restructure rbf kernel

This commit is contained in:
Zhenwen Dai 2014-05-21 16:42:35 +01:00
parent 04ab93a961
commit b945c20004
5 changed files with 372 additions and 620 deletions

View file

@ -2,6 +2,10 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt) # Licensed under the BSD 3-clause license (see LICENSE.txt)
from ....core.parameterization.parameter_core import Pickleable from ....core.parameterization.parameter_core import Pickleable
from GPy.util.caching import Cache_this
from ....core.parameterization import variational
import rbf_psi_comp
import ssrbf_psi_comp
class PSICOMP(Pickleable): class PSICOMP(Pickleable):
@ -17,3 +21,22 @@ class PSICOMP(Pickleable):
""" """
pass pass
class PSICOMP_RBF(Pickleable):
@Cache_this(limit=1, ignore_args=(0,))
def psicomputations(self, variance, lengthscale, Z, variational_posterior):
if isinstance(variational_posterior, variational.NormalPosterior):
return rbf_psi_comp.psicomputations(variance, lengthscale, Z, variational_posterior)
elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
return ssrbf_psi_comp.psicomputations(variance, lengthscale, Z, variational_posterior)
else:
raise ValueError, "unknown distriubtion received for psi-statistics"
@Cache_this(limit=1, ignore_args=(0,1,2,3))
def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
if isinstance(variational_posterior, variational.NormalPosterior):
return rbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior)
elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
return ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior)
else:
raise ValueError, "unknown distriubtion received for psi-statistics"

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@ -3,16 +3,9 @@ The module for psi-statistics for RBF kernel
""" """
import numpy as np import numpy as np
from . import PSICOMP from GPy.util.caching import Cacher
from GPy.util.caching import Cache_this
from ....util.misc import param_to_array
from scipy import weave
from ....util.config import *
class PSICOMP_RBF(PSICOMP): def psicomputations(variance, lengthscale, Z, variational_posterior):
@Cache_this(limit=1, ignore_args=(0,))
def psicomputations(self, variance, lengthscale, Z, variational_posterior):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -27,12 +20,11 @@ class PSICOMP_RBF(PSICOMP):
psi0 = np.empty(mu.shape[0]) psi0 = np.empty(mu.shape[0])
psi0[:] = variance psi0[:] = variance
psi1 = self._psi1computations(variance, lengthscale, Z, mu, S) psi1 = _psi1computations(variance, lengthscale, Z, mu, S)
psi2 = self._psi2computations(variance, lengthscale, Z, mu, S).sum(axis=0) psi2 = _psi2computations(variance, lengthscale, Z, mu, S).sum(axis=0)
return psi0, psi1, psi2 return psi0, psi1, psi2
@Cache_this(limit=1, ignore_args=(0,)) def __psi1computations(variance, lengthscale, Z, mu, S):
def _psi1computations(self, variance, lengthscale, Z, mu, S):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -52,8 +44,7 @@ class PSICOMP_RBF(PSICOMP):
return _psi1 return _psi1
@Cache_this(limit=1, ignore_args=(0,)) def __psi2computations(variance, lengthscale, Z, mu, S):
def _psi2computations(self, variance, lengthscale, Z, mu, S):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -76,12 +67,11 @@ class PSICOMP_RBF(PSICOMP):
return _psi2 return _psi2
@Cache_this(limit=1, ignore_args=(0,1,2,3)) def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
ARD = (len(lengthscale)!=1) ARD = (len(lengthscale)!=1)
dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1 = self._psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance) dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance)
dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2 = self._psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance) dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance)
dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2 dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
@ -95,7 +85,7 @@ class PSICOMP_RBF(PSICOMP):
return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS
def _psi1compDer(self, dL_dpsi1, variance, lengthscale, Z, mu, S): def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S):
""" """
dL_dpsi1 - NxM dL_dpsi1 - NxM
Z - MxQ Z - MxQ
@ -114,7 +104,7 @@ class PSICOMP_RBF(PSICOMP):
lengthscale2 = np.square(lengthscale) lengthscale2 = np.square(lengthscale)
_psi1 = self._psi1computations(variance, lengthscale, Z, mu, S) _psi1 = _psi1computations(variance, lengthscale, Z, mu, S)
Lpsi1 = dL_dpsi1*_psi1 Lpsi1 = dL_dpsi1*_psi1
Zmu = Z[None,:,:]-mu[:,None,:] # NxMxQ Zmu = Z[None,:,:]-mu[:,None,:] # NxMxQ
denom = 1./(S+lengthscale2) denom = 1./(S+lengthscale2)
@ -127,7 +117,7 @@ class PSICOMP_RBF(PSICOMP):
return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS
def _psi2compDer(self, dL_dpsi2, variance, lengthscale, Z, mu, S): def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -148,7 +138,7 @@ class PSICOMP_RBF(PSICOMP):
denom = 1./(2*S+lengthscale2) denom = 1./(2*S+lengthscale2)
denom2 = np.square(denom) denom2 = np.square(denom)
_psi2 = self._psi2computations(variance, lengthscale, Z, mu, S) # NxMxM _psi2 = _psi2computations(variance, lengthscale, Z, mu, S) # NxMxM
Lpsi2 = dL_dpsi2[None,:,:]*_psi2 Lpsi2 = dL_dpsi2[None,:,:]*_psi2
Lpsi2sum = np.einsum('nmo->n',Lpsi2) #N Lpsi2sum = np.einsum('nmo->n',Lpsi2) #N
@ -168,3 +158,5 @@ class PSICOMP_RBF(PSICOMP):
return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS
_psi1computations = Cacher(__psi1computations, limit=1)
_psi2computations = Cacher(__psi2computations, limit=1)

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@ -6,13 +6,8 @@ The package for the psi statistics computation
""" """
import numpy as np import numpy as np
from . import PSICOMP
from GPy.util.caching import Cache_this
class PSICOMP_SSRBF(PSICOMP): def psicomputations(variance, lengthscale, Z, variational_posterior):
@Cache_this(limit=1, ignore_args=(0,))
def psicomputations(self, variance, lengthscale, Z, variational_posterior):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -28,11 +23,11 @@ class PSICOMP_SSRBF(PSICOMP):
psi0 = np.empty(mu.shape[0]) psi0 = np.empty(mu.shape[0])
psi0[:] = variance psi0[:] = variance
psi1 = self._psi1computations(variance, lengthscale, Z, mu, S, gamma) psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma)
psi2 = self._psi2computations(variance, lengthscale, Z, mu, S, gamma) psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma)
return psi0, psi1, psi2 return psi0, psi1, psi2
def _psi1computations(self, variance, lengthscale, Z, mu, S, gamma): def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -60,7 +55,7 @@ class PSICOMP_SSRBF(PSICOMP):
return _psi1 return _psi1
def _psi2computations(self, variance, lengthscale, Z, mu, S, gamma): def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ
@ -93,12 +88,11 @@ class PSICOMP_SSRBF(PSICOMP):
return _psi2 return _psi2
@Cache_this(limit=1, ignore_args=(0,1,2,3)) def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
ARD = (len(lengthscale)!=1) ARD = (len(lengthscale)!=1)
dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = self._psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob) dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = self._psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob) dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2 dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
@ -113,7 +107,7 @@ class PSICOMP_SSRBF(PSICOMP):
return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma
def _psi1compDer(self, dL_dpsi1, variance, lengthscale, Z, mu, S, gamma): def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma):
""" """
dL_dpsi1 - NxM dL_dpsi1 - NxM
Z - MxQ Z - MxQ
@ -156,7 +150,7 @@ class PSICOMP_SSRBF(PSICOMP):
return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
def _psi2compDer(self, dL_dpsi2, variance, lengthscale, Z, mu, S, gamma): def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma):
""" """
Z - MxQ Z - MxQ
mu - NxQ mu - NxQ

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@ -8,7 +8,7 @@ from ...util.misc import param_to_array
from stationary import Stationary from stationary import Stationary
from GPy.util.caching import Cache_this from GPy.util.caching import Cache_this
from ...core.parameterization import variational from ...core.parameterization import variational
from psi_comp import ssrbf_psi_comp,ssrbf_psi_gpucomp,rbf_psi_comp from psi_comp import PSICOMP_RBF
from ...util.config import * from ...util.config import *
class RBF(Stationary): class RBF(Stationary):
@ -25,13 +25,7 @@ class RBF(Stationary):
super(RBF, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name, useGPU=useGPU) super(RBF, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name, useGPU=useGPU)
self.weave_options = {} self.weave_options = {}
self.group_spike_prob = False self.group_spike_prob = False
self.psicomp = rbf_psi_comp.PSICOMP_RBF() self.psicomp = PSICOMP_RBF()
def set_for_SpikeAndSlab(self):
if self.useGPU:
self.psicomp = ssrbf_psi_gpucomp.PSICOMP_SSRBF()
else:
self.psicomp = ssrbf_psi_comp.PSICOMP_SSRBF()
def K_of_r(self, r): def K_of_r(self, r):
return self.variance * np.exp(-0.5 * r**2) return self.variance * np.exp(-0.5 * r**2)
@ -44,289 +38,39 @@ class RBF(Stationary):
#---------------------------------------# #---------------------------------------#
def psi0(self, Z, variational_posterior): def psi0(self, Z, variational_posterior):
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[0] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[0]
else: else:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[0] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[0]
else:
# return self.Kdiag(variational_posterior.mean)
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[0]
def psi1(self, Z, variational_posterior): def psi1(self, Z, variational_posterior):
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[1] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[1]
else: else:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[1] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[1]
else:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[1]
def psi2(self, Z, variational_posterior): def psi2(self, Z, variational_posterior):
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[2] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[2]
else: else:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[2] return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[2]
else:
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior)[2]
def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
# Spike-and-Slab GPLVM
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
self.psicomp.update_gradients_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) self.psicomp.update_gradients_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
else: else:
dL_dvar, dL_dlengscale, _, _, _, _ = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) dL_dvar, dL_dlengscale = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)[:2]
self.variance.gradient = dL_dvar self.variance.gradient = dL_dvar
self.lengthscale.gradient = dL_dlengscale self.lengthscale.gradient = dL_dlengscale
elif isinstance(variational_posterior, variational.NormalPosterior):
dL_dvar, dL_dlengscale, _, _, _ = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
