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linear kernel now has an ARD flag
This commit is contained in:
Nicolas
parent
1680c71445
commit
2f68f6de86
5 changed files with 208 additions and 204 deletions
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@ -2,5 +2,5 @@
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, linear_ARD, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52
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from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52
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from kern import kern
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@ -8,7 +8,6 @@ from kern import kern
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from rbf import rbf as rbfpart
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from white import white as whitepart
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from linear import linear as linearpart
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from linear_ARD import linear_ARD as linear_ARD_part
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from exponential import exponential as exponentialpart
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from Matern32 import Matern32 as Matern32part
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from Matern52 import Matern52 as Matern52part
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@ -40,28 +39,17 @@ def rbf(D,variance=1., lengthscale=None,ARD=False):
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part = rbfpart(D,variance,lengthscale,ARD)
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return kern(D, [part])
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def linear(D,lengthscales=None):
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def linear(D,variances=None,ARD=True):
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"""
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Construct a linear kernel.
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Arguments
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---------
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D (int), obligatory
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lengthscales (np.ndarray)
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variances (np.ndarray)
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ARD (boolean)
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"""
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part = linearpart(D,lengthscales)
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return kern(D, [part])
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def linear_ARD(D,lengthscales=None):
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"""
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Construct a linear ARD kernel.
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Arguments
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---------
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D (int), obligatory
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lengthscales (np.ndarray)
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"""
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part = linear_ARD_part(D,lengthscales)
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part = linearpart(D,variances,ARD)
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return kern(D, [part])
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def white(D,variance=1.):
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@ -1,124 +1,143 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kernpart import kernpart
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import numpy as np
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class linear(kernpart):
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"""
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Linear kernel
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.. math::
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k(x,y) = \sum_{i=1}^D \sigma^2_i x_iy_i
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:param D: the number of input dimensions
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:type D: int
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:param variance: variance
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:type variance: None|float
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:param variances: the vector of variances :math:`\sigma^2_i`
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:type variances: np.ndarray of size (1,) or (D,) depending on ARD
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:param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single variance parameter \sigma^2), otherwise there is one variance parameter per dimension.
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:type ARD: Boolean
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:rtype: kernel object
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"""
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def __init__(self, D, variance=None):
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def __init__(self,D,variances=None,ARD=True):
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self.D = D
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if variance is None:
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variance = 1.0
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self.Nparam = 1
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self.name = 'linear'
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self._set_params(variance)
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self._Xcache, self._X2cache = np.empty(shape=(2,))
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self.ARD = ARD
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if ARD == False:
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self.Nparam = 1
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self.name = 'linear'
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if variances is not None:
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assert variances.shape == (1,)
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else:
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variances = np.ones(1)
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self._Xcache, self._X2cache = np.empty(shape=(2,))
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else:
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self.Nparam = self.D
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self.name = 'linear_ARD'
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if variances is not None:
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assert variances.shape == (self.D,)
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else:
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variances = np.ones(self.D)
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self._set_params(variances)
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def _get_params(self):
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return self.variance
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return self.variances
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def _set_params(self,x):
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self.variance = x
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assert x.size==(self.Nparam)
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self.variances = x
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def _get_param_names(self):
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return ['variance']
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if self.Nparam == 1:
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return ['variance']
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else:
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return ['variance_%i'%i for i in range(self.variances.size)]
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def K(self,X,X2,target):
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self._K_computations(X, X2)
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target += self.variance * self._dot_product
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def Kdiag(self,X,target):
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np.add(target,np.sum(self.variance*np.square(X),-1),target)
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def dK_dtheta(self,partial,X,X2,target):
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"""
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Computes the derivatives wrt theta
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Return shape is NxMx(Ntheta)
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"""
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self._K_computations(X, X2)
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product = self._dot_product
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# product = np.dot(X, X2.T)
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target += np.sum(product*partial)
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def dK_dX(self,partial,X,X2,target):
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target += self.variance * np.sum(partial[:,None,:]*X2.T[None,:,:],-1)
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def dKdiag_dtheta(self,partial,X,target):
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target += np.sum(partial*np.square(X).sum(1))
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if self.ARD:
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XX = X*np.sqrt(self.variances)
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XX2 = X2*np.sqrt(self.variances)
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target += np.dot(XX, XX2.T)
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else:
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self._K_computations(X, X2)
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target += self.variances * self._dot_product
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def _K_computations(self,X,X2):
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# (Nicolo) changed the logic here. If X2 is None, we want to cache
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# (X,X). In practice X2 should always be passed.
