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Max Zwiessele 2014-02-24 14:50:23 +00:00
commit 22403a266f
15 changed files with 623 additions and 1138 deletions
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20
GPy/kern/__init__.py
View file

@ -1,34 +1,26 @@
from _src.rbf import RBF
from _src.white import White
from _src.kern import Kern
from _src.rbf import RBF
from _src.linear import Linear
from _src.bias import Bias
from _src.static import Bias, White
from _src.brownian import Brownian
from _src.stationary import Exponential, Matern32, Matern52, ExpQuad
from _src.stationary import Exponential, Matern32, Matern52, ExpQuad, RatQuad, Cosine
from _src.mlp import MLP
from _src.periodic import PeriodicExponential, PeriodicMatern32, PeriodicMatern52
from _src.independent_outputs import IndependentOutputs
#import coregionalize
#import exponential
#import eq_ode1
#import finite_dimensional
#import fixed
#import gibbs
#import hetero
#import hierarchical
#import independent_outputs
#import linear
#import Matern32
#import Matern52
#import mlp
#import ODE_1
#import periodic_exponential
#import periodic_Matern32
#import periodic_Matern52
#import poly
#import prod_orthogonal
#import prod
#import rational_quadratic
#import rbfcos
#import rbf
#import rbf_inv
#import spline
#import symmetric
#import white

104
GPy/kern/_src/independent_outputs.py
View file

@ -2,7 +2,7 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
from kern import Kern
import numpy as np
def index_to_slices(index):
@ -31,67 +31,89 @@ def index_to_slices(index):
[ret[ind_i].append(slice(*indexes_i)) for ind_i,indexes_i in zip(ind[switchpoints[:-1]],zip(switchpoints,switchpoints[1:]))]
return ret
class IndependentOutputs(Kernpart):
class IndependentOutputs(Kern):
"""
A kernel part shich can reopresent several independent functions.
A kernel which can reopresent several independent functions.
this kernel 'switches off' parts of the matrix where the output indexes are different.
The index of the functions is given by the last column in the input X
the rest of the columns of X are passed to the kernel for computation (in blocks).
the rest of the columns of X are passed to the underlying kernel for computation (in blocks).
"""
def __init__(self,k):
self.input_dim = k.input_dim + 1
self.num_params = k.num_params
self.name = 'iops('+ k.name + ')'
self.k = k
def __init__(self, kern, name='independ'):
super(IndependentOutputs, self).__init__(kern.input_dim+1, name)
self.kern = kern
self.add_parameters(self.kern)
def _get_params(self):
return self.k._get_params()
def K(self,X ,X2=None):
X, slices = X[:,:-1], index_to_slices(X[:,-1])
if X2 is None:
target = np.zeros((X.shape[0], X.shape[0]))
[[np.copyto(target[s,s], self.kern.K(X[s], None)) for s in slices_i] for slices_i in slices]
else:
X2, slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
target = np.zeros((X.shape[0], X2.shape[0]))
[[[np.copyto(target[s, s2], self.kern.K(X[s],X2[s2])) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
return target
def _set_params(self,x):
self.k._set_params(x)
self.params = x
def Kdiag(self,X):
X, slices = X[:,:-1], index_to_slices(X[:,-1])
target = np.zeros(X.shape[0])
[[np.copyto(target[s], self.kern.Kdiag(X[s])) for s in slices_i] for slices_i in slices]
return target
def _get_param_names(self):
return self.k._get_param_names()
def update_gradients_full(self,dL_dK,X,X2=None):
target = np.zeros(self.kern.size)
def collate_grads(dL, X, X2):
self.kern.update_gradients_full(dL,X,X2)
self.kern._collect_gradient(target)
def K(self,X,X2,target):
#Sort out the slices from the input data
X,slices = X[:,:-1],index_to_slices(X[:,-1])
if X2 is None:
X2,slices2 = X,slices
[[collate_grads(dL_dK[s,s], X[s], None) for s in slices_i] for slices_i in slices]
else:
X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
X2, slices2 = X2[:,:-1], index_to_slices(X2[:,-1])
[[[collate_grads(dL_dK[s,s2],X[s],X2[s2]) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
[[[self.k.K(X[s],X2[s2],target[s,s2]) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
self.kern._set_gradient(target)
def Kdiag(self,X,target):
X,slices = X[:,:-1],index_to_slices(X[:,-1])
[[self.k.Kdiag(X[s],target[s]) for s in slices_i] for slices_i in slices]
def _param_grad_helper(self,dL_dK,X,X2,target):
X,slices = X[:,:-1],index_to_slices(X[:,-1])
def gradients_X(self,dL_dK, X, X2=None):
target = np.zeros_like(X)
X, slices = X[:,:-1],index_to_slices(X[:,-1])
if X2 is None:
X2,slices2 = X,slices
[[np.copyto(target[s,:-1], self.kern.gradients_X(dL_dK[s,s],X[s],None)) for s in slices_i] for slices_i in slices]
