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Merged conflict of model.py

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Neil Lawrence 2013-09-14 20:05:42 +01:00
commit dffa9541c2
42 changed files with 2297 additions and 453 deletions
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67
GPy/kern/constructors.py
View file

@ -73,9 +73,9 @@ def gibbs(input_dim,variance=1., mapping=None):
Gibbs and MacKay non-stationary covariance function.
.. math::
r = sqrt((x_i - x_j)'*(x_i - x_j))
k(x_i, x_j) = \sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x')))
Z = \sqrt{2*l(x)*l(x')/(l(x)*l(x) + l(x')*l(x')}
@ -89,7 +89,7 @@ def gibbs(input_dim,variance=1., mapping=None):
The parameters are :math:`\sigma^2`, the process variance, and the parameters of l(x) which is a function that can be specified by the user, by default an multi-layer peceptron is used is used.
:param input_dim: the number of input dimensions
:type input_dim: int
:type input_dim: int
:param variance: the variance :math:`\sigma^2`
:type variance: float
:param mapping: the mapping that gives the lengthscale across the input space.
@ -346,29 +346,30 @@ def symmetric(k):
k_.parts = [symmetric.Symmetric(p) for p in k.parts]
return k_
def coregionalise(output_dim, rank=1, W=None, kappa=None):
def coregionalise(num_outputs,W_columns=1, W=None, kappa=None):
"""
Coregionalisation kernel.
Used for computing covariance functions of the form
.. math::
k_2(x, y)=\mathbf{B} k(x, y)
where
Coregionlization matrix B, of the form:
.. math::
\mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I}
:param output_dim: the number of output dimensions
:type output_dim: int
:param rank: the rank of the coregionalisation matrix.
:type rank: int
:param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B.
:type W: ndarray
:param kappa: a diagonal term which allows the outputs to behave independently.
An intrinsic/linear coregionalization kernel of the form
.. math::
k_2(x, y)=\mathbf{B} k(x, y)
it is obtainded as the tensor product between a kernel k(x,y) and B.
:param num_outputs: the number of outputs to corregionalise
:type num_outputs: int
:param W_columns: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
:type W_colunns: int
:param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B
:type W: numpy array of dimensionality (num_outpus, W_columns)
:param kappa: a vector which allows the outputs to behave independently
:type kappa: numpy array of dimensionality (num_outputs,)
:rtype: kernel object
.. Note: see coregionalisation examples in GPy.examples.regression for some usage.
"""
p = parts.coregionalise.Coregionalise(output_dim,rank,W,kappa)
p = parts.coregionalise.Coregionalise(num_outputs,W_columns,W,kappa)
return kern(1,[p])
@ -427,3 +428,31 @@ def hierarchical(k):
# assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)"
_parts = [parts.hierarchical.Hierarchical(k.parts)]
return kern(k.input_dim+len(k.parts),_parts)
def build_lcm(input_dim, num_outputs, kernel_list = [], W_columns=1,W=None,kappa=None):
"""
Builds a kernel of a linear coregionalization model
:input_dim: Input dimensionality
:num_outputs: Number of outputs
:kernel_list: List of coregionalized kernels, each element in the list will be multiplied by a different corregionalization matrix
:type kernel_list: list of GPy kernels
:param W_columns: number tuples of the corregionalization parameters 'coregion_W'
:type W_columns: integer
..Note the kernels dimensionality is overwritten to fit input_dim
"""
for k in kernel_list:
if k.input_dim <> input_dim:
k.input_dim = input_dim
warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")
k_coreg = coregionalise(num_outputs,W_columns,W,kappa)
kernel = kernel_list[0]**k_coreg.copy()
for k in kernel_list[1:]:
k_coreg = coregionalise(num_outputs,W_columns,W,kappa)
kernel += k**k_coreg.copy()
return kernel