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if X2 is None:
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X2 = X
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if not (np.all(X==self._Xcache) and np.all(X2==self._X2cache)):
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self._Xcache = X
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self._X2cache = X2
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self._dot_product = np.dot(X,X2.T)
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self._dot_product = np.dot(X,X2.T)
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else:
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# print "Cache hit!"
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pass # TODO: insert debug message here (logging framework)
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def Kdiag(self,X,target):
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np.add(target,np.sum(self.variances*np.square(X),-1),target)
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# def psi0(self,Z,mu,S,target):
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# expected = np.square(mu) + S
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# np.add(target,np.sum(self.variance*expected),target)
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def dK_dtheta(self,partial,X,X2,target):
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if self.ARD:
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product = X[:,None,:]*X2[None,:,:]
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target += (partial[:,:,None]*product).sum(0).sum(0)
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else:
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self._K_computations(X, X2)
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target += np.sum(self._dot_product*partial)
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# def dpsi0_dtheta(self,Z,mu,S,target):
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# expected = np.square(mu) + S
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# return -2.*np.sum(expected,0)
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def dK_dX(self,partial,X,X2,target):
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target += (((X2[:, None, :] * self.variances)) * partial[:,:, None]).sum(0)
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# def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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# np.add(target_mu,2*mu*self.variances,target_mu)
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# np.add(target_S,self.variances,target_S)
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def psi0(self,Z,mu,S,target):
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expected = np.square(mu) + S
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target += np.sum(self.variances*expected)
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# def dpsi0_dZ(self,Z,mu,S,target):
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# pass
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def dpsi0_dtheta(self,Z,mu,S,target):
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expected = np.square(mu) + S
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return -2.*np.sum(expected,0)
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# def psi1(self,Z,mu,S,target):
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# """the variance, it does nothing"""
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# self.K(mu,Z,target)
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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np.add(target_mu,2*mu*self.variances,target_mu)
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np.add(target_S,self.variances,target_S)
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# def dpsi1_dtheta(self,Z,mu,S,target):
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# """the variance, it does nothing"""
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# self.dK_dtheta(mu,Z,target)
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def dpsi0_dZ(self,Z,mu,S,target):
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pass
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# def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
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# """Do nothing for S, it does not affect psi1"""
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# np.add(target_mu,Z/self.variances2,target_mu)
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def psi1(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.K(mu,Z,target)
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# def dpsi1_dZ(self,Z,mu,S,target):
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# self.dK_dX(mu,Z,target)
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def dpsi1_dtheta(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.dK_dtheta(mu,Z,target)
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# def psi2(self,Z,mu,S,target):
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# """Think N,M,M,Q """
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# mu2_S = np.square(mu)+SN,Q,
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# ZZ = Z[:,None,:]*Z[None,:,:] M,M,Q
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# psi2 = ZZ*np.square(self.variances)*mu2_S
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# np.add(target, psi2.sum(-1),target) M,M
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def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Do nothing for S, it does not affect psi1"""
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np.add(target_mu,Z/self.variances2,target_mu)
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# def dpsi2_dtheta(self,Z,mu,S,target):
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# mu2_S = np.square(mu)+SN,Q,
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# ZZ = Z[:,None,:]*Z[None,:,:] M,M,Q
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# target += 2.*ZZ*mu2_S*self.variances
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def dpsi1_dZ(self,Z,mu,S,target):
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self.dK_dX(mu,Z,target)
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# def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
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# """Think N,M,M,Q """
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# mu2_S = np.sum(np.square(mu)+S,0)Q,
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# ZZ = Z[:,None,:]*Z[None,:,:] M,M,Q
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# tmp = ZZ*np.square(self.variances) M,M,Q
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# np.add(target_mu, tmp*2.*mu[:,None,None,:],target_mu) N,M,M,Q
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# np.add(target_S, tmp, target_S) N,M,M,Q
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def psi2(self,Z,mu,S,target):
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"""Think N,M,M,Q """
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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psi2 = ZZ*np.square(self.variances)*mu2_S
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np.add(target, psi2.sum(-1),target) # M,M
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# def dpsi2_dZ(self,Z,mu,S,target):