else:
X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
[[[self.k._param_grad_helper(dL_dK[s,s2],X[s],X2[s2],target) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
[[[np.copyto(target[s,:-1], self.kern.gradients_X(dL_dK[s,s2], X[s], X2[s2])) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
return target
def gradients_X_diag(self, dL_dKdiag, X):
X, slices = X[:,:-1], index_to_slices(X[:,-1])
target = np.zeros(X.shape)
[[np.copyto(target[s,:-1], self.kern.gradients_X_diag(dL_dKdiag[s],X[s])) for s in slices_i] for slices_i in slices]
return target
def gradients_X(self,dL_dK,X,X2,target):
def update_gradients_diag(self,dL_dKdiag,X,target):
target = np.zeros(self.kern.size)
def collate_grads(dL, X):
self.kern.update_gradients_diag(dL,X)
self.kern._collect_gradient(target)
X,slices = X[:,:-1],index_to_slices(X[:,-1])
if X2 is None:
X2,slices2 = X,slices
else:
X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
[[[self.k.gradients_X(dL_dK[s,s2],X[s],X2[s2],target[s,:-1]) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)]
[[collate_grads(dL_dKdiag[s], X[s,:]) for s in slices_i] for slices_i in slices]
self.kern._set_gradient(target)
def dKdiag_dX(self,dL_dKdiag,X,target):
X,slices = X[:,:-1],index_to_slices(X[:,-1])
[[self.k.dKdiag_dX(dL_dKdiag[s],X[s],target[s,:-1]) for s in slices_i] for slices_i in slices]
def Hierarchical(kern_f, kern_g, name='hierarchy'):
"""
A kernel which can reopresent a simple hierarchical model.
See Hensman et al 2013, "Hierarchical Bayesian modelling of gene expression time
series across irregularly sampled replicates and clusters"
http://www.biomedcentral.com/1471-2105/14/252
The index of the functions is given by the last column in the input X
the rest of the columns of X are passed to the underlying kernel for computation (in blocks).
"""
assert kern_f.input_dim == kern_g.input_dim
return kern_f + IndependentOutputs(kern_g)
def dKdiag_dtheta(self,dL_dKdiag,X,target):
X,slices = X[:,:-1],index_to_slices(X[:,-1])
[[self.k.dKdiag_dX(dL_dKdiag[s],X[s],target) for s in slices_i] for slices_i in slices]

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

@ -105,7 +105,7 @@ class Kern(Parameterized):
""" Here we overload the '*' operator. See self.prod for more information"""
return self.prod(other)
def __pow__(self, other, tensor=False):
def __pow__(self, other):
"""
Shortcut for tensor `prod`.
"""

123
GPy/kern/_src/mlp.py
View file

@ -1,11 +1,13 @@
# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
from kern import Kern
from ...core.parameterization import Param
from ...core.parameterization.transformations import Logexp
import numpy as np
four_over_tau = 2./np.pi
class MLP(Kernpart):
class MLP(Kern):
"""
Multi layer perceptron kernel (also known as arc sine kernel or neural network kernel)
@ -29,85 +31,58 @@ class MLP(Kernpart):
"""
def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=100., ARD=False):
self.input_dim = input_dim
self.ARD = ARD
if not ARD:
self.num_params=3
if weight_variance is not None:
weight_variance = np.asarray(weight_variance)
assert weight_variance.size == 1, "Only one weight variance needed for non-ARD kernel"
else:
weight_variance = 100.*np.ones(1)
else:
self.num_params = self.input_dim + 2
if weight_variance is not None:
weight_variance = np.asarray(weight_variance)
assert weight_variance.size == self.input_dim, "bad number of weight variances"
else:
weight_variance = np.ones(self.input_dim)
raise NotImplementedError
def __init__(self, input_dim, variance=1., weight_variance=1., bias_variance=100., name='mlp'):
super(MLP, self).__init__(input_dim, name)
self.variance = Param('variance', variance, Logexp())
self.weight_variance = Param('weight_variance', weight_variance, Logexp())
self.bias_variance = Param('bias_variance', bias_variance, Logexp())
self.add_parameters(self.variance, self.weight_variance, self.bias_variance)
self.name='mlp'
self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance)))
def _get_params(self):
return np.hstack((self.variance, self.weight_variance.flatten(), self.bias_variance))
def _set_params(self, x):
assert x.size == (self.num_params)
self.variance = x[0]
self.weight_variance = x[1:-1]
self.weight_std = np.sqrt(self.weight_variance)
self.bias_variance = x[-1]
def _get_param_names(self):
if self.num_params == 3:
return ['variance', 'weight_variance', 'bias_variance']
else:
return ['variance'] + ['weight_variance_%i' % i for i in range(self.lengthscale.size)] + ['bias_variance']
def K(self, X, X2, target):
"""Return covariance between X and X2."""
