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GPy/GPy/kern/src/add.py
Alexander Grigorievskiy 82cb626cd6 ENH: Added SDE for all basic kernels except Rationale Quadratic. 
Some necessary modifications for the previous code are performed.
2016-03-15 17:33:56 +02:00

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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import itertools
from paramz.caching import Cache_this
from .kern import CombinationKernel, Kern
from functools import reduce
class Add(CombinationKernel):
"""
Add given list of kernels together.
propagates gradients through.
This kernel will take over the active dims of it's subkernels passed in.
"""
def __init__(self, subkerns, name='sum'):
for i, kern in enumerate(subkerns[:]):
if isinstance(kern, Add):
del subkerns[i]
for part in kern.parts[::-1]:
#kern.unlink_parameter(part)
subkerns.insert(i, part.copy())
super(Add, self).__init__(subkerns, name)
self._exact_psicomp = self._check_exact_psicomp()
def _check_exact_psicomp(self):
from .. import RBF,Linear,Bias,White
n_kerns = len(self.parts)
n_rbf = len([k for k in self.parts if isinstance(k,RBF)])
n_linear = len([k for k in self.parts if isinstance(k,Linear)])
n_bias = len([k for k in self.parts if isinstance(k,Bias)])
n_white = len([k for k in self.parts if isinstance(k,White)])
n_others = n_kerns - n_rbf - n_linear - n_bias - n_white
if n_rbf+n_linear<=1 and n_bias<=1 and n_white<=1 and n_others==0:
return True
else:
return False
@Cache_this(limit=3, force_kwargs=['which_parts'])
def K(self, X, X2=None, which_parts=None):
"""
Add all kernels together.
If a list of parts (of this kernel!) `which_parts` is given, only
the parts of the list are taken to compute the covariance.
"""
if which_parts is None:
which_parts = self.parts
elif not isinstance(which_parts, (list, tuple)):
# if only one part is given
which_parts = [which_parts]
return reduce(np.add, (p.K(X, X2) for p in which_parts))
@Cache_this(limit=3, force_kwargs=['which_parts'])
def Kdiag(self, X, which_parts=None):
if which_parts is None:
which_parts = self.parts
elif not isinstance(which_parts, (list, tuple)):
# if only one part is given
which_parts = [which_parts]
return reduce(np.add, (p.Kdiag(X) for p in which_parts))
def update_gradients_full(self, dL_dK, X, X2=None):
[p.update_gradients_full(dL_dK, X, X2) for p in self.parts if not p.is_fixed]
def update_gradients_diag(self, dL_dK, X):
[p.update_gradients_diag(dL_dK, X) for p in self.parts]
def gradients_X(self, dL_dK, X, X2=None):
"""Compute the gradient of the objective function with respect to X.
:param dL_dK: An array of gradients of the objective function with respect to the covariance function.
:type dL_dK: np.ndarray (num_samples x num_inducing)
:param X: Observed data inputs
:type X: np.ndarray (num_samples x input_dim)
:param X2: Observed data inputs (optional, defaults to X)
:type X2: np.ndarray (num_inducing x input_dim)"""
target = np.zeros(X.shape)
[target.__iadd__(p.gradients_X(dL_dK, X, X2)) for p in self.parts]
return target
def gradients_X_diag(self, dL_dKdiag, X):
target = np.zeros(X.shape)
[target.__iadd__(p.gradients_X_diag(dL_dKdiag, X)) for p in self.parts]
return target
def gradients_XX(self, dL_dK, X, X2):
if X2 is None:
target = np.zeros((X.shape[0], X.shape[0], X.shape[1]))
else:
target = np.zeros((X.shape[0], X2.shape[0], X.shape[1]))
[target.__iadd__(p.gradients_XX(dL_dK, X, X2)) for p in self.parts]
return target
def gradients_XX_diag(self, dL_dKdiag, X):
target = np.zeros(X.shape)
[target.__iadd__(p.gradients_XX_diag(dL_dKdiag, X)) for p in self.parts]
return target
@Cache_this(limit=3, force_kwargs=['which_parts'])
def psi0(self, Z, variational_posterior):
if not self._exact_psicomp: return Kern.psi0(self,Z,variational_posterior)
return reduce(np.add, (p.psi0(Z, variational_posterior) for p in self.parts))
@Cache_this(limit=3, force_kwargs=['which_parts'])