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# mu2_S = np.sum(np.square(mu)+S,0)Q,
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# target += Z[:,None,:]*np.square(self.variances)*mu2_S
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def dpsi2_dtheta(self,Z,mu,S,target):
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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target += 2.*ZZ*mu2_S*self.variances
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def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Think N,M,M,Q """
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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tmp = ZZ*np.square(self.variances) # M,M,Q
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np.add(target_mu, tmp*2.*mu[:,None,None,:],target_mu) #N,M,M,Q
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np.add(target_S, tmp, target_S) #N,M,M,Q
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def dpsi2_dZ(self,Z,mu,S,target):
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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target += Z[:,None,:]*np.square(self.variances)*mu2_S
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@ -1,108 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kernpart import kernpart
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import numpy as np
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class linear_ARD(kernpart):
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"""
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Linear ARD kernel
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:param D: the number of input dimensions
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:type D: int
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:param variances: ARD variances
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:type variances: None|np.ndarray
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"""
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def __init__(self,D,variances=None):
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self.D = D
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if variances is not None:
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assert variances.shape==(self.D,)
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else:
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variances = np.ones(self.D)
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self.Nparam = int(self.D)
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self.name = 'linear'
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self._set_params(variances)
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def _get_params(self):
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return self.variances
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def _set_params(self,x):
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assert x.size==(self.Nparam)
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self.variances = x
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def _get_param_names(self):
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if self.D==1:
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return ['variance']
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else:
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return ['variance_%i'%i for i in range(self.variances.size)]
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def K(self,X,X2,target):
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XX = X*np.sqrt(self.variances)
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XX2 = X2*np.sqrt(self.variances)
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target += np.dot(XX, XX2.T)
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def Kdiag(self,X,target):
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np.add(target,np.sum(self.variances*np.square(X),-1),target)
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def dK_dtheta(self,partial,X,X2,target):
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product = X[:,None,:]*X2[None,:,:]
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target += (partial[:,:,None]*product).sum(0).sum(0)
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def dK_dX(self,partial,X,X2,target):
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target += (((X2[:, None, :] * self.variances)) * partial[:,:, None]).sum(0)
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def psi0(self,Z,mu,S,target):
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expected = np.square(mu) + S
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np.add(target,np.sum(self.variances*expected),target)
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def dpsi0_dtheta(self,Z,mu,S,target):
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expected = np.square(mu) + S
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return -2.*np.sum(expected,0)
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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np.add(target_mu,2*mu*self.variances,target_mu)
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np.add(target_S,self.variances,target_S)
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def dpsi0_dZ(self,Z,mu,S,target):
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pass
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def psi1(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.K(mu,Z,target)
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def dpsi1_dtheta(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.dK_dtheta(mu,Z,target)
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def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Do nothing for S, it does not affect psi1"""
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np.add(target_mu,Z/self.variances2,target_mu)
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def dpsi1_dZ(self,Z,mu,S,target):
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self.dK_dX(mu,Z,target)
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def psi2(self,Z,mu,S,target):
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"""Think N,M,M,Q """
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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psi2 = ZZ*np.square(self.variances)*mu2_S
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np.add(target, psi2.sum(-1),target) # M,M
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def dpsi2_dtheta(self,Z,mu,S,target):
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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target += 2.*ZZ*mu2_S*self.variances
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def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Think N,M,M,Q """
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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tmp = ZZ*np.square(self.variances) # M,M,Q
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np.add(target_mu, tmp*2.*mu[:,None,None,:],target_mu) #N,M,M,Q
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np.add(target_S, tmp, target_S) #N,M,M,Q
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def dpsi2_dZ(self,Z,mu,S,target):
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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target += Z[:,None,:]*np.square(self.variances)*mu2_S
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