def K(self, X, X2=None):
self._K_computations(X, X2)
target += self.variance*self._K_dvar
return self.variance*self._K_dvar
def Kdiag(self, X, target):
def Kdiag(self, X):
"""Compute the diagonal of the covariance matrix for X."""
self._K_diag_computations(X)
target+= self.variance*self._K_diag_dvar
return self.variance*self._K_diag_dvar
def _param_grad_helper(self, dL_dK, X, X2, target):
def update_gradients_full(self, dL_dK, X, X2=None):
"""Derivative of the covariance with respect to the parameters."""
self._K_computations(X, X2)
denom3 = self._K_denom*self._K_denom*self._K_denom
self.variance.gradient = np.sum(self._K_dvar*dL_dK)
denom3 = self._K_denom**3
base = four_over_tau*self.variance/np.sqrt(1-self._K_asin_arg*self._K_asin_arg)
base_cov_grad = base*dL_dK
if X2 is None:
vec = np.diag(self._K_inner_prod)
target[1] += ((self._K_inner_prod/self._K_denom
self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom
-.5*self._K_numer/denom3
*(np.outer((self.weight_variance*vec+self.bias_variance+1.), vec)
+np.outer(vec,(self.weight_variance*vec+self.bias_variance+1.))))*base_cov_grad).sum()
target[2] += ((1./self._K_denom
self.bias_variance.gradient = ((1./self._K_denom
-.5*self._K_numer/denom3
*((vec[None, :]+vec[:, None])*self.weight_variance
+2.*self.bias_variance + 2.))*base_cov_grad).sum()
else:
vec1 = (X*X).sum(1)
vec2 = (X2*X2).sum(1)
target[1] += ((self._K_inner_prod/self._K_denom
self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom
-.5*self._K_numer/denom3
*(np.outer((self.weight_variance*vec1+self.bias_variance+1.), vec2) + np.outer(vec1, self.weight_variance*vec2 + self.bias_variance+1.)))*base_cov_grad).sum()
target[2] += ((1./self._K_denom
self.bias_variance.gradient = ((1./self._K_denom
-.5*self._K_numer/denom3
*((vec1[:, None]+vec2[None, :])*self.weight_variance
+ 2*self.bias_variance + 2.))*base_cov_grad).sum()
target[0] += np.sum(self._K_dvar*dL_dK)
def update_gradients_diag(self, X):
raise NotImplementedError, "TODO"
def gradients_X(self, dL_dK, X, X2, target):
def gradients_X(self, dL_dK, X, X2):
"""Derivative of the covariance matrix with respect to X"""
self._K_computations(X, X2)
arg = self._K_asin_arg
@ -116,10 +91,10 @@ class MLP(Kernpart):
denom3 = denom*denom*denom
if X2 is not None:
vec2 = (X2*X2).sum(1)*self.weight_variance+self.bias_variance + 1.
target += four_over_tau*self.weight_variance*self.variance*((X2[None, :, :]/denom[:, :, None] - vec2[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
return four_over_tau*self.weight_variance*self.variance*((X2[None, :, :]/denom[:, :, None] - vec2[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
else:
vec = (X*X).sum(1)*self.weight_variance+self.bias_variance + 1.
