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[basisfuncs] updated kernel to better reflect linear trends and added ARD support

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mzwiessele 2015-04-21 11:18:31 +02:00
parent 440d7b6478
commit d428465e08
2 changed files with 58 additions and 21 deletions
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77
GPy/kern/_src/basis_funcs.py
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@ -5,33 +5,59 @@ from ...core.parameterization.param import Param
from ...core.parameterization.transformations import Logexp
import numpy as np
from ...util.caching import Cache_this
from ...util.linalg import tdot
from ...util.linalg import tdot, mdot
class BasisFuncKernel(Kern):
def __init__(self, input_dim, variance=1., active_dims=None, name='basis func kernel'):
def __init__(self, input_dim, variance=1., active_dims=None, ARD=False, name='basis func kernel'):
"""
Abstract superclass for kernels with explicit basis functions for use in GPy.
This class does NOT automatically add an offset to the design matrix phi!
"""
super(BasisFuncKernel, self).__init__(input_dim, active_dims, name)
self.ARD = ARD
if self.ARD:
phi_test = self._phi(np.random.normal(0, 1, (1, self.input_dim)))
variance = variance * np.ones(phi_test.shape[1])
else:
variance = np.array(variance)
self.variance = Param('variance', variance, Logexp())
self.link_parameter(self.variance)
def parameters_changed(self):
self.alpha = np.sqrt(self.variance)
#self.beta = 1./self.variance
@Cache_this(limit=3, ignore_args=())
def phi(self, X):
raise NotImplementedError('Overwrite this phi function, which maps the input X into the higher dimensional space and forms the design matrix Phi')
return self._phi(X)
def _phi(self, X):
raise NotImplementedError('Overwrite this _phi function, which maps the input X into the higher dimensional space and returns the design matrix Phi')
def K(self, X, X2=None):
return self.variance * self._K(X, X2)
return self._K(X, X2)
def Kdiag(self, X, X2=None):
return self.variance * np.diag(self._K(X, X2))
return np.diag(self._K(X, X2))
def update_gradients_full(self, dL_dK, X, X2=None):
self.variance.gradient = np.einsum('ij,ij', dL_dK, self._K(X, X2))
if self.ARD:
phi1 = self.phi(X)
if X2 is None or X is X2:
self.variance.gradient = np.einsum('ij,iq,jq->q', dL_dK, phi1, phi1)
else:
phi2 = self.phi(X2)
self.variance.gradient = np.einsum('ij,iq,jq->q', dL_dK, phi1, phi2)
else:
self.variance.gradient = np.einsum('ij,ij', dL_dK, self._K(X, X2))
def update_gradients_diag(self, dL_dKdiag, X):
self.variance.gradient = np.einsum('i,i', dL_dKdiag, self._K(X))
if self.ARD:
phi1 = self.phi(X)
self.variance.gradient = np.einsum('i,iq,iq->q', dL_dKdiag, phi1, phi1)
else:
self.variance.gradient = np.einsum('i,i', dL_dKdiag, self.Kdiag(X))
def concatenate_offset(self, X):
return np.c_[np.ones((X.shape[0], 1)), X]
@ -52,19 +78,19 @@ class BasisFuncKernel(Kern):
posterior = self._highest_parent_.posterior
except NameError:
raise RuntimeError("This kernel is not part of a model and cannot be used for posterior inference")
phi = self.phi(X)
return self.variance * phi.T.dot(posterior.woodbury_vector), self.variance * (1 - self.variance * phi.T.dot(posterior.woodbury_inv.dot(phi)))
phi_alpha = self.phi(X) * self.variance
return (phi_alpha).T.dot(posterior.woodbury_vector), (np.eye(phi_alpha.shape[1])*self.variance - mdot(phi_alpha.T, posterior.woodbury_inv, phi_alpha))
@Cache_this(limit=3, ignore_args=())
def _K(self, X, X2):
if X2 is None or X is X2:
phi = self.phi(X)
phi = self.phi(X) * self.alpha
if phi.ndim != 2:
phi = phi[:, None]
return tdot(phi)
else:
phi1 = self.phi(X)
phi2 = self.phi(X2)
phi1 = self.phi(X) * self.alpha
phi2 = self.phi(X2) * self.alpha
if phi1.ndim != 2:
phi1 = phi1[:, None]
phi2 = phi2[:, None]
@ -72,30 +98,43 @@ class BasisFuncKernel(Kern):
class LinearSlopeBasisFuncKernel(BasisFuncKernel):
def __init__(self, input_dim, start, stop, variance=1., active_dims=None, name='linear_segment'):
super(LinearSlopeBasisFuncKernel, self).__init__(input_dim, variance, active_dims, name)
def __init__(self, input_dim, start, stop, variance=1., active_dims=None, ARD=False, name='linear_segment'):
"""
A linear segment transformation. The segments start at start, \
are then linear to stop and constant again. The segments are
normalized, so that they have exactly as much mass above
as below the origin.
Start and stop can be tuples or lists of starts and stops.
Behaviour of start stop is as np.where(X<start) would do.
"""
self.start = np.array(start)
self.stop = np.array(stop)
super(LinearSlopeBasisFuncKernel, self).__init__(input_dim, variance, active_dims, ARD, name)
@Cache_this(limit=3, ignore_args=())
def phi(self, X):
def _phi(self, X):
phi = np.where(X < self.start, self.start, X)
phi = np.where(phi > self.stop, self.stop, phi)
return ((phi-(self.stop+self.start)/2.))#/(.5*(self.stop-self.start)))-1.
return self.concatenate_offset(phi) # ((phi-self.start)/(self.stop-self.start))-.5
class ChangePointBasisFuncKernel(BasisFuncKernel):
def __init__(self, input_dim, changepoint, variance=1., active_dims=None, name='changepoint'):
super(ChangePointBasisFuncKernel, self).__init__(input_dim, variance, active_dims, name)
def __init__(self, input_dim, changepoint, variance=1., active_dims=None, ARD=False, name='changepoint'):
self.changepoint = changepoint
super(ChangePointBasisFuncKernel, self).__init__(input_dim, variance, active_dims, ARD, name)
@Cache_this(limit=3, ignore_args=())
def phi(self, X):
def _phi(self, X):
return self.concatenate_offset(np.where((X < self.changepoint), -1, 1))
class DomainKernel(LinearSlopeBasisFuncKernel):
def __init__(self, input_dim, start, stop, variance=1., active_dims=None, ARD=False, name='constant_domain'):
super(DomainKernel, self).__init__(input_dim, start, stop, variance, active_dims, ARD, name)
@Cache_this(limit=3, ignore_args=())
def phi(self, X):
def _phi(self, X):
phi = np.where((X>self.start)*(X<self.stop), 1., 0.)
return phi#((phi-self.start)/(self.stop-self.start))-.5
return self.concatenate_offset(phi) # ((phi-self.start)/(self.stop-self.start))-.5

2
GPy/kern/_src/periodic.py
View file

@ -68,8 +68,6 @@ class Periodic(Kern):
return np.diag(self.K(X))
class PeriodicExponential(Periodic):
"""
Kernel of the periodic subspace (up to a given frequency) of a exponential