace=0.5)
pb.subplot(1,5,1)
m.plot()
pb.subplot(1,5,2)
pb.ylabel("= ",rotation='horizontal',fontsize='30')
pb.subplot(1,5,3)
m.plot(which_functions=[False,True,False,False])
pb.ylabel("cst +",rotation='horizontal',fontsize='30')
pb.subplot(1,5,4)
m.plot(which_functions=[False,False,True,False])
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
pb.subplot(1,5,5)
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
m.plot(which_functions=[False,False,False,True])
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.rbf(1, .5, .25)
ker1.plot()
ker2.plot()
ker3.plot()
#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
pb.figure(figsize=(16,12))
pb.subplots_adjust(wspace=.5, hspace=.5)
for i, kern in enumerate(kernels):
pb.subplot(3,4,i+1)
kern.plot(x=7.5,plot_limits=[0.00001,15.])
pb.title(kernel_names[i]+ '\n')
# actual plot for the noise
i = 11
X = np.linspace(0.,15.,201)
WN = 0*X
WN[100] = 1.
pb.subplot(3,4,i+1)
pb.plot(X,WN,'b')

18
GPy/kern/Matern32.py
View file

@ -76,7 +76,7 @@ class Matern32(kernpart):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
@ -84,29 +84,29 @@ class Matern32(kernpart):
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3
#dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar*partial)
target[0] += np.sum(dvar*dL_dK)
if self.ARD == True:
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
#dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
else:
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist)) * dist2M.sum(-1)*invdist
#dl = self.variance*dvar*dist2M.sum(-1)*invdist
target[1] += np.sum(dl*partial)
target[1] += np.sum(dl*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
target[0] += np.sum(partial)
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
def Gram_matrix(self,F,F1,F2,lower,upper):

18
GPy/kern/Matern52.py
View file

@ -74,7 +74,7 @@ class Matern52(kernpart):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
@ -82,29 +82,29 @@ class Matern52(kernpart):
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3
dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist)
dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar*partial)
target[0] += np.sum(dvar*dL_dK)
if self.ARD:
dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
#dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
else:
dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist)) * dist2M.sum(-1)*invdist
#dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist)) * dist2M.sum(-1)*invdist
target[1] += np.sum(dl*partial)
target[1] += np.sum(dl*dL_dK)
def dKdiag_dtheta(self,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
target[0] += np.sum(partial)
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
def Gram_matrix(self,F,F1,F2,F3,lower,upper):

38
GPy/kern/bias.py
View file

@ -35,16 +35,17 @@ class bias(kernpart):
def Kdiag(self,X,target):
target += self.variance
def dK_dtheta(self,partial,X,X2,target):
target += partial.sum()
def dK_dtheta(self,dL_dKdiag,X,X2,target):
target += dL_dKdiag.sum()
def dKdiag_dtheta(self,partial,X,target):
target += partial.sum()
def dK_dX(self, partial,X, X2, target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
target += dL_dKdiag.sum()
def dK_dX(self, dL_dK,X, X2, target):
pass
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
#---------------------------------------#
@ -60,30 +61,29 @@ class bias(kernpart):
def psi2(self, Z, mu, S, target):
target += self.variance**2
def dpsi0_dtheta(self, partial, Z, mu, S, target):
target += partial.sum()
def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S, target):
target += dL_dpsi0.sum()
def dpsi1_dtheta(self, partial, Z, mu, S, target):
target += partial.sum()
def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S, target):
target += dL_dpsi1.sum()
def dpsi2_dtheta(self, partial, Z, mu, S, target):
target += 2.*self.variance*partial.sum()
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target):
target += 2.*self.variance*dL_dpsi2.sum()
def dpsi0_dZ(self, partial, Z, mu, S, target):
def dpsi0_dZ(self, dL_dpsi0, Z, mu, S, target):
pass
def dpsi0_dmuS(self, partial, Z, mu, S, target_mu, target_S):
def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
pass
def dpsi1_dZ(self, partial, Z, mu, S, target):
def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
pass
def dpsi1_dmuS(self, partial, Z, mu, S, target_mu, target_S):
def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S):
pass
def dpsi2_dZ(self, partial, Z, mu, S, target):
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
pass
def dpsi2_dmuS(self, partial, Z, mu, S, target_mu, target_S):
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
pass

26
GPy/kern/coregionalise.py
View file

@ -53,7 +53,7 @@ class coregionalise(kernpart):
def Kdiag(self,index,target):
target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]
def dK_dtheta(self,partial,index,index2,target):
def dK_dtheta(self,dL_dK,index,index2,target):
index = np.asarray(index,dtype=np.int)
if index2 is None:
index2 = index
@ -62,28 +62,28 @@ class coregionalise(kernpart):
ii,jj = np.meshgrid(index,index2)
ii,jj = ii.T, jj.T
partial_small = np.zeros_like(self.B)
dL_dK_small = np.zeros_like(self.B)
for i in range(self.Nout):
for j in range(self.Nout):
tmp = np.sum(partial[(ii==i)*(jj==j)])
partial_small[i,j] = tmp
tmp = np.sum(dL_dK[(ii==i)*(jj==j)])
dL_dK_small[i,j] = tmp
dkappa = np.diag(partial_small)
partial_small += partial_small.T
dW = (self.W[:,None,:]*partial_small[:,:,None]).sum(0)
dkappa = np.diag(dL_dK_small)
dL_dK_small += dL_dK_small.T
dW = (self.W[:,None,:]*dL_dK_small[:,:,None]).sum(0)
target += np.hstack([dW.flatten(),dkappa])
def dKdiag_dtheta(self,partial,index,target):
def dKdiag_dtheta(self,dL_dKdiag,index,target):
index = np.asarray(index,dtype=np.int).flatten()
partial_small = np.zeros(self.Nout)
dL_dKdiag_small = np.zeros(self.Nout)
for i in range(self.Nout):
partial_small[i] += np.sum(partial[index==i])
dW = 2.*self.W*partial_small[:,None]
dkappa = partial_small
dL_dKdiag_small[i] += np.sum(dL_dKdiag[index==i])
dW = 2.*self.W*dL_dKdiag_small[:,None]
dkappa = dL_dKdiag_small
target += np.hstack([dW.flatten(),dkappa])
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
pass

18
GPy/kern/exponential.py
View file

@ -74,35 +74,35 @@ class exponential(kernpart):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3
dvar = np.exp(-dist)
target[0] += np.sum(dvar*partial)
target[0] += np.sum(dvar*dL_dK)
if self.ARD == True:
dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
else:
dl = self.variance*dvar*dist2M.sum(-1)*invdist
target[1] += np.sum(dl*partial)
target[1] += np.sum(dl*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
#NB: derivative of diagonal elements wrt lengthscale is 0
target[0] += np.sum(partial)
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(self.variance*np.exp(-dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
def Gram_matrix(self,F,F1,lower,upper):