target += 2*four_over_tau*self.weight_variance*self.variance*((X[None, :, :]/denom[:, :, None] - vec[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
return 2*four_over_tau*self.weight_variance*self.variance*((X[None, :, :]/denom[:, :, None] - vec[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
def dKdiag_dX(self, dL_dKdiag, X, target):
"""Gradient of diagonal of covariance with respect to X"""
@ -127,36 +102,28 @@ class MLP(Kernpart):
arg = self._K_diag_asin_arg
denom = self._K_diag_denom
numer = self._K_diag_numer
target += four_over_tau*2.*self.weight_variance*self.variance*X*(1/denom*(1 - arg)*dL_dKdiag/(np.sqrt(1-arg*arg)))[:, None]
return four_over_tau*2.*self.weight_variance*self.variance*X*(1./denom*(1. - arg)*dL_dKdiag/(np.sqrt(1-arg*arg)))[:, None]
def _K_computations(self, X, X2):
"""Pre-computations for the covariance matrix (used for computing the covariance and its gradients."""
if self.ARD:
pass
if X2 is None:
self._K_inner_prod = np.dot(X,X.T)
self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
vec = np.diag(self._K_numer) + 1.
self._K_denom = np.sqrt(np.outer(vec,vec))
else:
if X2 is None:
self._K_inner_prod = np.dot(X,X.T)
self._K_numer = self._K_inner_prod*self.weight_variance+self.bias_variance
vec = np.diag(self._K_numer) + 1.
self._K_denom = np.sqrt(np.outer(vec,vec))
self._K_asin_arg = self._K_numer/self._K_denom
self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
else:
self._K_inner_prod = np.dot(X,X2.T)
self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
vec1 = (X*X).sum(1)*self.weight_variance + self.bias_variance + 1.
vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
self._K_denom = np.sqrt(np.outer(vec1,vec2))
self._K_asin_arg = self._K_numer/self._K_denom
self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
self._K_inner_prod = np.dot(X,X2.T)
self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
vec1 = (X*X).sum(1)*self.weight_variance + self.bias_variance + 1.
vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
self._K_denom = np.sqrt(np.outer(vec1,vec2))
self._K_asin_arg = self._K_numer/self._K_denom
self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
def _K_diag_computations(self, X):
"""Pre-computations concerning the diagonal terms (used for computation of diagonal and its gradients)."""
if self.ARD:
pass
else:
self._K_diag_numer = (X*X).sum(1)*self.weight_variance + self.bias_variance
self._K_diag_denom = self._K_diag_numer+1.
self._K_diag_asin_arg = self._K_diag_numer/self._K_diag_denom
self._K_diag_dvar = four_over_tau*np.arcsin(self._K_diag_asin_arg)
self._K_diag_numer = (X*X).sum(1)*self.weight_variance + self.bias_variance
self._K_diag_denom = self._K_diag_numer+1.
self._K_diag_asin_arg = self._K_diag_numer/self._K_diag_denom
self._K_diag_dvar = four_over_tau*np.arcsin(self._K_diag_asin_arg)

435
GPy/kern/_src/periodic_Matern52.py → GPy/kern/_src/periodic.py
View file

@ -2,12 +2,287 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
from kern import Kern
from ...util.linalg import mdot
from ...util.decorators import silence_errors
from ...core.parameterization.param import Param
from ...core.parameterization.transformations import Logexp
class PeriodicMatern52(Kernpart):
class Periodic(Kern):
def __init__(self, input_dim, variance, lengthscale, period, n_freq, lower, upper, name):
"""
:type input_dim: int
:param variance: the variance of the Matern kernel
:type variance: float
:param lengthscale: the lengthscale of the Matern kernel
:type lengthscale: np.ndarray of size (input_dim,)
:param period: the period
:type period: float
:param n_freq: the number of frequencies considered for the periodic subspace
:type n_freq: int
:rtype: kernel object
"""
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
super(Periodic, self).__init__(input_dim, name)
self.input_dim = input_dim
self.lower,self.upper = lower, upper
self.n_freq = n_freq
self.n_basis = 2*n_freq
self.variance = Param('variance', np.float64(variance), Logexp())
self.lengthscale = Param('lengthscale', np.float64(lengthscale), Logexp())
self.period = Param('period', np.float64(period), Logexp())
self.add_parameters(self.variance, self.lengthscale, self.period)
self.parameters_changed()
def _cos(self, alpha, omega, phase):
def f(x):
return alpha*np.cos(omega*x + phase)
return f
@silence_errors
def _cos_factorization(self, alpha, omega, phase):
r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None]
r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None]
r = np.sqrt(r1**2 + r2**2)
psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2))
return r,omega[:,0:1], psi
@silence_errors
def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2):
Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) )
Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower)
Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1)
return Gint
def K(self, X, X2=None):
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
if X2 is None:
FX2 = FX
else:
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
return mdot(FX,self.Gi,FX2.T)
def Kdiag(self,X):
return np.diag(self.K(X))
class PeriodicExponential(Periodic):
"""
Kernel of the periodic subspace (up to a given frequency) of a exponential
(Matern 1/2) RKHS.