def psi1(self, Z, variational_posterior):
if not self._exact_psicomp: return Kern.psi1(self,Z,variational_posterior)
return reduce(np.add, (p.psi1(Z, variational_posterior) for p in self.parts))
@Cache_this(limit=3, force_kwargs=['which_parts'])
def psi2(self, Z, variational_posterior):
if not self._exact_psicomp: return Kern.psi2(self,Z,variational_posterior)
psi2 = reduce(np.add, (p.psi2(Z, variational_posterior) for p in self.parts))
#return psi2
# compute the "cross" terms
from .static import White, Bias
from .rbf import RBF
#from rbf_inv import RBFInv
from .linear import Linear
#ffrom fixed import Fixed
for p1, p2 in itertools.combinations(self.parts, 2):
# i1, i2 = p1._all_dims_active, p2._all_dims_active
# white doesn;t combine with anything
if isinstance(p1, White) or isinstance(p2, White):
pass
# rbf X bias
#elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)):
elif isinstance(p1, Bias) and isinstance(p2, (RBF, Linear)):
tmp = p2.psi1(Z, variational_posterior).sum(axis=0)
psi2 += p1.variance * (tmp[:,None]+tmp[None,:]) #(tmp[:, :, None] + tmp[:, None, :])
#elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)):
elif isinstance(p2, Bias) and isinstance(p1, (RBF, Linear)):
tmp = p1.psi1(Z, variational_posterior).sum(axis=0)
psi2 += p2.variance * (tmp[:,None]+tmp[None,:]) #(tmp[:, :, None] + tmp[:, None, :])
elif isinstance(p2, (RBF, Linear)) and isinstance(p1, (RBF, Linear)):
assert np.intersect1d(p1._all_dims_active, p2._all_dims_active).size == 0, "only non overlapping kernel dimensions allowed so far"
tmp1 = p1.psi1(Z, variational_posterior)
tmp2 = p2.psi1(Z, variational_posterior)
psi2 += np.einsum('nm,no->mo',tmp1,tmp2)+np.einsum('nm,no->mo',tmp2,tmp1)
#(tmp1[:, :, None] * tmp2[:, None, :]) + (tmp2[:, :, None] * tmp1[:, None, :])
else:
raise NotImplementedError("psi2 cannot be computed for this kernel")
return psi2
@Cache_this(limit=3, force_kwargs=['which_parts'])
def psi2n(self, Z, variational_posterior):
if not self._exact_psicomp: return Kern.psi2n(self, Z, variational_posterior)
psi2 = reduce(np.add, (p.psi2n(Z, variational_posterior) for p in self.parts))
#return psi2
# compute the "cross" terms
from .static import White, Bias
from .rbf import RBF
#from rbf_inv import RBFInv
from .linear import Linear
#ffrom fixed import Fixed
for p1, p2 in itertools.combinations(self.parts, 2):
# i1, i2 = p1._all_dims_active, p2._all_dims_active
# white doesn;t combine with anything
if isinstance(p1, White) or isinstance(p2, White):
pass
# rbf X bias
#elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)):
elif isinstance(p1, Bias) and isinstance(p2, (RBF, Linear)):
tmp = p2.psi1(Z, variational_posterior)
psi2 += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
#elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)):
elif isinstance(p2, Bias) and isinstance(p1, (RBF, Linear)):
tmp = p1.psi1(Z, variational_posterior)
psi2 += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
elif isinstance(p2, (RBF, Linear)) and isinstance(p1, (RBF, Linear)):
assert np.intersect1d(p1._all_dims_active, p2._all_dims_active).size == 0, "only non overlapping kernel dimensions allowed so far"
tmp1 = p1.psi1(Z, variational_posterior)
tmp2 = p2.psi1(Z, variational_posterior)
psi2 += np.einsum('nm,no->nmo',tmp1,tmp2)+np.einsum('nm,no->nmo',tmp2,tmp1)
#(tmp1[:, :, None] * tmp2[:, None, :]) + (tmp2[:, :, None] * tmp1[:, None, :])
else:
raise NotImplementedError("psi2 cannot be computed for this kernel")
return psi2
def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
tmp = dL_dpsi2.sum(0)+ dL_dpsi2.sum(1) if len(dL_dpsi2.shape)==2 else dL_dpsi2.sum(2)+ dL_dpsi2.sum(1)
if not self._exact_psicomp: return Kern.update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior)
from .static import White, Bias
for p1 in self.parts:
#compute the effective dL_dpsi1. Extra terms appear becaue of the cross terms in psi2!