73
GPy/kern/kern.py
View file

@ -271,10 +271,10 @@ class kern(parameterised):
[p.K(X[s1,i_s],X2[s2,i_s],target=target[s1,s2]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
return target
def dK_dtheta(self,partial,X,X2=None,slices1=None,slices2=None):
def dK_dtheta(self,dL_dK,X,X2=None,slices1=None,slices2=None):
"""
:param partial: An array of partial derivaties, dL_dK
:type partial: Np.ndarray (N x M)
:param dL_dK: An array of dL_dK derivaties, dL_dK
:type dL_dK: Np.ndarray (N x M)
:param X: Observed data inputs
:type X: np.ndarray (N x D)
:param X2: Observed dara inputs (optional, defaults to X)
@ -288,16 +288,16 @@ class kern(parameterised):
if X2 is None:
X2 = X
target = np.zeros(self.Nparam)
[p.dK_dtheta(partial[s1,s2],X[s1,i_s],X2[s2,i_s],target[ps]) for p,i_s,ps,s1,s2 in zip(self.parts, self.input_slices, self.param_slices, slices1, slices2)]
[p.dK_dtheta(dL_dK[s1,s2],X[s1,i_s],X2[s2,i_s],target[ps]) for p,i_s,ps,s1,s2 in zip(self.parts, self.input_slices, self.param_slices, slices1, slices2)]
return self._transform_gradients(target)
def dK_dX(self,partial,X,X2=None,slices1=None,slices2=None):
def dK_dX(self,dL_dK,X,X2=None,slices1=None,slices2=None):
if X2 is None:
X2 = X
slices1, slices2 = self._process_slices(slices1,slices2)
target = np.zeros_like(X)
[p.dK_dX(partial[s1,s2],X[s1,i_s],X2[s2,i_s],target[s1,i_s]) for p, i_s, s1, s2 in zip(self.parts, self.input_slices, slices1, slices2)]
[p.dK_dX(dL_dK[s1,s2],X[s1,i_s],X2[s2,i_s],target[s1,i_s]) for p, i_s, s1, s2 in zip(self.parts, self.input_slices, slices1, slices2)]
return target
def Kdiag(self,X,slices=None):
@ -307,20 +307,20 @@ class kern(parameterised):
[p.Kdiag(X[s,i_s],target=target[s]) for p,i_s,s in zip(self.parts,self.input_slices,slices)]
return target
def dKdiag_dtheta(self,partial,X,slices=None):
def dKdiag_dtheta(self,dL_dKdiag,X,slices=None):
assert X.shape[1]==self.D
assert len(partial.shape)==1
assert partial.size==X.shape[0]
assert len(dL_dKdiag.shape)==1
assert dL_dKdiag.size==X.shape[0]
slices = self._process_slices(slices,False)
target = np.zeros(self.Nparam)
[p.dKdiag_dtheta(partial[s],X[s,i_s],target[ps]) for p,i_s,s,ps in zip(self.parts,self.input_slices,slices,self.param_slices)]
[p.dKdiag_dtheta(dL_dKdiag[s],X[s,i_s],target[ps]) for p,i_s,s,ps in zip(self.parts,self.input_slices,slices,self.param_slices)]
return self._transform_gradients(target)
def dKdiag_dX(self, partial, X, slices=None):
def dKdiag_dX(self, dL_dKdiag, X, slices=None):
assert X.shape[1]==self.D
slices = self._process_slices(slices,False)
target = np.zeros_like(X)
[p.dKdiag_dX(partial[s],X[s,i_s],target[s,i_s]) for p,i_s,s in zip(self.parts,self.input_slices,slices)]
[p.dKdiag_dX(dL_dKdiag[s],X[s,i_s],target[s,i_s]) for p,i_s,s in zip(self.parts,self.input_slices,slices)]
return target
def psi0(self,Z,mu,S,slices=None):
@ -329,16 +329,16 @@ class kern(parameterised):
[p.psi0(Z,mu[s],S[s],target[s]) for p,s in zip(self.parts,slices)]
return target
def dpsi0_dtheta(self,partial,Z,mu,S,slices=None):
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,slices=None):
slices = self._process_slices(slices,False)
target = np.zeros(self.Nparam)
[p.dpsi0_dtheta(partial[s],Z,mu[s],S[s],target[ps]) for p,ps,s in zip(self.parts, self.param_slices,slices)]
[p.dpsi0_dtheta(dL_dpsi0[s],Z,mu[s],S[s],target[ps]) for p,ps,s in zip(self.parts, self.param_slices,slices)]
return self._transform_gradients(target)
def dpsi0_dmuS(self,partial,Z,mu,S,slices=None):
def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,slices=None):
slices = self._process_slices(slices,False)
target_mu,target_S = np.zeros_like(mu),np.zeros_like(S)
[p.dpsi0_dmuS(partial,Z,mu[s],S[s],target_mu[s],target_S[s]) for p,s in zip(self.parts,slices)]
[p.dpsi0_dmuS(dL_dpsi0,Z,mu[s],S[s],target_mu[s],target_S[s]) for p,s in zip(self.parts,slices)]
return target_mu,target_S
def psi1(self,Z,mu,S,slices1=None,slices2=None):
@ -348,25 +348,25 @@ class kern(parameterised):
[p.psi1(Z[s2],mu[s1],S[s1],target[s1,s2]) for p,s1,s2 in zip(self.parts,slices1,slices2)]
return target
def dpsi1_dtheta(self,partial,Z,mu,S,slices1=None,slices2=None):
def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,slices1=None,slices2=None):
"""N,M,(Ntheta)"""
slices1, slices2 = self._process_slices(slices1,slices2)
target = np.zeros((self.Nparam))
[p.dpsi1_dtheta(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,ps,s1,s2,i_s in zip(self.parts, self.param_slices,slices1,slices2,self.input_slices)]
[p.dpsi1_dtheta(dL_dpsi1[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,ps,s1,s2,i_s in zip(self.parts, self.param_slices,slices1,slices2,self.input_slices)]
return self._transform_gradients(target)
def dpsi1_dZ(self,partial,Z,mu,S,slices1=None,slices2=None):
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,slices1=None,slices2=None):
"""N,M,Q"""
slices1, slices2 = self._process_slices(slices1,slices2)
target = np.zeros_like(Z)
[p.dpsi1_dZ(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
[p.dpsi1_dZ(dL_dpsi1[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
return target
def dpsi1_dmuS(self,partial,Z,mu,S,slices1=None,slices2=None):
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,slices1=None,slices2=None):
"""return shapes are N,M,Q"""
slices1, slices2 = self._process_slices(slices1,slices2)
target_mu, target_S = np.zeros((2,mu.shape[0],mu.shape[1]))
[p.dpsi1_dmuS(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
[p.dpsi1_dmuS(dL_dpsi1[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
return target_mu, target_S
def psi2(self,Z,mu,S,slices1=None,slices2=None):
@ -399,10 +399,11 @@ class kern(parameterised):
return target
def dpsi2_dtheta(self,partial,partial1,Z,mu,S,slices1=None,slices2=None):
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,slices1=None,slices2=None):
"""Returns shape (N,M,M,Ntheta)"""
slices1, slices2 = self._process_slices(slices1,slices2)
target = np.zeros(self.Nparam)
[p.dpsi2_dtheta(partial[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,i_s,s1,s2,ps in zip(self.parts,self.input_slices,slices1,slices2,self.param_slices)]
[p.dpsi2_dtheta(dL_dpsi2[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,i_s,s1,s2,ps in zip(self.parts,self.input_slices,slices1,slices2,self.param_slices)]
#compute the "cross" terms
#TODO: better looping
@ -416,11 +417,11 @@ class kern(parameterised):
pass
#rbf X bias
elif p1.name=='bias' and p2.name=='rbf':
p2.dpsi1_dtheta(partial.sum(1)*p1.variance,Z,mu,S,target[ps2])
p1.dpsi1_dtheta(partial.sum(1)*p2._psi1,Z,mu,S,target[ps1])
p2.dpsi1_dtheta(dL_dpsi2.sum(1)*p1.variance,Z,mu,S,target[ps2])
p1.dpsi1_dtheta(dL_dpsi2.sum(1)*p2._psi1,Z,mu,S,target[ps1])
elif p2.name=='bias' and p1.name=='rbf':
p1.dpsi1_dtheta(partial.sum(1)*p2.variance,Z,mu,S,target[ps1])
p2.dpsi1_dtheta(partial.sum(1)*p1._psi1,Z,mu,S,target[ps2])
p1.dpsi1_dtheta(dL_dpsi2.sum(1)*p2.variance,Z,mu,S,target[ps1])
p2.dpsi1_dtheta(dL_dpsi2.sum(1)*p1._psi1,Z,mu,S,target[ps2])
#rbf X linear
elif p1.name=='linear' and p2.name=='rbf':
raise NotImplementedError #TODO
@ -431,10 +432,10 @@ class kern(parameterised):
return self._transform_gradients(target)
def dpsi2_dZ(self,partial,Z,mu,S,slices1=None,slices2=None):
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,slices1=None,slices2=None):
slices1, slices2 = self._process_slices(slices1,slices2)
target = np.zeros_like(Z)
[p.dpsi2_dZ(partial[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
[p.dpsi2_dZ(dL_dpsi2[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
#compute the "cross" terms
for p1, p2 in itertools.combinations(self.parts,2):
@ -443,9 +444,9 @@ class kern(parameterised):
pass
#rbf X bias
elif p1.name=='bias' and p2.name=='rbf':
target += p2.dpsi1_dX(partial.sum(1)*p1.variance,Z,mu,S,target)
p2.dpsi1_dX(dL_dpsi2.sum(1)*p1.variance,Z,mu,S,target)
elif p2.name=='bias' and p1.name=='rbf':
target += p1.dpsi1_dZ(partial.sum(2)*p2.variance,Z,mu,S,target)
p1.dpsi1_dZ(dL_dpsi2.sum(2)*p2.variance,Z,mu,S,target)
#rbf X linear
elif p1.name=='linear' and p2.name=='rbf':
raise NotImplementedError #TODO
@ -457,11 +458,11 @@ class kern(parameterised):
return target
def dpsi2_dmuS(self,partial,Z,mu,S,slices1=None,slices2=None):
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,slices1=None,slices2=None):
"""return shapes are N,M,M,Q"""
slices1, slices2 = self._process_slices(slices1,slices2)
target_mu, target_S = np.zeros((2,mu.shape[0],mu.shape[1]))
[p.dpsi2_dmuS(partial[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
[p.dpsi2_dmuS(dL_dpsi2[s1,s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
#compute the "cross" terms
for p1, p2 in itertools.combinations(self.parts,2):
@ -470,9 +471,9 @@ class kern(parameterised):
pass
#rbf X bias
elif p1.name=='bias' and p2.name=='rbf':
target += p2.dpsi1_dmuS(partial.sum(1)*p1.variance,Z,mu,S,target_mu,target_S)
p2.dpsi1_dmuS(partial.sum(1)*p1.variance,Z,mu,S,target_mu,target_S)
elif p2.name=='bias' and p1.name=='rbf':
target += p1.dpsi1_dmuS(partial.sum(2)*p2.variance,Z,mu,S,target_mu,target_S)
p1.dpsi1_dmuS(partial.sum(2)*p2.variance,Z,mu,S,target_mu,target_S)
#rbf X linear
elif p1.name=='linear' and p2.name=='rbf':
raise NotImplementedError #TODO

18
GPy/kern/kernpart.py
View file

@ -26,31 +26,31 @@ class kernpart(object):
raise NotImplementedError
def Kdiag(self,X,target):
raise NotImplementedError
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
raise NotImplementedError
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
raise NotImplementedError
def psi0(self,Z,mu,S,target):
raise NotImplementedError
def dpsi0_dtheta(self,partial,Z,mu,S,target):
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
raise NotImplementedError
def dpsi0_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S):
raise NotImplementedError
def psi1(self,Z,mu,S,target):
raise NotImplementedError
def dpsi1_dtheta(self,Z,mu,S,target):
raise NotImplementedError
def dpsi1_dZ(self,partial,Z,mu,S,target):
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target):
raise NotImplementedError
def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S):
raise NotImplementedError
def psi2(self,Z,mu,S,target):
raise NotImplementedError
def dpsi2_dZ(self,partial,Z,mu,S,target):
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target):
raise NotImplementedError
def dpsi2_dtheta(self,partial,Z,mu,S,target):
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target):
raise NotImplementedError
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
raise NotImplementedError
def dK_dX(self,X,X2,target):
raise NotImplementedError