Only defined for input_dim=1.
"""
def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, name='periodic_exponential'):
super(PeriodicExponential, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, name)
def parameters_changed(self):
self.a = [1./self.lengthscale, 1.]
self.b = [1]
self.basis_alpha = np.ones((self.n_basis,))
self.basis_omega = np.array(sum([[i*2*np.pi/self.period]*2 for i in range(1,self.n_freq+1)],[]))[:,0]
self.basis_phi = np.array(sum([[-np.pi/2, 0.] for i in range(1,self.n_freq+1)],[]))
self.G = self.Gram_matrix()
self.Gi = np.linalg.inv(self.G)
def Gram_matrix(self):
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
Lo = np.column_stack((self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
return(self.lengthscale/(2*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T))
#@silence_errors
def update_gradients_full(self, dL_dK, X, X2=None):
"""derivative of the covariance matrix with respect to the parameters (shape is N x num_inducing x num_params)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
Lo = np.column_stack((self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
#dK_dlen
da_dlen = [-1./self.lengthscale**2,0.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = 1./2*Gint + self.lengthscale/2*dGint_dlen
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
# SIMPLIFY!!! IPPprim1 = (self.upper - self.lower)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
IPPprim = np.where(np.logical_or(np.isnan(IPPprim1), np.isinf(IPPprim1)), IPPprim2, IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
#IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2))
r2,omega2,phi2 = dLa_dper2.T,Lo[:,0:1],dLp_dper2.T
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale/2*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)))
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
self.variance.gradient = np.sum(dK_dvar*dL_dK)
self.lengthscale.gradient = np.sum(dK_dlen*dL_dK)
self.period.gradient = np.sum(dK_dper*dL_dK)
class PeriodicMatern32(Periodic):
"""
Kernel of the periodic subspace (up to a given frequency) of a Matern 3/2 RKHS. Only defined for input_dim=1.
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance: the variance of the Matern kernel
:type variance: float
:param lengthscale: the lengthscale of the Matern kernel
:type lengthscale: np.ndarray of size (input_dim,)
:param period: the period
:type period: float
:param n_freq: the number of frequencies considered for the periodic subspace
:type n_freq: int
:rtype: kernel object
"""
def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, name='periodic_Matern32'):
super(PeriodicMatern32, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, name)
def parameters_changed(self):
self.a = [3./self.lengthscale**2, 2*np.sqrt(3)/self.lengthscale, 1.]
self.b = [1,self.lengthscale**2/3]
self.basis_alpha = np.ones((self.n_basis,))
self.basis_omega = np.array(sum([[i*2*np.pi/self.period]*2 for i in range(1,self.n_freq+1)],[]))
self.basis_phi = np.array(sum([[-np.pi/2, 0.] for i in range(1,self.n_freq+1)],[]))
self.G = self.Gram_matrix()
self.Gi = np.linalg.inv(self.G)
def Gram_matrix(self):
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2))
Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
return(self.lengthscale**3/(12*np.sqrt(3)*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscale**2/(3.*self.variance)*np.dot(F1lower,F1lower.T))
@silence_errors
def update_gradients_full(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is num_data x num_inducing x num_params)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2))
Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
#dK_dlen
da_dlen = [-6/self.lengthscale**3,-2*np.sqrt(3)/self.lengthscale**2,0.]
db_dlen = [0.,2*self.lengthscale/3.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega,da_dlen[2]*self.basis_omega**2))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = self.lengthscale**2/(4*np.sqrt(3))*Gint + self.lengthscale**3/(12*np.sqrt(3))*dGint_dlen + db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F1lower,F1lower.T)
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale**3/(12*np.sqrt(3))*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)) + self.b[1]*(np.dot(dF1lower_dper,F1lower.T)+np.dot(F1lower,dF1lower_dper.T)))
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
self.variance.gradient = np.sum(dK_dvar*dL_dK)
self.lengthscale.gradient = np.sum(dK_dlen*dL_dK)
self.period.gradient = np.sum(dK_dper*dL_dK)
class PeriodicMatern52(Periodic):
"""
Kernel of the periodic subspace (up to a given frequency) of a Matern 5/2 RKHS. Only defined for input_dim=1.