self.variance.gradient = dL_dvar
self.lengthscale.gradient = dL_dlengscale
# l2 = self.lengthscale**2
# if l2.size != self.input_dim:
# l2 = l2*np.ones(self.input_dim)
# #contributions from psi0:
# self.variance.gradient = np.sum(dL_dpsi0)
# self.lengthscale.gradient = 0.
#
# # #from psi1
# denom, _, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
# d_length = psi1[:,:,None] * ((dist_sq - 1.)/(self.lengthscale*denom) +1./self.lengthscale)
# dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
# print dpsi1_dlength.sum(0).sum(0)
# if self.ARD:
# self.lengthscale.gradient += dpsi1_dlength.sum(0).sum(0)
# else:
# self.lengthscale.gradient += dpsi1_dlength.sum()
# self.variance.gradient += np.sum(dL_dpsi1 * psi1) / self.variance
# #from psi2
# S = variational_posterior.variance
# _, Zdist_sq, _, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
# if not self.ARD:
# self.lengthscale.gradient += self._weave_psi2_lengthscale_grads(dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2).sum()
# else:
# self.lengthscale.gradient += self._weave_psi2_lengthscale_grads(dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2)
# # print self._weave_psi2_lengthscale_grads(dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2)
#
# self.variance.gradient += 2.*np.sum(dL_dpsi2 * psi2)/self.variance
else:
raise ValueError, "unknown distriubtion received for psi-statistics"
def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
# Spike-and-Slab GPLVM
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
return self.psicomp.gradients_Z_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) return self.psicomp.gradients_Z_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
else: else:
_, _, dL_dZ, _, _, _ = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) return self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)[2]
return dL_dZ
elif isinstance(variational_posterior, variational.NormalPosterior):
_, _, dL_dZ, _, _ = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
return dL_dZ
#
# l2 = self.lengthscale **2
#
# #psi1
# denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
# grad = np.einsum('ij,ij,ijk,ijk->jk', dL_dpsi1, psi1, dist, -1./(denom*l2))
#
# #psi2
# Zdist, Zdist_sq, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
# term1 = Zdist / l2 # M, M, Q
# S = variational_posterior.variance
# term2 = mudist / (2.*S[:,None,None,:] + l2) # N, M, M, Q
#
# grad += 2.*np.einsum('ijk,ijk,ijkl->kl', dL_dpsi2, psi2, term1[None,:,:,:] + term2)
#
# return grad
else:
raise ValueError, "unknown distriubtion received for psi-statistics"
def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
# Spike-and-Slab GPLVM
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
if self.useGPU: if self.useGPU:
return self.psicomp.gradients_qX_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) return self.psicomp.gradients_qX_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
else: else:
_, _, _, dL_dmu, dL_dS, dL_dgamma = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior) return self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)[3:]
return dL_dmu, dL_dS, dL_dgamma
elif isinstance(variational_posterior, variational.NormalPosterior):
_, _, _, dL_dmu, dL_dS = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
# l2 = self.lengthscale **2
# #psi1
# denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
# tmp = psi1[:, :, None] / l2 / denom
# grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * dist, 1)
# grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (dist_sq - 1), 1)
# #psi2
# _, _, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
# S = variational_posterior.variance
# tmp = psi2[:, :, :, None] / (2.*S[:,None,None,:] + l2)
# grad_mu += -2.*np.einsum('jk,ijkl,ijkl->il', dL_dpsi2, tmp , mudist)
# grad_S += np.einsum('jk,ijkl,ijkl->il', dL_dpsi2 , tmp , (2.*mudist_sq - 1))
return dL_dmu, dL_dS
else:
raise ValueError, "unknown distriubtion received for psi-statistics"
#return grad_mu, grad_S
#---------------------------------------#
# Precomputations #
#---------------------------------------#
@Cache_this(limit=1)
def _psi1computations(self, Z, vp):
mu, S = vp.mean, vp.variance