eff_dL_dpsi1 = dL_dpsi1.copy()
for p2 in self.parts:
if p2 is p1:
continue
if isinstance(p2, White):
continue
elif isinstance(p2, Bias):
eff_dL_dpsi1 += tmp * p2.variance
else:# np.setdiff1d(p1._all_dims_active, ar2, assume_unique): # TODO: Careful, not correct for overlapping _all_dims_active
eff_dL_dpsi1 += tmp * p2.psi1(Z, variational_posterior)
p1.update_gradients_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
def gradients_Z_expectations(self, dL_psi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
tmp = dL_dpsi2.sum(0)+ dL_dpsi2.sum(1) if len(dL_dpsi2.shape)==2 else dL_dpsi2.sum(2)+ dL_dpsi2.sum(1)
if not self._exact_psicomp: return Kern.gradients_Z_expectations(self, dL_psi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior)
from .static import White, Bias
target = np.zeros(Z.shape)
for p1 in self.parts:
#compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
eff_dL_dpsi1 = dL_dpsi1.copy()
for p2 in self.parts:
if p2 is p1:
continue
if isinstance(p2, White):
continue
elif isinstance(p2, Bias):
eff_dL_dpsi1 += tmp * p2.variance
else:
eff_dL_dpsi1 += tmp * p2.psi1(Z, variational_posterior)
target += p1.gradients_Z_expectations(dL_psi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
return target
def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
tmp = dL_dpsi2.sum(0)+ dL_dpsi2.sum(1) if len(dL_dpsi2.shape)==2 else dL_dpsi2.sum(2)+ dL_dpsi2.sum(1)
if not self._exact_psicomp: return Kern.gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior)
from .static import White, Bias
target_grads = [np.zeros(v.shape) for v in variational_posterior.parameters]
for p1 in self.parameters:
#compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
eff_dL_dpsi1 = dL_dpsi1.copy()
for p2 in self.parameters:
if p2 is p1:
continue
if isinstance(p2, White):
continue
elif isinstance(p2, Bias):
eff_dL_dpsi1 += tmp * p2.variance
else:
eff_dL_dpsi1 += tmp * p2.psi1(Z, variational_posterior)
grads = p1.gradients_qX_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
[np.add(target_grads[i],grads[i],target_grads[i]) for i in range(len(grads))]
return target_grads
#def add(self, other):
# parts = self.parts
# if 0:#isinstance(other, Add):
# #other_params = other.parameters[:]
# for p in other.parts[:]:
# other.unlink_parameter(p)
# parts.extend(other.parts)
# #self.link_parameters(*other_params)
#
# else:
# #self.link_parameter(other)
# parts.append(other)
# #self.input_dim, self._all_dims_active = self.get_input_dim_active_dims(parts)
# return Add([p for p in parts], self.name)
def input_sensitivity(self, summarize=True):
if summarize:
i_s = np.zeros((self.input_dim))
for k in self.parts:
i_s[k._all_dims_active] += k.input_sensitivity(summarize)
return i_s
else:
return super(Add, self).input_sensitivity(summarize)
def sde_update_gradient_full(self, gradients):
"""
Update gradient in the order in which parameters are represented in the