@ -25,53 +300,10 @@ class PeriodicMatern52(Kernpart):
"""
def __init__(self,input_dim=1,variance=1.,lengthscale=None,period=2*np.pi,n_freq=10,lower=0.,upper=4*np.pi):
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
self.name = 'periodic_Mat52'
self.input_dim = input_dim
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == 1, "Wrong size: only one lengthscale needed"
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self._set_params(np.hstack((variance,lengthscale,period)))
def _cos(self,alpha,omega,phase):
def f(x):
return alpha*np.cos(omega*x+phase)
return f
@silence_errors
def _cos_factorization(self,alpha,omega,phase):
r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None]
r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None]
r = np.sqrt(r1**2 + r2**2)
psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2))
return r,omega[:,0:1], psi
@silence_errors
def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2):
Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) )
Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower)
#Gint2[0,0] = 2.*(self.upper-self.lower)*np.cos(phi1[0,0])*np.cos(phi2[0,0])
Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1)
return Gint
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale,self.period))
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size==3
self.variance = x[0]
self.lengthscale = x[1]
self.period = x[2]
def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, name='periodic_Matern52'):
super(PeriodicMatern52, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, name)
def parameters_changed(self):
self.a = [5*np.sqrt(5)/self.lengthscale**3, 15./self.lengthscale**2,3*np.sqrt(5)/self.lengthscale, 1.]
self.b = [9./8, 9*self.lengthscale**4/200., 3*self.lengthscale**2/5., 3*self.lengthscale**2/(5*8.), 3*self.lengthscale**2/(5*8.)]
@ -82,10 +314,6 @@ class PeriodicMatern52(Kernpart):
self.G = self.Gram_matrix()
self.Gi = np.linalg.inv(self.G)
def _get_param_names(self):
"""return parameter names."""
return ['variance','lengthscale','period']
def Gram_matrix(self):
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)), self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2, self.a[3]*self.basis_omega**3))
Lo = np.column_stack((self.basis_omega, self.basis_omega, self.basis_omega, self.basis_omega))
@ -99,23 +327,8 @@ class PeriodicMatern52(Kernpart):
lower_terms = self.b[0]*np.dot(Flower,Flower.T) + self.b[1]*np.dot(F2lower,F2lower.T) + self.b[2]*np.dot(F1lower,F1lower.T) + self.b[3]*np.dot(F2lower,Flower.T) + self.b[4]*np.dot(Flower,F2lower.T)
return(3*self.lengthscale**5/(400*np.sqrt(5)*self.variance) * Gint + 1./self.variance*lower_terms)
def K(self,X,X2,target):
"""Compute the covariance matrix between X and X2."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
if X2 is None:
FX2 = FX
else:
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
np.add(mdot(FX,self.Gi,FX2.T), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
@silence_errors
def _param_grad_helper(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is num_data x num_inducing x num_params)"""
def update_gradients_full(self, dL_dK, X, X2=None):
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
@ -156,14 +369,12 @@ class PeriodicMatern52(Kernpart):
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
#IPPprim2[0,0] = 2*(self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
#IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period, -3*self.a[3]*self.basis_omega**3/self.period))
@ -186,81 +397,7 @@ class PeriodicMatern52(Kernpart):
dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper)
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
# np.add(target[:,:,0],dK_dvar, target[:,:,0])
target[0] += np.sum(dK_dvar*dL_dK)
#np.add(target[:,:,1],dK_dlen, target[:,:,1])
target[1] += np.sum(dK_dlen*dL_dK)
#np.add(target[:,:,2],dK_dper, target[:,:,2])
target[2] += np.sum(dK_dper*dL_dK)
self.variance.gradient = np.sum(dK_dvar*dL_dK)
self.lengthscale.gradient = np.sum(dK_dlen*dL_dK)
self.period.gradient = np.sum(dK_dper*dL_dK)
@silence_errors
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)), self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2, self.a[3]*self.basis_omega**3))
Lo = np.column_stack((self.basis_omega, self.basis_omega, self.basis_omega, self.basis_omega))
Lp = np.column_stack((self.basis_phi, self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
F2lower = np.array(self._cos(self.basis_alpha*self.basis_omega**2,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1. / self.variance * mdot(FX, self.Gi, FX.T)
#dK_dlen
da_dlen = [-3*self.a[0]/self.lengthscale, -2*self.a[1]/self.lengthscale, -self.a[2]/self.lengthscale, 0.]