50
GPy/kern/linear.py
View file

@ -73,16 +73,16 @@ class linear(kernpart):
def Kdiag(self,X,target):
np.add(target,np.sum(self.variances*np.square(X),-1),target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
if self.ARD:
product = X[:,None,:]*X2[None,:,:]
target += (partial[:,:,None]*product).sum(0).sum(0)
target += (dL_dK[:,:,None]*product).sum(0).sum(0)
else:
self._K_computations(X, X2)
target += np.sum(self._dot_product*partial)
target += np.sum(self._dot_product*dL_dK)
def dK_dX(self,partial,X,X2,target):
target += (((X2[:, None, :] * self.variances)) * partial[:,:, None]).sum(0)
def dK_dX(self,dL_dK,X,X2,target):
target += (((X2[:, None, :] * self.variances)) * dL_dK[:,:, None]).sum(0)
#---------------------------------------#
# PSI statistics #
@ -92,40 +92,40 @@ class linear(kernpart):
self._psi_computations(Z,mu,S)
target += np.sum(self.variances*self.mu2_S,1)
def dKdiag_dtheta(self,partial, X, target):
tmp = partial[:,None]*X**2
def dKdiag_dtheta(self,dL_dKdiag, X, target):
tmp = dL_dKdiag[:,None]*X**2
if self.ARD:
target += tmp.sum(0)
else:
target += tmp.sum()
def dpsi0_dtheta(self,partial,Z,mu,S,target):
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
self._psi_computations(Z,mu,S)
tmp = partial[:, None] * self.mu2_S
tmp = dL_dpsi0[:, None] * self.mu2_S
if self.ARD:
target += tmp.sum(0)
else:
target += tmp.sum()
def dpsi0_dmuS(self,partial, Z,mu,S,target_mu,target_S):
target_mu += partial[:, None] * (2.0*mu*self.variances)
target_S += partial[:, None] * self.variances
def dpsi0_dmuS(self,dL_dpsi0, Z,mu,S,target_mu,target_S):
target_mu += dL_dpsi0[:, None] * (2.0*mu*self.variances)
target_S += dL_dpsi0[:, None] * self.variances
def psi1(self,Z,mu,S,target):
"""the variance, it does nothing"""
self.K(mu,Z,target)
def dpsi1_dtheta(self,partial,Z,mu,S,target):
def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,target):
"""the variance, it does nothing"""
self.dK_dtheta(partial,mu,Z,target)
self.dK_dtheta(dL_dpsi1,mu,Z,target)
def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S):
"""Do nothing for S, it does not affect psi1"""
self._psi_computations(Z,mu,S)
target_mu += (partial.T[:,:, None]*(Z*self.variances)).sum(1)
target_mu += (dL_dpsi1.T[:,:, None]*(Z*self.variances)).sum(1)
def dpsi1_dZ(self,partial,Z,mu,S,target):
self.dK_dX(partial.T,Z,mu,target)
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target):
self.dK_dX(dL_dpsi1.T,Z,mu,target)
def psi2(self,Z,mu,S,target):
"""
@ -135,25 +135,25 @@ class linear(kernpart):
psi2 = self.ZZ*np.square(self.variances)*self.mu2_S[:, None, None, :]
target += psi2.sum(-1)
def dpsi2_dtheta(self,partial,Z,mu,S,target):
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target):
self._psi_computations(Z,mu,S)
tmp = (partial[:,:,:,None]*(2.*self.ZZ*self.mu2_S[:,None,None,:]*self.variances))
tmp = (dL_dpsi2[:,:,:,None]*(2.*self.ZZ*self.mu2_S[:,None,None,:]*self.variances))
if self.ARD:
target += tmp.sum(0).sum(0).sum(0)
else:
target += tmp.sum()
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
"""Think N,M,M,Q """
self._psi_computations(Z,mu,S)
tmp = self.ZZ*np.square(self.variances) # M,M,Q
target_mu += (partial[:,:,:,None]*tmp*2.*mu[:,None,None,:]).sum(1).sum(1)
target_S += (partial[:,:,:,None]*tmp).sum(1).sum(1)
target_mu += (dL_dpsi2[:,:,:,None]*tmp*2.*mu[:,None,None,:]).sum(1).sum(1)
target_S += (dL_dpsi2[:,:,:,None]*tmp).sum(1).sum(1)
def dpsi2_dZ(self,partial,Z,mu,S,target):
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target):
self._psi_computations(Z,mu,S)
mu2_S = np.sum(self.mu2_S,0)# Q,
target += (partial[:,:,:,None] * (self.mu2_S[:,None,None,:]*(Z*np.square(self.variances)[None,:])[None,None,:,:])).sum(0).sum(1)
target += (dL_dpsi2[:,:,:,None] * (self.mu2_S[:,None,None,:]*(Z*np.square(self.variances)[None,:])[None,None,:,:])).sum(0).sum(1)
#---------------------------------------#
# Precomputations #

16
GPy/kern/periodic_Matern32.py
View file

@ -101,7 +101,7 @@ class periodic_Matern32(kernpart):
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -166,13 +166,13 @@ class periodic_Matern32(kernpart):
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
# np.add(target[:,:,0],dK_dvar, target[:,:,0])
target[0] += np.sum(dK_dvar*partial)
target[0] += np.sum(dK_dvar*dL_dK)
#np.add(target[:,:,1],dK_dlen, target[:,:,1])
target[1] += np.sum(dK_dlen*partial)
target[1] += np.sum(dK_dlen*dL_dK)
#np.add(target[:,:,2],dK_dper, target[:,:,2])
target[2] += np.sum(dK_dper*partial)
target[2] += np.sum(dK_dper*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -231,6 +231,6 @@ class periodic_Matern32(kernpart):
dK_dper = 2* mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*partial)
target[1] += np.sum(np.diag(dK_dlen)*partial)
target[2] += np.sum(np.diag(dK_dper)*partial)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

16
GPy/kern/periodic_Matern52.py
View file

@ -105,7 +105,7 @@ class periodic_Matern52(kernpart):
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -178,13 +178,13 @@ class periodic_Matern52(kernpart):
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
# np.add(target[:,:,0],dK_dvar, target[:,:,0])
target[0] += np.sum(dK_dvar*partial)
target[0] += np.sum(dK_dvar*dL_dK)
#np.add(target[:,:,1],dK_dlen, target[:,:,1])
target[1] += np.sum(dK_dlen*partial)
target[1] += np.sum(dK_dlen*dL_dK)
#np.add(target[:,:,2],dK_dper, target[:,:,2])
target[2] += np.sum(dK_dper*partial)
target[2] += np.sum(dK_dper*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -251,6 +251,6 @@ class periodic_Matern52(kernpart):
dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper)
dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*partial)
target[1] += np.sum(np.diag(dK_dlen)*partial)
target[2] += np.sum(np.diag(dK_dper)*partial)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

16
GPy/kern/periodic_exponential.py
View file

@ -101,7 +101,7 @@ class periodic_exponential(kernpart):
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -162,11 +162,11 @@ class periodic_exponential(kernpart):
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
target[0] += np.sum(dK_dvar*partial)
target[1] += np.sum(dK_dlen*partial)
target[2] += np.sum(dK_dper*partial)
target[0] += np.sum(dK_dvar*dL_dK)
target[1] += np.sum(dK_dlen*dL_dK)
target[2] += np.sum(dK_dper*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
@ -222,7 +222,7 @@ class periodic_exponential(kernpart):
dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*partial)
target[1] += np.sum(np.diag(dK_dlen)*partial)
target[2] += np.sum(np.diag(dK_dper)*partial)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

24
GPy/kern/prod.py
View file

@ -55,7 +55,7 @@ class prod(kernpart):
self.k2.Kdiag(X,target2)
target += target1 * target2
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
K1 = np.zeros((X.shape[0],X2.shape[0]))
@ -65,13 +65,13 @@ class prod(kernpart):
k1_target = np.zeros(self.k1.Nparam)
k2_target = np.zeros(self.k2.Nparam)
self.k1.dK_dtheta(partial*K2, X, X2, k1_target)
self.k2.dK_dtheta(partial*K1, X, X2, k2_target)
self.k1.dK_dtheta(dL_dK*K2, X, X2, k1_target)
self.k2.dK_dtheta(dL_dK*K1, X, X2, k2_target)
target[:self.k1.Nparam] += k1_target
target[self.k1.Nparam:] += k2_target
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
K1 = np.zeros((X.shape[0],X2.shape[0]))
@ -79,19 +79,19 @@ class prod(kernpart):
self.k1.K(X,X2,K1)
self.k2.K(X,X2,K2)
self.k1.dK_dX(partial*K2, X, X2, target)
self.k2.dK_dX(partial*K1, X, X2, target)
self.k1.dK_dX(dL_dK*K2, X, X2, target)
self.k2.dK_dX(dL_dK*K1, X, X2, target)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
target1 = np.zeros((X.shape[0],))
target2 = np.zeros((X.shape[0],))
self.k1.Kdiag(X,target1)
self.k2.Kdiag(X,target2)
self.k1.dKdiag_dX(partial*target2, X, target)
self.k2.dKdiag_dX(partial*target1, X, target)
self.k1.dKdiag_dX(dL_dKdiag*target2, X, target)
self.k2.dKdiag_dX(dL_dKdiag*target1, X, target)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
target1 = np.zeros((X.shape[0],))
target2 = np.zeros((X.shape[0],))
@ -100,8 +100,8 @@ class prod(kernpart):
k1_target = np.zeros(self.k1.Nparam)
k2_target = np.zeros(self.k2.Nparam)
self.k1.dKdiag_dtheta(partial*target2, X, k1_target)
self.k2.dKdiag_dtheta(partial*target1, X, k2_target)
self.k1.dKdiag_dtheta(dL_dKdiag*target2, X, k1_target)
self.k2.dKdiag_dtheta(dL_dKdiag*target1, X, k2_target)
target[:self.k1.Nparam] += k1_target
target[self.k1.Nparam:] += k2_target