kernel
"""
part_start_param_index = 0
for p in self.parts:
if not p.is_fixed:
part_param_num = len(p.param_array) # number of parameters in the part
p.sde_update_gradient_full(gradients[part_start_param_index:(part_start_param_index+part_param_num)])
part_start_param_index += part_param_num
def sde(self):
"""
Support adding kernels for sde representation
"""
import scipy.linalg as la
F = None
L = None
Qc = None
H = None
Pinf = None
P0 = None
dF = None
dQc = None
dPinf = None
dP0 = None
n = 0
nq = 0
nd = 0
# Assign models
for p in self.parts:
(Ft,Lt,Qct,Ht,Pinft,P0t,dFt,dQct,dPinft,dP0t) = p.sde()
F = la.block_diag(F,Ft) if (F is not None) else Ft
L = la.block_diag(L,Lt) if (L is not None) else Lt
Qc = la.block_diag(Qc,Qct) if (Qc is not None) else Qct
H = np.hstack((H,Ht)) if (H is not None) else Ht
Pinf = la.block_diag(Pinf,Pinft) if (Pinf is not None) else Pinft
P0 = la.block_diag(P0,P0t) if (P0 is not None) else P0t
if dF is not None:
dF = np.pad(dF,((0,dFt.shape[0]),(0,dFt.shape[1]),(0,dFt.shape[2])),
'constant', constant_values=0)
dF[-dFt.shape[0]:,-dFt.shape[1]:,-dFt.shape[2]:] = dFt
else:
dF = dFt
if dQc is not None:
dQc = np.pad(dQc,((0,dQct.shape[0]),(0,dQct.shape[1]),(0,dQct.shape[2])),
'constant', constant_values=0)
dQc[-dQct.shape[0]:,-dQct.shape[1]:,-dQct.shape[2]:] = dQct
else:
dQc = dQct
if dPinf is not None:
dPinf = np.pad(dPinf,((0,dPinft.shape[0]),(0,dPinft.shape[1]),(0,dPinft.shape[2])),
'constant', constant_values=0)
dPinf[-dPinft.shape[0]:,-dPinft.shape[1]:,-dPinft.shape[2]:] = dPinft
else:
dPinf = dPinft
if dP0 is not None:
dP0 = np.pad(dP0,((0,dP0t.shape[0]),(0,dP0t.shape[1]),(0,dP0t.shape[2])),
'constant', constant_values=0)
dP0[-dP0t.shape[0]:,-dP0t.shape[1]:,-dP0t.shape[2]:] = dP0t
else:
dP0 = dP0t
n += Ft.shape[0]
nq += Qct.shape[0]
nd += dFt.shape[2]
assert (F.shape[0] == n and F.shape[1]==n), "SDE add: Check of F Dimensions failed"
assert (L.shape[0] == n and L.shape[1]==nq), "SDE add: Check of L Dimensions failed"
assert (Qc.shape[0] == nq and Qc.shape[1]==nq), "SDE add: Check of Qc Dimensions failed"
assert (H.shape[0] == 1 and H.shape[1]==n), "SDE add: Check of H Dimensions failed"
assert (Pinf.shape[0] == n and Pinf.shape[1]==n), "SDE add: Check of Pinf Dimensions failed"
assert (P0.shape[0] == n and P0.shape[1]==n), "SDE add: Check of P0 Dimensions failed"
assert (dF.shape[0] == n and dF.shape[1]==n and dF.shape[2]==nd), "SDE add: Check of dF Dimensions failed"
assert (dQc.shape[0] == nq and dQc.shape[1]==nq and dQc.shape[2]==nd), "SDE add: Check of dQc Dimensions failed"
assert (dPinf.shape[0] == n and dPinf.shape[1]==n and dPinf.shape[2]==nd), "SDE add: Check of dPinf Dimensions failed"
assert (dP0.shape[0] == n and dP0.shape[1]==n and dP0.shape[2]==nd), "SDE add: Check of dP0 Dimensions failed"
return (F,L,Qc,H,Pinf,P0,dF,dQc,dPinf,dP0)
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