db_dlen = [0., 4*self.b[1]/self.lengthscale, 2*self.b[2]/self.lengthscale, 2*self.b[3]/self.lengthscale, 2*self.b[4]/self.lengthscale]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)), da_dlen[1]*self.basis_omega, da_dlen[2]*self.basis_omega**2, da_dlen[3]*self.basis_omega**3))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dlower_terms_dlen = db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F2lower,F2lower.T) + db_dlen[2]*np.dot(F1lower,F1lower.T) + db_dlen[3]*np.dot(F2lower,Flower.T) + db_dlen[4]*np.dot(Flower,F2lower.T)
dG_dlen = 15*self.lengthscale**4/(400*np.sqrt(5))*Gint + 3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dlen + dlower_terms_dlen
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period, -self.a[3]*self.basis_omega**4/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2,self.basis_phi))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + .5*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + .5*self.lower**2*np.cos(phi-phi1.T)
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period, -3*self.a[3]*self.basis_omega**3/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2))
r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dF2lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**3/self.period,self.basis_omega,self.basis_phi+np.pi*3/2)(self.lower) + self._cos(-2*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None]
dlower_terms_dper = self.b[0] * (np.dot(dFlower_dper,Flower.T) + np.dot(Flower.T,dFlower_dper))
dlower_terms_dper += self.b[1] * (np.dot(dF2lower_dper,F2lower.T) + np.dot(F2lower,dF2lower_dper.T)) - 4*self.b[1]/self.period*np.dot(F2lower,F2lower.T)
dlower_terms_dper += self.b[2] * (np.dot(dF1lower_dper,F1lower.T) + np.dot(F1lower,dF1lower_dper.T)) - 2*self.b[2]/self.period*np.dot(F1lower,F1lower.T)
dlower_terms_dper += self.b[3] * (np.dot(dF2lower_dper,Flower.T) + np.dot(F2lower,dFlower_dper.T)) - 2*self.b[3]/self.period*np.dot(F2lower,Flower.T)
dlower_terms_dper += self.b[4] * (np.dot(dFlower_dper,F2lower.T) + np.dot(Flower,dF2lower_dper.T)) - 2*self.b[4]/self.period*np.dot(Flower,F2lower.T)
dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper)
dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

248
GPy/kern/_src/periodic_Matern32.py
View file

@ -1,248 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
class PeriodicMatern32(Kernpart):
"""
Kernel of the periodic subspace (up to a given frequency) of a Matern 3/2 RKHS. Only defined for input_dim=1.
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance: the variance of the Matern kernel
:type variance: float
:param lengthscale: the lengthscale of the Matern kernel
:type lengthscale: np.ndarray of size (input_dim,)
:param period: the period
:type period: float
:param n_freq: the number of frequencies considered for the periodic subspace
:type n_freq: int
:rtype: kernel object
"""
def __init__(self, input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
self.name = 'periodic_Mat32'
self.input_dim = input_dim
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == 1, "Wrong size: only one lengthscale needed"
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self._set_params(np.hstack((variance,lengthscale,period)))
def _cos(self,alpha,omega,phase):
def f(x):
return alpha*np.cos(omega*x+phase)
return f
@silence_errors
def _cos_factorization(self,alpha,omega,phase):
r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None]
r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None]
r = np.sqrt(r1**2 + r2**2)
psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2))
return r,omega[:,0:1], psi
@silence_errors
def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2):
Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) )
Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower)
#Gint2[0,0] = 2.*(self.upper-self.lower)*np.cos(phi1[0,0])*np.cos(phi2[0,0])
Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1)
return Gint
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale,self.period))
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size==3
self.variance = x[0]
self.lengthscale = x[1]
self.period = x[2]
self.a = [3./self.lengthscale**2, 2*np.sqrt(3)/self.lengthscale, 1.]
self.b = [1,self.lengthscale**2/3]
self.basis_alpha = np.ones((self.n_basis,))
self.basis_omega = np.array(sum([[i*2*np.pi/self.period]*2 for i in range(1,self.n_freq+1)],[]))
self.basis_phi = np.array(sum([[-np.pi/2, 0.] for i in range(1,self.n_freq+1)],[]))
self.G = self.Gram_matrix()
self.Gi = np.linalg.inv(self.G)
def _get_param_names(self):
"""return parameter names."""
return ['variance','lengthscale','period']
def Gram_matrix(self):
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2))
Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
return(self.lengthscale**3/(12*np.sqrt(3)*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscale**2/(3.*self.variance)*np.dot(F1lower,F1lower.T))
def K(self,X,X2,target):
"""Compute the covariance matrix between X and X2."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
if X2 is None:
FX2 = FX
else:
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
np.add(mdot(FX,self.Gi,FX2.T), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
@silence_errors
def _param_grad_helper(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is num_data x num_inducing x num_params)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2))
Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
#dK_dlen
da_dlen = [-6/self.lengthscale**3,-2*np.sqrt(3)/self.lengthscale**2,0.]