24
GPy/kern/prod_orthogonal.py
View file

@ -46,7 +46,7 @@ class prod_orthogonal(kernpart):
self.k2.K(X[:,self.k1.D:],X2[:,self.k1.D:],target2)
target += target1 * target2
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
K1 = np.zeros((X.shape[0],X2.shape[0]))
@ -54,8 +54,8 @@ class prod_orthogonal(kernpart):
self.k1.K(X[:,:self.k1.D],X2[:,:self.k1.D],K1)
self.k2.K(X[:,self.k1.D:],X2[:,self.k1.D:],K2)
self.k1.dK_dtheta(partial*K2, X[:,:self.k1.D], X2[:,:self.k1.D], target[:self.k1.Nparam])
self.k2.dK_dtheta(partial*K1, X[:,self.k1.D:], X2[:,self.k1.D:], target[self.k1.Nparam:])
self.k1.dK_dtheta(dL_dK*K2, X[:,:self.k1.D], X2[:,:self.k1.D], target[:self.k1.Nparam])
self.k2.dK_dtheta(dL_dK*K1, X[:,self.k1.D:], X2[:,self.k1.D:], target[self.k1.Nparam:])
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
@ -65,15 +65,15 @@ class prod_orthogonal(kernpart):
self.k2.Kdiag(X[:,self.k1.D:],target2)
target += target1 * target2
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
K1 = np.zeros(X.shape[0])
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,:self.k1.D],K1)
self.k2.Kdiag(X[:,self.k1.D:],K2)
self.k1.dKdiag_dtheta(partial*K2,X[:,:self.k1.D],target[:self.k1.Nparam])
self.k2.dKdiag_dtheta(partial*K1,X[:,self.k1.D:],target[self.k1.Nparam:])
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,:self.k1.D],target[:self.k1.Nparam])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.k1.D:],target[self.k1.Nparam:])
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
K1 = np.zeros((X.shape[0],X2.shape[0]))
@ -81,15 +81,15 @@ class prod_orthogonal(kernpart):
self.k1.K(X[:,0:self.k1.D],X2[:,0:self.k1.D],K1)
self.k2.K(X[:,self.k1.D:],X2[:,self.k1.D:],K2)
self.k1.dK_dX(partial*K2, X[:,:self.k1.D], X2[:,:self.k1.D], target)
self.k2.dK_dX(partial*K1, X[:,self.k1.D:], X2[:,self.k1.D:], target)
self.k1.dK_dX(dL_dK*K2, X[:,:self.k1.D], X2[:,:self.k1.D], target)
self.k2.dK_dX(dL_dK*K1, X[:,self.k1.D:], X2[:,self.k1.D:], target)
def dKdiag_dX(self, partial, X, target):
def dKdiag_dX(self, dL_dKdiag, X, target):
K1 = np.zeros(X.shape[0])
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,0:self.k1.D],K1)
self.k2.Kdiag(X[:,self.k1.D:],K2)
self.k1.dK_dX(partial*K2, X[:,:self.k1.D], target)
self.k2.dK_dX(partial*K1, X[:,self.k1.D:], target)
self.k1.dK_dX(dL_dKdiag*K2, X[:,:self.k1.D], target)
self.k2.dK_dX(dL_dKdiag*K1, X[:,self.k1.D:], target)

58
GPy/kern/rbf.py
View file

@ -82,27 +82,27 @@ class rbf(kernpart):
def Kdiag(self,X,target):
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
self._K_computations(X,X2)
target[0] += np.sum(self._K_dvar*partial)
target[0] += np.sum(self._K_dvar*dL_dK)
if self.ARD == True:
dl = self._K_dvar[:,:,None]*self.variance*self._K_dist2/self.lengthscale
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
else:
target[1] += np.sum(self._K_dvar*self.variance*(self._K_dist2.sum(-1))/self.lengthscale*partial)
#np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*partial)
target[1] += np.sum(self._K_dvar*self.variance*(self._K_dist2.sum(-1))/self.lengthscale*dL_dK)
#np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*dL_dK)
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
#NB: derivative of diagonal elements wrt lengthscale is 0
target[0] += np.sum(partial)
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
self._K_computations(X,X2)
_K_dist = X[:,None,:]-X2[None,:,:]
dK_dX = np.transpose(-self.variance*self._K_dvar[:,:,np.newaxis]*_K_dist/self.lengthscale2,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
@ -113,69 +113,69 @@ class rbf(kernpart):
def psi0(self,Z,mu,S,target):
target += self.variance
def dpsi0_dtheta(self,partial,Z,mu,S,target):
target[0] += np.sum(partial)
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
target[0] += np.sum(dL_dpsi0)
def dpsi0_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S):
pass
def psi1(self,Z,mu,S,target):
self._psi_computations(Z,mu,S)
target += self._psi1
def dpsi1_dtheta(self,partial,Z,mu,S,target):
def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,target):
self._psi_computations(Z,mu,S)
denom_deriv = S[:,None,:]/(self.lengthscale**3+self.lengthscale*S[:,None,:])
d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv)
target[0] += np.sum(partial*self._psi1/self.variance)
dpsi1_dlength = d_length*partial[:,:,None]
target[0] += np.sum(dL_dpsi1*self._psi1/self.variance)
dpsi1_dlength = d_length*dL_dpsi1[:,:,None]
if not self.ARD:
target[1] += dpsi1_dlength.sum()
else:
target[1:] += dpsi1_dlength.sum(0).sum(0)
def dpsi1_dZ(self,partial,Z,mu,S,target):
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target):
self._psi_computations(Z,mu,S)
denominator = (self.lengthscale2*(self._psi1_denom))
dpsi1_dZ = - self._psi1[:,:,None] * ((self._psi1_dist/denominator))
target += np.sum(partial.T[:,:,None] * dpsi1_dZ, 0)
target += np.sum(dL_dpsi1.T[:,:,None] * dpsi1_dZ, 0)
def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S):
self._psi_computations(Z,mu,S)
tmp = self._psi1[:,:,None]/self.lengthscale2/self._psi1_denom
target_mu += np.sum(partial.T[:, :, None]*tmp*self._psi1_dist,1)
target_S += np.sum(partial.T[:, :, None]*0.5*tmp*(self._psi1_dist_sq-1),1)
target_mu += np.sum(dL_dpsi1.T[:, :, None]*tmp*self._psi1_dist,1)
target_S += np.sum(dL_dpsi1.T[:, :, None]*0.5*tmp*(self._psi1_dist_sq-1),1)
def psi2(self,Z,mu,S,target):
self._psi_computations(Z,mu,S)
target += self._psi2
def dpsi2_dtheta(self,partial,Z,mu,S,target):
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target):
"""Shape N,M,M,Ntheta"""
self._psi_computations(Z,mu,S)
d_var = 2.*self._psi2/self.variance
d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom)
target[0] += np.sum(partial*d_var)
dpsi2_dlength = d_length*partial[:,:,:,None]
target[0] += np.sum(dL_dpsi2*d_var)
dpsi2_dlength = d_length*dL_dpsi2[:,:,:,None]
if not self.ARD:
target[1] += dpsi2_dlength.sum()
else:
target[1:] += dpsi2_dlength.sum(0).sum(0).sum(0)
def dpsi2_dZ(self,partial,Z,mu,S,target):
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target):
self._psi_computations(Z,mu,S)
term1 = 0.5*self._psi2_Zdist/self.lengthscale2 # M, M, Q
term2 = self._psi2_mudist/self._psi2_denom/self.lengthscale2 # N, M, M, Q
dZ = self._psi2[:,:,:,None] * (term1[None] + term2)
target += (partial[:,:,:,None]*dZ).sum(0).sum(0)
target += (dL_dpsi2[:,:,:,None]*dZ).sum(0).sum(0)
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
"""Think N,M,M,Q """
self._psi_computations(Z,mu,S)
tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom
target_mu += (partial[:,:,:,None]*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
target_S += (partial[:,:,:,None]*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
target_mu += (dL_dpsi2[:,:,:,None]*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
target_S += (dL_dpsi2[:,:,:,None]*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
#---------------------------------------#

24
GPy/kern/symmetric.py
View file

@ -51,7 +51,7 @@ class symmetric(kernpart):
self.k.K(X,AX2,target)
self.k.K(AX,AX2,target)
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
AX = np.dot(X,self.transform)
if X2 is None:
@ -59,13 +59,13 @@ class symmetric(kernpart):
ZX2 = AX
else:
AX2 = np.dot(X2, self.transform)
self.k.dK_dtheta(partial,X,X2,target)
self.k.dK_dtheta(partial,AX,X2,target)
self.k.dK_dtheta(partial,X,AX2,target)
self.k.dK_dtheta(partial,AX,AX2,target)
self.k.dK_dtheta(dL_dK,X,X2,target)
self.k.dK_dtheta(dL_dK,AX,X2,target)
self.k.dK_dtheta(dL_dK,X,AX2,target)
self.k.dK_dtheta(dL_dK,AX,AX2,target)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
AX = np.dot(X,self.transform)
if X2 is None:
@ -73,10 +73,10 @@ class symmetric(kernpart):
ZX2 = AX
else:
AX2 = np.dot(X2, self.transform)
self.k.dK_dX(partial, X, X2, target)
self.k.dK_dX(partial, AX, X2, target)
self.k.dK_dX(partial, X, AX2, target)
self.k.dK_dX(partial, AX ,AX2, target)
self.k.dK_dX(dL_dK, X, X2, target)
self.k.dK_dX(dL_dK, AX, X2, target)
self.k.dK_dX(dL_dK, X, AX2, target)
self.k.dK_dX(dL_dK, AX ,AX2, target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
@ -84,9 +84,9 @@ class symmetric(kernpart):
self.K(X,X,foo)
target += np.diag(foo)
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
raise NotImplementedError
def dKdiag_dtheta(self,partial,X,target):
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
raise NotImplementedError