24
GPy/kern/kern.py
View file

@ -421,19 +421,19 @@ class kern(Parameterized):
# TODO: input_slices needed
crossterms = 0
for p1, p2 in itertools.combinations(self.parts, 2):
for [p1, i_s1], [p2, i_s2] in itertools.combinations(zip(self.parts, self.input_slices), 2):
if i_s1 == i_s2:
# TODO psi1 this must be faster/better/precached/more nice
tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
p1.psi1(Z[:, i_s1], mu[:, i_s1], S[:, i_s1], tmp1)
tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
p2.psi1(Z[:, i_s2], mu[:, i_s2], S[:, i_s2], tmp2)
prod = np.multiply(tmp1, tmp2)
crossterms += prod[:, :, None] + prod[:, None, :]
# TODO psi1 this must be faster/better/precached/more nice
tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
p1.psi1(Z, mu, S, tmp1)
tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
p2.psi1(Z, mu, S, tmp2)
prod = np.multiply(tmp1, tmp2)
crossterms += prod[:, :, None] + prod[:, None, :]
target += crossterms
return target
# target += crossterms
return target + crossterms
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
"""Gradient of the psi2 statistics with respect to the parameters."""

84
GPy/kern/parts/coregionalise.py
View file

@ -9,42 +9,45 @@ from scipy import weave
class Coregionalise(Kernpart):
"""
Coregionalisation kernel.
Kernel for intrinsic/linear coregionalization models
Used for computing covariance functions of the form
This kernel has the form
.. math::
k_2(x, y)=B k(x, y)
where
.. math::
B = WW^\top + diag(kappa)
\mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I}
:param output_dim: the number of output dimensions
:type output_dim: int
:param rank: the rank of the coregionalisation matrix.
:type rank: int
:param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B.
:type W: ndarray
:param kappa: a diagonal term which allows the outputs to behave independently.
:rtype: kernel object
An intrinsic/linear coregionalization kernel of the form
.. math::
k_2(x, y)=\mathbf{B} k(x, y)
it is obtainded as the tensor product between a kernel k(x,y) and B.
:param num_outputs: number of outputs to coregionalize
:type num_outputs: int
:param W_columns: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
:type W_colunns: int
:param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B
:type W: numpy array of dimensionality (num_outpus, W_columns)
:param kappa: a vector which allows the outputs to behave independently
:type kappa: numpy array of dimensionality (num_outputs,)
.. Note: see coregionalisation examples in GPy.examples.regression for some usage.
"""
def __init__(self,output_dim,rank=1, W=None, kappa=None):
def __init__(self,num_outputs,W_columns=1, W=None, kappa=None):
self.input_dim = 1
self.name = 'coregion'
self.output_dim = output_dim
self.rank = rank
self.num_outputs = num_outputs
self.W_columns = W_columns
if W is None:
self.W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
self.W = 0.5*np.random.randn(self.num_outputs,self.W_columns)/np.sqrt(self.W_columns)
else:
assert W.shape==(self.output_dim,self.rank)
assert W.shape==(self.num_outputs,self.W_columns)
self.W = W
if kappa is None:
kappa = 0.5*np.ones(self.output_dim)
kappa = 0.5*np.ones(self.num_outputs)
else:
assert kappa.shape==(self.output_dim,)
assert kappa.shape==(self.num_outputs,)
self.kappa = kappa
self.num_params = self.output_dim*(self.rank + 1)
self.num_params = self.num_outputs*(self.W_columns + 1)
self._set_params(np.hstack([self.W.flatten(),self.kappa]))
def _get_params(self):
@ -52,12 +55,12 @@ class Coregionalise(Kernpart):
def _set_params(self,x):
assert x.size == self.num_params
self.kappa = x[-self.output_dim:]
self.W = x[:-self.output_dim].reshape(self.output_dim,self.rank)
self.kappa = x[-self.num_outputs:]
self.W = x[:-self.num_outputs].reshape(self.num_outputs,self.W_columns)
self.B = np.dot(self.W,self.W.T) + np.diag(self.kappa)
def _get_param_names(self):
return sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.output_dim)],[]) + ['kappa_%i'%i for i in range(self.output_dim)]