l2 = self.lengthscale **2
denom = S[:, None, :] / l2 + 1. # N,1,Q
dist = Z[None, :, :] - mu[:, None, :] # N,M,Q
dist_sq = np.square(dist) / l2 / denom # N,M,Q
exponent = -0.5 * np.sum(dist_sq + np.log(denom), -1)#N,M
psi1 = self.variance * np.exp(exponent) # N,M
return denom, dist, dist_sq, psi1
@Cache_this(limit=1, ignore_args=(0,))
def _Z_distances(self, Z):
Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
return Zhat, Zdist
@Cache_this(limit=1)
def _psi2computations(self, Z, vp):
if config.getboolean('parallel', 'openmp'):
pragma_string = '#pragma omp parallel for private(tmp, exponent_tmp)'
header_string = '#include <omp.h>'
libraries = ['gomp']
else:
pragma_string = ''
header_string = ''
libraries = []
mu, S = vp.mean, vp.variance
N, Q = mu.shape
M = Z.shape[0]
#compute required distances
Zhat, Zdist = self._Z_distances(Z)
Zdist_sq = np.square(Zdist / self.lengthscale) # M,M,Q
#allocate memory for the things we want to compute
mudist = np.empty((N, M, M, Q))
mudist_sq = np.empty((N, M, M, Q))
psi2 = np.empty((N, M, M))
l2 = self.lengthscale **2
denom = (2.*S[:,None,None,:] / l2) + 1. # N,Q
half_log_denom = 0.5 * np.log(denom[:,0,0,:])
denom_l2 = denom[:,0,0,:]*l2
variance_sq = float(np.square(self.variance))
code = """
double tmp, exponent_tmp;
%s
for (int n=0; n<N; n++)
{
for (int m=0; m<M; m++)
{
for (int mm=0; mm<(m+1); mm++)
{
exponent_tmp = 0.0;
for (int q=0; q<Q; q++)
{
//compute mudist
tmp = mu(n,q) - Zhat(m,mm,q);
mudist(n,m,mm,q) = tmp;
mudist(n,mm,m,q) = tmp;
//now mudist_sq
tmp = tmp*tmp/denom_l2(n,q);
mudist_sq(n,m,mm,q) = tmp;
mudist_sq(n,mm,m,q) = tmp;
//now exponent
tmp = -Zdist_sq(m,mm,q) - tmp - half_log_denom(n,q);
exponent_tmp += tmp;
}
//compute psi2 by exponentiating
psi2(n,m,mm) = variance_sq * exp(exponent_tmp);
psi2(n,mm,m) = psi2(n,m,mm);
}
}
}
""" % pragma_string
support_code = """
%s
#include <math.h>
""" % header_string
mu = param_to_array(mu)
weave.inline(code, support_code=support_code, libraries=libraries,
arg_names=['N', 'M', 'Q', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'denom_l2', 'Zdist_sq', 'half_log_denom', 'psi2', 'variance_sq'],
type_converters=weave.converters.blitz, **self.weave_options)
return Zdist, Zdist_sq, mudist, mudist_sq, psi2
def _weave_psi2_lengthscale_grads(self, dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2):
#here's the einsum equivalent, it's ~3 times slower
#return 2.*np.einsum( 'ijk,ijk,ijkl,il->l', dL_dpsi2, psi2, Zdist_sq * (2.*S[:,None,None,:]/l2 + 1.) + mudist_sq + S[:, None, None, :] / l2, 1./(2.*S + l2))*self.lengthscale
result = np.zeros(self.input_dim)
if config.getboolean('parallel', 'openmp'):
pragma_string = '#pragma omp parallel for reduction(+:tmp)'
header_string = '#include <omp.h>'
libraries = ['gomp']
else:
pragma_string = ''
header_string = ''
libraries = []
code = """
double tmp;
for(int q=0; q<Q; q++)
{
tmp = 0.0;
%s
for(int n=0; n<N; n++)
{
for(int m=0; m<M; m++)
{
//diag terms
tmp += dL_dpsi2(n,m,m) * psi2(n,m,m) * (Zdist_sq(m,m,q) * (2.0*S(n,q)/l2(q) + 1.0) + mudist_sq(n,m,m,q) + S(n,q)/l2(q)) / (2.0*S(n,q) + l2(q)) ;
//off-diag terms
for(int mm=0; mm<m; mm++)
{
tmp += 2.0 * dL_dpsi2(n,m,mm) * psi2(n,m,mm) * (Zdist_sq(m,mm,q) * (2.0*S(n,q)/l2(q) + 1.0) + mudist_sq(n,m,mm,q) + S(n,q)/l2(q)) / (2.0*S(n,q) + l2(q)) ;
}
}
}
result(q) = tmp;
}
""" % pragma_string
support_code = """
%s
#include <math.h>
""" % header_string
N,Q = S.shape
M = psi2.shape[-1]
S = param_to_array(S)
weave.inline(code, support_code=support_code, libraries=libraries,
arg_names=['psi2', 'dL_dpsi2', 'N', 'M', 'Q', 'mudist_sq', 'l2', 'Zdist_sq', 'S', 'result'],
type_converters=weave.converters.blitz, **self.weave_options)
return 2.*result*self.lengthscale

View file

@ -64,7 +64,6 @@ class SSGPLVM(SparseGP):
if kernel is None: if kernel is None:
kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=True) # + kern.white(input_dim) kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=True) # + kern.white(input_dim)
kernel.set_for_SpikeAndSlab()
if inference_method is None: if inference_method is None:
inference_method = VarDTC_minibatch(mpi_comm=mpi_comm) inference_method = VarDTC_minibatch(mpi_comm=mpi_comm)