30
GPy/kern/white.py
View file

@ -37,50 +37,50 @@ class white(kernpart):
def Kdiag(self,X,target):
target += self.variance
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self,dL_dK,X,X2,target):
if X.shape==X2.shape:
if np.all(X==X2):
target += np.trace(partial)
target += np.trace(dL_dK)
def dKdiag_dtheta(self,partial,X,target):
target += np.sum(partial)
def dKdiag_dtheta(self,dL_dKdiag,X,target):
target += np.sum(dL_dKdiag)
def dK_dX(self,partial,X,X2,target):
def dK_dX(self,dL_dK,X,X2,target):
pass
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self,dL_dKdiag,X,target):
pass
def psi0(self,Z,mu,S,target):
target += self.variance
def dpsi0_dtheta(self,partial,Z,mu,S,target):
target += partial.sum()
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
target += dL_dpsi0.sum()
def dpsi0_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S):
pass
def psi1(self,Z,mu,S,target):
pass
def dpsi1_dtheta(self,partial,Z,mu,S,target):
def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,target):
pass
def dpsi1_dZ(self,partial,Z,mu,S,target):
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target):
pass
def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S):
pass
def psi2(self,Z,mu,S,target):
pass
def dpsi2_dZ(self,partial,Z,mu,S,target):
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target):
pass
def dpsi2_dtheta(self,partial,Z,mu,S,target):
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target):
pass
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
pass

10
GPy/likelihoods/EP.py
View file

@ -110,7 +110,7 @@ class EP(likelihood):
Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K
B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
L = jitchol(B)
V,info = linalg.flapack.dtrtrs(L,Sroot_tilde_K,lower=1)
V,info = linalg.lapack.flapack.dtrtrs(L,Sroot_tilde_K,lower=1)
Sigma = K - np.dot(V.T,V)
mu = np.dot(Sigma,self.v_tilde)
epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
@ -187,7 +187,7 @@ class EP(likelihood):
#Posterior distribution parameters update
LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau
L = jitchol(LLT)
V,info = linalg.flapack.dtrtrs(L,Kmn,lower=1)
V,info = linalg.lapack.flapack.dtrtrs(L,Kmn,lower=1)
Sigma_diag = np.sum(V*V,-2)
si = np.sum(V.T*V[:,i],-1)
mu = mu + (Delta_v-Delta_tau*mu[i])*si
@ -195,8 +195,8 @@ class EP(likelihood):
#Sigma recomputation with Cholesky decompositon
LLT0 = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T)
L = jitchol(LLT)
V,info = linalg.flapack.dtrtrs(L,Kmn,lower=1)
V2,info = linalg.flapack.dtrtrs(L.T,V,lower=0)
V,info = linalg.lapack.flapack.dtrtrs(L,Kmn,lower=1)
V2,info = linalg.lapack.flapack.dtrtrs(L.T,V,lower=0)
Sigma_diag = np.sum(V*V,-2)
Knmv_tilde = np.dot(Kmn,self.v_tilde)
mu = np.dot(V2.T,Knmv_tilde)
@ -295,7 +295,7 @@ class EP(likelihood):
P = (Diag / Diag0)[:,None] * P0
RPT0 = np.dot(R0,P0.T)
L = jitchol(np.eye(M) + np.dot(RPT0,(1./Diag0 - Diag/(Diag0**2))[:,None]*RPT0.T))
R,info = linalg.flapack.dtrtrs(L,R0,lower=1)
R,info = linalg.lapack.flapack.dtrtrs(L,R0,lower=1)
RPT = np.dot(R,P.T)
Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1)
self.w = Diag * self.v_tilde

4
GPy/likelihoods/Gaussian.py
View file

@ -8,7 +8,7 @@ class Gaussian(likelihood):
self.Z = 0. # a correction factor which accounts for the approximation made
N, self.D = data.shape
#normalisation
#normaliztion
if normalize:
self._mean = data.mean(0)[None,:]
self._std = data.std(0)[None,:]
@ -45,7 +45,7 @@ class Gaussian(likelihood):
def predictive_values(self,mu,var):
"""
Un-normalise the prediction and add the likelihood variance, then return the 5%, 95% interval
Un-normalize the prediction and add the likelihood variance, then return the 5%, 95% interval
"""
mean = mu*self._std + self._mean
true_var = (var + self._variance)*self._std**2

17
GPy/models/GP.py
View file

@ -30,7 +30,6 @@ class GP(model):
.. Note:: Multiple independent outputs are allowed using columns of Y
"""
#FIXME normalize vs normalise
def __init__(self, X, likelihood, kernel, normalize_X=False, Xslices=None):
# parse arguments
@ -41,7 +40,7 @@ class GP(model):
assert isinstance(kernel, kern.kern)
self.kern = kernel
#here's some simple normalisation for the inputs
#here's some simple normalization for the inputs
if normalize_X:
self._Xmean = X.mean(0)[None,:]
self._Xstd = X.std(0)[None,:]
@ -129,12 +128,12 @@ class GP(model):
For the likelihood parameters, pass in alpha = K^-1 y
"""
return np.hstack((self.kern.dK_dtheta(partial=self.dL_dK,X=self.X,slices1=self.Xslices,slices2=self.Xslices), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK,X=self.X,slices1=self.Xslices,slices2=self.Xslices), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
def _raw_predict(self,_Xnew,slices=None, full_cov=False):
"""
Internal helper function for making predictions, does not account
for normalisation or likelihood
for normalization or likelihood
"""
Kx = self.kern.K(self.X,_Xnew, slices1=self.Xslices,slices2=slices)
mu = np.dot(np.dot(Kx.T,self.Ki),self.likelihood.Y)
@ -172,10 +171,10 @@ class GP(model):
- If a list of booleans, specifying which kernel parts are active
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
This is to allow for different normalisations of the output dimensions.
This is to allow for different normalizations of the output dimensions.
"""
#normalise X values
#normalize X values
Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
mu, var = self._raw_predict(Xnew, slices, full_cov)
@ -187,7 +186,7 @@ class GP(model):
def plot_f(self, samples=0, plot_limits=None, which_data='all', which_functions='all', resolution=None, full_cov=False):
"""
Plot the GP's view of the world, where the data is normalised and the likelihood is Gaussian
Plot the GP's view of the world, where the data is normalized and the likelihood is Gaussian
:param samples: the number of a posteriori samples to plot
:param which_data: which if the training data to plot (default all)
@ -203,7 +202,7 @@ class GP(model):
- In higher dimensions, we've no implemented this yet !TODO!
Can plot only part of the data and part of the posterior functions using which_data and which_functions
Plot the data's view of the world, with non-normalised values and GP predictions passed through the likelihood
Plot the data's view of the world, with non-normalized values and GP predictions passed through the likelihood
"""
if which_functions=='all':
which_functions = [True]*self.kern.Nparts
@ -221,7 +220,7 @@ class GP(model):
Ysim = np.random.multivariate_normal(m.flatten(),v,samples)
gpplot(Xnew,m,m-2*np.sqrt(np.diag(v)[:,None]),m+2*np.sqrt(np.diag(v))[:,None])
for i in range(samples):
pb.plot(Xnew,Ysim[i,:],Tango.coloursHex['darkBlue'],linewidth=0.25)
pb.plot(Xnew,Ysim[i,:],Tango.colorsHex['darkBlue'],linewidth=0.25)
pb.plot(self.X[which_data],self.likelihood.Y[which_data],'kx',mew=1.5)
pb.xlim(xmin,xmax)
ymin,ymax = min(np.append(self.likelihood.Y,m-2*np.sqrt(np.diag(v)[:,None]))), max(np.append(self.likelihood.Y,m+2*np.sqrt(np.diag(v)[:,None])))

6
GPy/models/sparse_GP.py
View file

@ -54,7 +54,7 @@ class sparse_GP(GP):
GP.__init__(self, X, likelihood, kernel=kernel, normalize_X=normalize_X, Xslices=Xslices)
#normalise X uncertainty also
#normalize X uncertainty also
if self.has_uncertain_inputs:
self.X_uncertainty /= np.square(self._Xstd)
@ -208,7 +208,7 @@ class sparse_GP(GP):
if self.has_uncertain_inputs:
dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z,self.X,self.X_uncertainty)
dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.dL_dpsi1.T, self.Z,self.X, self.X_uncertainty)
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z,self.X, self.X_uncertainty)
else:
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1,self.Z,self.X)
dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
@ -228,7 +228,7 @@ class sparse_GP(GP):
return dL_dZ
def _raw_predict(self, Xnew, slices, full_cov=False):
"""Internal helper function for making predictions, does not account for normalisation"""
"""Internal helper function for making predictions, does not account for normalization"""
Kx = self.kern.K(self.Z, Xnew)
mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)

2
GPy/models/sparse_GPLVM.py
View file

@ -43,7 +43,7 @@ class sparse_GPLVM(sparse_GP_regression, GPLVM):
def dL_dX(self):
dL_dX = self.kern.dKdiag_dX(self.dL_dpsi0,self.X)
dL_dX += self.kern.dK_dX(self.dL_dpsi1,self.X,self.Z)
dL_dX += self.kern.dK_dX(self.dL_dpsi1.T,self.X,self.Z)
return dL_dX

2
GPy/models/uncollapsed_sparse_GP.py
View file

@ -93,7 +93,7 @@ class uncollapsed_sparse_GP(sparse_GP):
return A+B+C+D+E
def _raw_predict(self, Xnew, slices,full_cov=False):
"""Internal helper function for making predictions, does not account for normalisation"""
"""Internal helper function for making predictions, does not account for normalization"""
Kx = self.kern.K(Xnew,self.Z)
mu = mdot(Kx,self.Kmmi,self.q_u_expectation[0])

0
GPy/testing/__init__.py Normal file
View file

29
GPy/testing/bgplvm_tests.py
View file

@ -12,6 +12,7 @@ class BGPLVMTests(unittest.TestCase):
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
Y -= Y.mean(axis=0)
k = GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(rbf|bias|noise|white|S)')
@ -24,6 +25,7 @@ class BGPLVMTests(unittest.TestCase):
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
Y -= Y.mean(axis=0)
k = GPy.kern.linear(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(linear|bias|noise|white|S)')
@ -36,12 +38,39 @@ class BGPLVMTests(unittest.TestCase):
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
Y -= Y.mean(axis=0)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(rbf|bias|noise|white|S)')
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_bias_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
Y -= Y.mean(axis=0)
k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(rbf|bias|noise|white|S)')
m.randomize()
self.assertTrue(m.checkgrad())
def test_linear_bias_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.linear(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
Y -= Y.mean(axis=0)
k = GPy.kern.linear(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(linear|bias|noise|white|S)')
m.randomize()
self.assertTrue(m.checkgrad())
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."