return sum([['W%i_%i'%(i,j) for j in range(self.W_columns)] for i in range(self.num_outputs)],[]) + ['kappa_%i'%i for i in range(self.num_outputs)]
def K(self,index,index2,target):
index = np.asarray(index,dtype=np.int)
@ -75,26 +78,26 @@ class Coregionalise(Kernpart):
if index2 is None:
code="""
for(int i=0;i<N; i++){
target[i+i*N] += B[index[i]+output_dim*index[i]];
target[i+i*N] += B[index[i]+num_outputs*index[i]];
for(int j=0; j<i; j++){
target[j+i*N] += B[index[i]+output_dim*index[j]];
target[j+i*N] += B[index[i]+num_outputs*index[j]];
target[i+j*N] += target[j+i*N];
}
}
"""
N,B,output_dim = index.size, self.B, self.output_dim
weave.inline(code,['target','index','N','B','output_dim'])
N,B,num_outputs = index.size, self.B, self.num_outputs
weave.inline(code,['target','index','N','B','num_outputs'])
else:
index2 = np.asarray(index2,dtype=np.int)
code="""
for(int i=0;i<num_inducing; i++){
for(int j=0; j<N; j++){
target[i+j*num_inducing] += B[output_dim*index[j]+index2[i]];
target[i+j*num_inducing] += B[num_outputs*index[j]+index2[i]];
}
}
"""
N,num_inducing,B,output_dim = index.size,index2.size, self.B, self.output_dim
weave.inline(code,['target','index','index2','N','num_inducing','B','output_dim'])
N,num_inducing,B,num_outputs = index.size,index2.size, self.B, self.num_outputs
weave.inline(code,['target','index','index2','N','num_inducing','B','num_outputs'])
def Kdiag(self,index,target):
@ -111,12 +114,12 @@ class Coregionalise(Kernpart):
code="""
for(int i=0; i<num_inducing; i++){
for(int j=0; j<N; j++){
dL_dK_small[index[j] + output_dim*index2[i]] += dL_dK[i+j*num_inducing];
dL_dK_small[index[j] + num_outputs*index2[i]] += dL_dK[i+j*num_inducing];
}
}
"""
N, num_inducing, output_dim = index.size, index2.size, self.output_dim
weave.inline(code, ['N','num_inducing','output_dim','dL_dK','dL_dK_small','index','index2'])
N, num_inducing, num_outputs = index.size, index2.size, self.num_outputs
weave.inline(code, ['N','num_inducing','num_outputs','dL_dK','dL_dK_small','index','index2'])
dkappa = np.diag(dL_dK_small)
dL_dK_small += dL_dK_small.T
@ -133,8 +136,8 @@ class Coregionalise(Kernpart):
ii,jj = ii.T, jj.T
dL_dK_small = np.zeros_like(self.B)
for i in range(self.output_dim):
for j in range(self.output_dim):
for i in range(self.num_outputs):
for j in range(self.num_outputs):
tmp = np.sum(dL_dK[(ii==i)*(jj==j)])
dL_dK_small[i,j] = tmp
@ -146,8 +149,8 @@ class Coregionalise(Kernpart):
def dKdiag_dtheta(self,dL_dKdiag,index,target):
index = np.asarray(index,dtype=np.int).flatten()
dL_dKdiag_small = np.zeros(self.output_dim)
for i in range(self.output_dim):
dL_dKdiag_small = np.zeros(self.num_outputs)
for i in range(self.num_outputs):
dL_dKdiag_small[i] += np.sum(dL_dKdiag[index==i])
dW = 2.*self.W*dL_dKdiag_small[:,None]
dkappa = dL_dKdiag_small
@ -155,6 +158,3 @@ class Coregionalise(Kernpart):
def dK_dX(self,dL_dK,X,X2,target):
pass

2
GPy/kern/parts/prod.py
View file

@ -18,7 +18,7 @@ class Prod(Kernpart):
"""
def __init__(self,k1,k2,tensor=False):
self.num_params = k1.num_params + k2.num_params
self.name = k1.name + '<times>' + k2.name
self.name = '['+k1.name + '(x)' + k2.name +']'
self.k1 = k1
self.k2 = k2
if tensor:

5
GPy/kern/parts/rbf.py
View file

@ -242,13 +242,14 @@ class RBF(Kernpart):
def _psi_computations(self, Z, mu, S):
# here are the "statistics" for psi1 and psi2
if not fast_array_equal(Z, self._Z):
Z_changed = not fast_array_equal(Z, self._Z)
if Z_changed:
# Z has changed, compute Z specific stuff
self._psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
self._psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
self._psi2_Zdist_sq = np.square(self._psi2_Zdist / self.lengthscale) # M,M,Q
if not fast_array_equal(Z, self._Z) or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S):
if Z_changed or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S):
# something's changed. recompute EVERYTHING
# psi1