26
GPy/testing/examples_tests.py Normal file
View file

@ -0,0 +1,26 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import unittest
import numpy as np
import GPy
class ExamplesTests(unittest.TestCase):
def test_check_model_returned(self):
pass
def test_model_checkgrads(self):
pass
def test_all_examples(self):
pass
#Load models
#Loop through models
#for model in models:
#self.assertTrue(m.checkgrad())
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."
unittest.main()

47
GPy/testing/gplvm_tests.py Normal file
View file

@ -0,0 +1,47 @@
# Copyright (c) 2012, Nicolo Fusi
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import unittest
import numpy as np
import GPy
class GPLVMTests(unittest.TestCase):
def test_bias_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.GPLVM(Y, Q, kernel = k)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_linear_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.linear(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.GPLVM(Y, Q, kernel = k)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.GPLVM(Y, Q, kernel = k)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."
unittest.main()

1
GPy/testing/kernel_tests.py
View file

@ -13,7 +13,6 @@ class KernelTests(unittest.TestCase):
X = np.random.rand(5,5)
Y = np.ones((5,1))
m = GPy.models.GP_regression(X,Y,K)
print m
self.assertTrue(m.checkgrad())
def test_coregionalisation(self):

48
GPy/testing/sparse_gplvm_tests.py Normal file
View file

@ -0,0 +1,48 @@
# Copyright (c) 2012, Nicolo Fusi, James Hensman
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import unittest
import numpy as np
import GPy
class sparse_GPLVMTests(unittest.TestCase):
def test_bias_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.sparse_GPLVM(Y, Q, kernel = k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@unittest.skip('linear kernels do not have dKdiag_dX')
def test_linear_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.linear(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.sparse_GPLVM(Y, Q, kernel = k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_kern(self):
N, M, Q, D = 10, 3, 2, 4
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
m = GPy.models.sparse_GPLVM(Y, Q, kernel = k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."
unittest.main()

11
GPy/testing/unit_tests.py
View file

@ -192,17 +192,6 @@ class GradientTests(unittest.TestCase):
m.approximate_likelihood()
self.assertTrue(m.checkgrad())
def test_warped_GP(self):
xmin, xmax = 1, 2.5*np.pi
b, C, SNR = 1, 0, 0.1
X = np.linspace(xmin, xmax, 500)
y = b*X + C + 1*np.sin(X)
y += 0.05*np.random.randn(len(X))
X, y = X[:, None], y[:, None]
m = GPy.models.warpedGP(X, y, warping_terms = 3)
m.constrain_positive('(tanh_a|tanh_b|rbf|white|bias)')
self.assertTrue(m.checkgrad())
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."

132
GPy/util/Tango.py
View file

@ -25,7 +25,7 @@ def fewerXticks(ax=None,divideby=2):
ax.set_xticks(ax.get_xticks()[::divideby])
coloursHex = {\
colorsHex = {\
"Aluminium6":"#2e3436",\
"Aluminium5":"#555753",\
"Aluminium4":"#888a85",\
@ -54,9 +54,9 @@ coloursHex = {\
"mediumButter":"#edd400",\
"darkButter":"#c4a000"}
darkList = [coloursHex['darkBlue'],coloursHex['darkRed'],coloursHex['darkGreen'], coloursHex['darkOrange'], coloursHex['darkButter'], coloursHex['darkPurple'], coloursHex['darkChocolate'], coloursHex['Aluminium6']]
mediumList = [coloursHex['mediumBlue'], coloursHex['mediumRed'],coloursHex['mediumGreen'], coloursHex['mediumOrange'], coloursHex['mediumButter'], coloursHex['mediumPurple'], coloursHex['mediumChocolate'], coloursHex['Aluminium5']]
lightList = [coloursHex['lightBlue'], coloursHex['lightRed'],coloursHex['lightGreen'], coloursHex['lightOrange'], coloursHex['lightButter'], coloursHex['lightPurple'], coloursHex['lightChocolate'], coloursHex['Aluminium4']]
darkList = [colorsHex['darkBlue'],colorsHex['darkRed'],colorsHex['darkGreen'], colorsHex['darkOrange'], colorsHex['darkButter'], colorsHex['darkPurple'], colorsHex['darkChocolate'], colorsHex['Aluminium6']]
mediumList = [colorsHex['mediumBlue'], colorsHex['mediumRed'],colorsHex['mediumGreen'], colorsHex['mediumOrange'], colorsHex['mediumButter'], colorsHex['mediumPurple'], colorsHex['mediumChocolate'], colorsHex['Aluminium5']]
lightList = [colorsHex['lightBlue'], colorsHex['lightRed'],colorsHex['lightGreen'], colorsHex['lightOrange'], colorsHex['lightButter'], colorsHex['lightPurple'], colorsHex['lightChocolate'], colorsHex['Aluminium4']]
def currentDark():
return darkList[-1]
@ -76,85 +76,85 @@ def nextLight():
return lightList[-1]
def reset():
while not darkList[0]==coloursHex['darkBlue']:
while not darkList[0]==colorsHex['darkBlue']:
darkList.append(darkList.pop(0))
while not mediumList[0]==coloursHex['mediumBlue']:
while not mediumList[0]==colorsHex['mediumBlue']:
mediumList.append(mediumList.pop(0))
while not lightList[0]==coloursHex['lightBlue']:
while not lightList[0]==colorsHex['lightBlue']:
lightList.append(lightList.pop(0))
def setLightFigures():
mpl.rcParams['axes.edgecolor']=coloursHex['Aluminium6']
mpl.rcParams['axes.facecolor']=coloursHex['Aluminium2']
mpl.rcParams['axes.labelcolor']=coloursHex['Aluminium6']
mpl.rcParams['figure.edgecolor']=coloursHex['Aluminium6']
mpl.rcParams['figure.facecolor']=coloursHex['Aluminium2']
mpl.rcParams['grid.color']=coloursHex['Aluminium6']
mpl.rcParams['savefig.edgecolor']=coloursHex['Aluminium2']
mpl.rcParams['savefig.facecolor']=coloursHex['Aluminium2']
mpl.rcParams['text.color']=coloursHex['Aluminium6']
mpl.rcParams['xtick.color']=coloursHex['Aluminium6']
mpl.rcParams['ytick.color']=coloursHex['Aluminium6']
mpl.rcParams['axes.edgecolor']=colorsHex['Aluminium6']
mpl.rcParams['axes.facecolor']=colorsHex['Aluminium2']
mpl.rcParams['axes.labelcolor']=colorsHex['Aluminium6']
mpl.rcParams['figure.edgecolor']=colorsHex['Aluminium6']
mpl.rcParams['figure.facecolor']=colorsHex['Aluminium2']
mpl.rcParams['grid.color']=colorsHex['Aluminium6']
mpl.rcParams['savefig.edgecolor']=colorsHex['Aluminium2']
mpl.rcParams['savefig.facecolor']=colorsHex['Aluminium2']
mpl.rcParams['text.color']=colorsHex['Aluminium6']
mpl.rcParams['xtick.color']=colorsHex['Aluminium6']
mpl.rcParams['ytick.color']=colorsHex['Aluminium6']
def setDarkFigures():
mpl.rcParams['axes.edgecolor']=coloursHex['Aluminium2']
mpl.rcParams['axes.facecolor']=coloursHex['Aluminium6']
mpl.rcParams['axes.labelcolor']=coloursHex['Aluminium2']
mpl.rcParams['figure.edgecolor']=coloursHex['Aluminium2']
mpl.rcParams['figure.facecolor']=coloursHex['Aluminium6']
mpl.rcParams['grid.color']=coloursHex['Aluminium2']
mpl.rcParams['savefig.edgecolor']=coloursHex['Aluminium6']
mpl.rcParams['savefig.facecolor']=coloursHex['Aluminium6']
mpl.rcParams['text.color']=coloursHex['Aluminium2']
mpl.rcParams['xtick.color']=coloursHex['Aluminium2']
mpl.rcParams['ytick.color']=coloursHex['Aluminium2']
mpl.rcParams['axes.edgecolor']=colorsHex['Aluminium2']
mpl.rcParams['axes.facecolor']=colorsHex['Aluminium6']
mpl.rcParams['axes.labelcolor']=colorsHex['Aluminium2']
mpl.rcParams['figure.edgecolor']=colorsHex['Aluminium2']
mpl.rcParams['figure.facecolor']=colorsHex['Aluminium6']
mpl.rcParams['grid.color']=colorsHex['Aluminium2']
mpl.rcParams['savefig.edgecolor']=colorsHex['Aluminium6']
mpl.rcParams['savefig.facecolor']=colorsHex['Aluminium6']
mpl.rcParams['text.color']=colorsHex['Aluminium2']
mpl.rcParams['xtick.color']=colorsHex['Aluminium2']
mpl.rcParams['ytick.color']=colorsHex['Aluminium2']
def hex2rgb(hexcolor):
hexcolor = [hexcolor[1+2*i:1+2*(i+1)] for i in range(3)]
r,g,b = [int(n,16) for n in hexcolor]
return (r,g,b)
coloursRGB = dict([(k,hex2rgb(i)) for k,i in coloursHex.items()])
colorsRGB = dict([(k,hex2rgb(i)) for k,i in colorsHex.items()])
cdict_RB = {'red' :((0.,coloursRGB['mediumRed'][0]/256.,coloursRGB['mediumRed'][0]/256.),
(.5,coloursRGB['mediumPurple'][0]/256.,coloursRGB['mediumPurple'][0]/256.),
(1.,coloursRGB['mediumBlue'][0]/256.,coloursRGB['mediumBlue'][0]/256.)),
'green':((0.,coloursRGB['mediumRed'][1]/256.,coloursRGB['mediumRed'][1]/256.),
(.5,coloursRGB['mediumPurple'][1]/256.,coloursRGB['mediumPurple'][1]/256.),
(1.,coloursRGB['mediumBlue'][1]/256.,coloursRGB['mediumBlue'][1]/256.)),
'blue':((0.,coloursRGB['mediumRed'][2]/256.,coloursRGB['mediumRed'][2]/256.),
(.5,coloursRGB['mediumPurple'][2]/256.,coloursRGB['mediumPurple'][2]/256.),
(1.,coloursRGB['mediumBlue'][2]/256.,coloursRGB['mediumBlue'][2]/256.))}
cdict_RB = {'red' :((0.,colorsRGB['mediumRed'][0]/256.,colorsRGB['mediumRed'][0]/256.),
(.5,colorsRGB['mediumPurple'][0]/256.,colorsRGB['mediumPurple'][0]/256.),
(1.,colorsRGB['mediumBlue'][0]/256.,colorsRGB['mediumBlue'][0]/256.)),
'green':((0.,colorsRGB['mediumRed'][1]/256.,colorsRGB['mediumRed'][1]/256.),
(.5,colorsRGB['mediumPurple'][1]/256.,colorsRGB['mediumPurple'][1]/256.),
(1.,colorsRGB['mediumBlue'][1]/256.,colorsRGB['mediumBlue'][1]/256.)),
'blue':((0.,colorsRGB['mediumRed'][2]/256.,colorsRGB['mediumRed'][2]/256.),
(.5,colorsRGB['mediumPurple'][2]/256.,colorsRGB['mediumPurple'][2]/256.),
(1.,colorsRGB['mediumBlue'][2]/256.,colorsRGB['mediumBlue'][2]/256.))}
cdict_BGR = {'red' :((0.,coloursRGB['mediumBlue'][0]/256.,coloursRGB['mediumBlue'][0]/256.),
(.5,coloursRGB['mediumGreen'][0]/256.,coloursRGB['mediumGreen'][0]/256.),
(1.,coloursRGB['mediumRed'][0]/256.,coloursRGB['mediumRed'][0]/256.)),
'green':((0.,coloursRGB['mediumBlue'][1]/256.,coloursRGB['mediumBlue'][1]/256.),
(.5,coloursRGB['mediumGreen'][1]/256.,coloursRGB['mediumGreen'][1]/256.),
(1.,coloursRGB['mediumRed'][1]/256.,coloursRGB['mediumRed'][1]/256.)),
'blue':((0.,coloursRGB['mediumBlue'][2]/256.,coloursRGB['mediumBlue'][2]/256.),
(.5,coloursRGB['mediumGreen'][2]/256.,coloursRGB['mediumGreen'][2]/256.),
(1.,coloursRGB['mediumRed'][2]/256.,coloursRGB['mediumRed'][2]/256.))}
cdict_BGR = {'red' :((0.,colorsRGB['mediumBlue'][0]/256.,colorsRGB['mediumBlue'][0]/256.),
(.5,colorsRGB['mediumGreen'][0]/256.,colorsRGB['mediumGreen'][0]/256.),
(1.,colorsRGB['mediumRed'][0]/256.,colorsRGB['mediumRed'][0]/256.)),
'green':((0.,colorsRGB['mediumBlue'][1]/256.,colorsRGB['mediumBlue'][1]/256.),
(.5,colorsRGB['mediumGreen'][1]/256.,colorsRGB['mediumGreen'][1]/256.),
(1.,colorsRGB['mediumRed'][1]/256.,colorsRGB['mediumRed'][1]/256.)),
'blue':((0.,colorsRGB['mediumBlue'][2]/256.,colorsRGB['mediumBlue'][2]/256.),
(.5,colorsRGB['mediumGreen'][2]/256.,colorsRGB['mediumGreen'][2]/256.),
(1.,colorsRGB['mediumRed'][2]/256.,colorsRGB['mediumRed'][2]/256.))}
cdict_Alu = {'red' :((0./5,coloursRGB['Aluminium1'][0]/256.,coloursRGB['Aluminium1'][0]/256.),
(1./5,coloursRGB['Aluminium2'][0]/256.,coloursRGB['Aluminium2'][0]/256.),
(2./5,coloursRGB['Aluminium3'][0]/256.,coloursRGB['Aluminium3'][0]/256.),
(3./5,coloursRGB['Aluminium4'][0]/256.,coloursRGB['Aluminium4'][0]/256.),
(4./5,coloursRGB['Aluminium5'][0]/256.,coloursRGB['Aluminium5'][0]/256.),
(5./5,coloursRGB['Aluminium6'][0]/256.,coloursRGB['Aluminium6'][0]/256.)),
'green' :((0./5,coloursRGB['Aluminium1'][1]/256.,coloursRGB['Aluminium1'][1]/256.),
(1./5,coloursRGB['Aluminium2'][1]/256.,coloursRGB['Aluminium2'][1]/256.),
(2./5,coloursRGB['Aluminium3'][1]/256.,coloursRGB['Aluminium3'][1]/256.),
(3./5,coloursRGB['Aluminium4'][1]/256.,coloursRGB['Aluminium4'][1]/256.),
(4./5,coloursRGB['Aluminium5'][1]/256.,coloursRGB['Aluminium5'][1]/256.),
(5./5,coloursRGB['Aluminium6'][1]/256.,coloursRGB['Aluminium6'][1]/256.)),
'blue' :((0./5,coloursRGB['Aluminium1'][2]/256.,coloursRGB['Aluminium1'][2]/256.),
(1./5,coloursRGB['Aluminium2'][2]/256.,coloursRGB['Aluminium2'][2]/256.),
(2./5,coloursRGB['Aluminium3'][2]/256.,coloursRGB['Aluminium3'][2]/256.),
(3./5,coloursRGB['Aluminium4'][2]/256.,coloursRGB['Aluminium4'][2]/256.),
(4./5,coloursRGB['Aluminium5'][2]/256.,coloursRGB['Aluminium5'][2]/256.),
(5./5,coloursRGB['Aluminium6'][2]/256.,coloursRGB['Aluminium6'][2]/256.))}
cdict_Alu = {'red' :((0./5,colorsRGB['Aluminium1'][0]/256.,colorsRGB['Aluminium1'][0]/256.),
(1./5,colorsRGB['Aluminium2'][0]/256.,colorsRGB['Aluminium2'][0]/256.),
(2./5,colorsRGB['Aluminium3'][0]/256.,colorsRGB['Aluminium3'][0]/256.),
(3./5,colorsRGB['Aluminium4'][0]/256.,colorsRGB['Aluminium4'][0]/256.),
(4./5,colorsRGB['Aluminium5'][0]/256.,colorsRGB['Aluminium5'][0]/256.),
(5./5,colorsRGB['Aluminium6'][0]/256.,colorsRGB['Aluminium6'][0]/256.)),
'green' :((0./5,colorsRGB['Aluminium1'][1]/256.,colorsRGB['Aluminium1'][1]/256.),
(1./5,colorsRGB['Aluminium2'][1]/256.,colorsRGB['Aluminium2'][1]/256.),
(2./5,colorsRGB['Aluminium3'][1]/256.,colorsRGB['Aluminium3'][1]/256.),
(3./5,colorsRGB['Aluminium4'][1]/256.,colorsRGB['Aluminium4'][1]/256.),
(4./5,colorsRGB['Aluminium5'][1]/256.,colorsRGB['Aluminium5'][1]/256.),
(5./5,colorsRGB['Aluminium6'][1]/256.,colorsRGB['Aluminium6'][1]/256.)),
'blue' :((0./5,colorsRGB['Aluminium1'][2]/256.,colorsRGB['Aluminium1'][2]/256.),
(1./5,colorsRGB['Aluminium2'][2]/256.,colorsRGB['Aluminium2'][2]/256.),
(2./5,colorsRGB['Aluminium3'][2]/256.,colorsRGB['Aluminium3'][2]/256.),
(3./5,colorsRGB['Aluminium4'][2]/256.,colorsRGB['Aluminium4'][2]/256.),
(4./5,colorsRGB['Aluminium5'][2]/256.,colorsRGB['Aluminium5'][2]/256.),
(5./5,colorsRGB['Aluminium6'][2]/256.,colorsRGB['Aluminium6'][2]/256.))}
# cmap_Alu = mpl.colors.LinearSegmentedColormap('TangoAluminium',cdict_Alu,256)
# cmap_BGR = mpl.colors.LinearSegmentedColormap('TangoRedBlue',cdict_BGR,256)
# cmap_RB = mpl.colors.LinearSegmentedColormap('TangoRedBlue',cdict_RB,256)

2
GPy/util/datasets.py
View file

@ -46,7 +46,7 @@ def oil_100(seed=default_seed):
return {'X': X, 'Y': Y, 'info': "Subsample of the oil data extracting 100 values randomly without replacement."}
def pumadyn(seed=default_seed):
# Data is variance 1, no need to normalise.
# Data is variance 1, no need to normalize.
data = np.loadtxt(os.path.join(data_path, 'pumadyn-32nm/Dataset.data.gz'))
indices = np.random.permutation(data.shape[0])
indicesTrain = indices[0:7168]

6
GPy/util/linalg.py
View file

@ -11,7 +11,7 @@ import re
import pdb
import cPickle
import types
import scipy.lib.lapack.flapack
#import scipy.lib.lapack.flapack
import scipy as sp
def mdot(*args):
@ -101,7 +101,7 @@ def chol_inv(L):
"""
return linalg.flapack.dtrtri(L, lower = True)[0]
return linalg.lapack.flapack.dtrtri(L, lower = True)[0]
def multiple_pdinv(A):
@ -118,7 +118,7 @@ def multiple_pdinv(A):
N = A.shape[-1]
chols = [jitchol(A[:,:,i]) for i in range(N)]
halflogdets = [np.sum(np.log(np.diag(L[0]))) for L in chols]
invs = [linalg.flapack.dpotri(L[0],True)[0] for L in chols]
invs = [linalg.lapack.flapack.dpotri(L[0],True)[0] for L in chols]
invs = [np.triu(I)+np.triu(I,1).T for I in invs]
return np.dstack(invs),np.array(halflogdets)

2
GPy/util/plot.py
View file

@ -6,7 +6,7 @@ import Tango
import pylab as pb
import numpy as np
def gpplot(x,mu,lower,upper,edgecol=Tango.coloursHex['darkBlue'],fillcol=Tango.coloursHex['lightBlue'],axes=None,**kwargs):
def gpplot(x,mu,lower,upper,edgecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue'],axes=None,**kwargs):
if axes is None:
axes = pb.gca()
mu = mu.flatten()

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16
doc/GPy.examples.rst
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@ -73,6 +73,22 @@ examples Package
:undoc-members:
:show-inheritance:
:mod:`tuto_GP_regression` Module
--------------------------------
.. automodule:: GPy.examples.tuto_GP_regression
:members:
:undoc-members:
:show-inheritance:
:mod:`tuto_kernel_overview` Module
----------------------------------
.. automodule:: GPy.examples.tuto_kernel_overview
:members:
:undoc-members:
:show-inheritance:
:mod:`uncertain_input_GP_regression_demo` Module
------------------------------------------------

28
doc/GPy.kern.rst
View file

@ -49,6 +49,14 @@ kern Package
:undoc-members:
:show-inheritance:
:mod:`coregionalise` Module
---------------------------
.. automodule:: GPy.kern.coregionalise
:members:
:undoc-members:
:show-inheritance:
:mod:`exponential` Module
-------------------------
@ -113,18 +121,18 @@ kern Package
:undoc-members:
:show-inheritance:
:mod:`product` Module
---------------------
:mod:`prod` Module
------------------
.. automodule:: GPy.kern.product
.. automodule:: GPy.kern.prod
:members:
:undoc-members:
:show-inheritance:
:mod:`product_orthogonal` Module
--------------------------------
:mod:`prod_orthogonal` Module
-----------------------------
.. automodule:: GPy.kern.product_orthogonal
.. automodule:: GPy.kern.prod_orthogonal
:members:
:undoc-members:
:show-inheritance:
@ -145,6 +153,14 @@ kern Package
:undoc-members:
:show-inheritance:
:mod:`symmetric` Module
-----------------------
.. automodule:: GPy.kern.symmetric
:members:
:undoc-members:
:show-inheritance:
:mod:`sympykern` Module
-----------------------

46
doc/kernel_implementation.rst
View file

@ -3,15 +3,45 @@
List of implemented kernels
***************************
The :math:`\checkmark` symbol represents the functions that have been implemented for each kernel.
The following table shows the implemented kernels in GPy and gives the details of the implemented function for each kernel.
.. |tick|
==================== =========== ====== ======= =========== =============== ======= =========== ====== ====== =======
NAME get/set K Kdiag dK_dtheta dKdiag_dtheta dK_dX dKdiag_dX psi0 psi1 psi2
==================== =========== ====== ======= =========== =============== ======= =========== ====== ====== =======
bias |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
Brownian |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
exponential |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
finite_dimensional |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
linear |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
Matern32 |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
Matern52 |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
periodic_exponential |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
periodic_Matern32 |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
periodic_Matern52 |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
rbf |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
spline |tick| |tick| |tick| |tick| |tick| |tick|
-------------------- ----------- ------ ------- ----------- --------------- ------- ----------- ------ ------ -------
white |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick| |tick|
==================== =========== ====== ======= =========== =============== ======= =========== ====== ====== =======
.. |tick| image:: tick.png
Depending on the use, all functions may not be required
* ``get/set, K, Kdiag``: compulsory
* ``dK_dtheta``: necessary to optimize the model
* ``dKdiag_dtheta``: sparse models, BGPLVM, GPs with uncertain inputs
* ``dK_dX``: sparse models, GPLVM, BGPLVM, GPs with uncertain inputs
* ``dKdiag_dX``: sparse models, BGPLVM, GPs with uncertain inputs
* ``psi0, psi1, psi2``: BGPLVM, GPs with uncertain inputs
====== =========== === ======= =========== =============== ======= =========== ====== ====== =======
NAME get/set K Kdiag dK_dtheta dKdiag_dtheta dK_dX dKdiag_dX psi0 psi1 psi2
====== =========== === ======= =========== =============== ======= =========== ====== ====== =======
rbf \\checkmark y
====== =========== === ======= =========== =============== ======= =========== ====== ====== =======
.. |tick| image:: Figures/tick.png

2
doc/tuto_GP_regression.rst
View file

@ -2,7 +2,7 @@
Gaussian process regression tutorial
*************************************
We will see in this tutorial the basics for building a 1 dimensional and a 2 dimensional Gaussian process regression model, also known as a kriging model. The code shown in this tutorial can be found without the comments at GPy/examples/tuto_GP_regression.py.
We will see in this tutorial the basics for building a 1 dimensional and a 2 dimensional Gaussian process regression model, also known as a kriging model. The code shown in this tutorial can be obtained at GPy/examples/tutorials.py, or by running ``GPy.examples.tutorials.tuto_GP_regression()``.
We first import the libraries we will need: ::

60
doc/tuto_interacting_with_models.rst Normal file
View file

@ -0,0 +1,60 @@
*************************************
Interacting with models
*************************************
The GPy model class has a set of features which are designed to make it simple to explore the parameter space of the model. By default, the scipy optimisers are used to fit GPy models (via model.optimize()), for which we provide mechanisms for 'free' optimisation: GPy can ensure that naturally positive parameters (such as variances) remain positive. But these mechanisms are much more powerful than simple reparameterisation, as we shall see.
All of the examples included in GPy return an instance of a model class. We'll use GPy.examples.?? as an example::
import pylab as pb
pb.ion()
import GPy
m = GPy.examples.??
Examining the model using print
===============================
To see the current state of the model parameters, and the model's (marginal) likelihood just print the model::
print m
?? output
Getting the model's likelihood and gradients
===========================================
foobar
Setting and fetching parameters by name
=======================================
foobar
Constraining and optimising the model
=====================================
A simple task in GPy is to ensure that the models' variances remain positive during optimisation. the models class has a function called constrain_positive(), which accepts a regex string as above. To constrain the models' variance to be positive::
m.constrain_positive('variance')
print m
Now we see that the variance of the model is constrained to be postive. GPy handles the effective change of gradients: see how m.objective_gradients has changed approriately
For convenience, we also provide a catch all function which ensures that anything which appears to require positivity is constrianed appropriately::
m.ensure_default_constraints()
Fixing parameters
=================
Tying Parameters
================
Bounding parameters
===================
Further Reading
===============
All of the mechansiams for dealing with parameters are baked right into GPy.core.model, from which all of the classes in GPy.models inherrit. To learn how to construct your own model, you might want to read ??link?? creating_new_models.
By deafult, GPy uses the tnc optimizer (from scipy.optimize.tnc). To use other optimisers, and to control the setting of those optimisers, as well as other funky features like automated restarts and diagnostics, you can read the optimization tutorial ??link??.

4
doc/tuto_kernel_overview.rst
View file

@ -2,7 +2,7 @@
****************************
tutorial : A kernel overview
****************************
The aim of this tutorial is to give a better understanding of the kernel objects in GPy and to list the ones that are already implemented. The code shown in this tutorial can be found without the comments at GPy/examples/tuto_kernel_overview.py.
The aim of this tutorial is to give a better understanding of the kernel objects in GPy and to list the ones that are already implemented. The code shown in this tutorial can be obtained at GPy/examples/tutorials.py or by running ``GPy.examples.tutorials.tuto_kernel_overview()``.
First we import the libraries we will need ::
@ -39,7 +39,7 @@ return::
Implemented kernels
===================
Many kernels are already implemented in GPy. A comprehensive list can be found `here <kernel_implementation.html>`_ . The following figure gives a summary of most of them:
Many kernels are already implemented in GPy. A comprehensive list can be found `here <kernel_implementation.html>`_ and the following figure gives a summary of most of them:
.. figure:: Figures/tuto_kern_overview_allkern.png
:align: center

8
setup.py
View file

@ -3,8 +3,6 @@
import os
from setuptools import setup
#from numpy.distutils.core import Extension, setup
#from sphinx.setup_command import BuildDoc
# Version number
version = '0.1.3'
@ -14,12 +12,12 @@ def read(fname):
setup(name = 'GPy',
version = version,
author = 'James Hensman, Nicolo Fusi, Ricardo Andrade, Nicolas Durrande, Alan Saul, Neil D. Lawrence',
author = read('AUTHORS.txt'),
author_email = "james.hensman@gmail.com",
description = ("The Gaussian Process Toolbox"),
license = "BSD 3-clause",
keywords = "machine-learning gaussian-processes kernels",
url = "http://ml.sheffield.ac.uk/GPy/",
url = "http://sheffieldml.github.com/GPy/",
packages = ['GPy', 'GPy.core', 'GPy.kern', 'GPy.util', 'GPy.models', 'GPy.inference', 'GPy.examples', 'GPy.likelihoods'],
package_dir={'GPy': 'GPy'},
package_data = {'GPy': ['GPy/examples']},
@ -34,7 +32,5 @@ setup(name = 'GPy',
#setup_requires=['sphinx'],
#cmdclass = {'build_sphinx': BuildDoc},
classifiers=[
"Development Status :: 1 - Alpha",
"Topic :: Machine Learning",
"License :: OSI Approved :: BSD License"],
)