db_dlen = [0.,2*self.lengthscale/3.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega,da_dlen[2]*self.basis_omega**2))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = self.lengthscale**2/(4*np.sqrt(3))*Gint + self.lengthscale**3/(12*np.sqrt(3))*dGint_dlen + db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F1lower,F1lower.T)
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
#IPPprim2[0,0] = 2*(self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
#IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale**3/(12*np.sqrt(3))*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)) + self.b[1]*(np.dot(dF1lower_dper,F1lower.T)+np.dot(F1lower,dF1lower_dper.T)))
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
# np.add(target[:,:,0],dK_dvar, target[:,:,0])
target[0] += np.sum(dK_dvar*dL_dK)
#np.add(target[:,:,1],dK_dlen, target[:,:,1])
target[1] += np.sum(dK_dlen*dL_dK)
#np.add(target[:,:,2],dK_dper, target[:,:,2])
target[2] += np.sum(dK_dper*dL_dK)
@silence_errors
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2))
Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX.T)
#dK_dlen
da_dlen = [-6/self.lengthscale**3,-2*np.sqrt(3)/self.lengthscale**2,0.]
db_dlen = [0.,2*self.lengthscale/3.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega,da_dlen[2]*self.basis_omega**2))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = self.lengthscale**2/(4*np.sqrt(3))*Gint + self.lengthscale**3/(12*np.sqrt(3))*dGint_dlen + db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F1lower,F1lower.T)
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale**3/(12*np.sqrt(3))*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)) + self.b[1]*(np.dot(dF1lower_dper,F1lower.T)+np.dot(F1lower,dF1lower_dper.T)))
dK_dper = 2* mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

237
GPy/kern/_src/periodic_exponential.py
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@ -1,237 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
from GPy.core.parameterization.param import Param
class PeriodicExponential(Kernpart):
"""
Kernel of the periodic subspace (up to a given frequency) of a exponential (Matern 1/2) RKHS. Only defined for input_dim=1.
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance: the variance of the Matern kernel
:type variance: float
:param lengthscale: the lengthscale of the Matern kernel
:type lengthscale: np.ndarray of size (input_dim,)
:param period: the period
:type period: float
:param n_freq: the number of frequencies considered for the periodic subspace
:type n_freq: int
:rtype: kernel object
"""
def __init__(self, input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi, name='periodic_exp'):
super(PeriodicExponential, self).__init__(input_dim, name)
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
self.input_dim = input_dim
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == 1, "Wrong size: only one lengthscale needed"
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self.variance = Param('variance', variance)
self.lengthscale = Param('lengthscale', lengthscale)
self.period = Param('period', period)
self.parameters_changed()
#self._set_params(np.hstack((variance,lengthscale,period)))
def _cos(self,alpha,omega,phase):
def f(x):
return alpha*np.cos(omega*x+phase)
return f
@silence_errors
def _cos_factorization(self,alpha,omega,phase):
r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None]
r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None]
r = np.sqrt(r1**2 + r2**2)
psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2))
return r,omega[:,0:1], psi
@silence_errors
def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2):
Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) )
Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower)
#Gint2[0,0] = 2.*(self.upper-self.lower)*np.cos(phi1[0,0])*np.cos(phi2[0,0])
Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1)
return Gint
#def _get_params(self):
# """return the value of the parameters."""
# return np.hstack((self.variance,self.lengthscale,self.period))
def parameters_changed(self):
"""set the value of the parameters."""
self.a = [1./self.lengthscale, 1.]
self.b = [1]
self.basis_alpha = np.ones((self.n_basis,))
self.basis_omega = np.array(sum([[i*2*np.pi/self.period]*2 for i in range(1,self.n_freq+1)],[]))[:,0]
self.basis_phi = np.array(sum([[-np.pi/2, 0.] for i in range(1,self.n_freq+1)],[]))
self.G = self.Gram_matrix()
self.Gi = np.linalg.inv(self.G)
#def _get_param_names(self):
# """return parameter names."""
# return ['variance','lengthscale','period']
def Gram_matrix(self):
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
Lo = np.column_stack((self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
return(self.lengthscale/(2*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T))
def K(self,X,X2,target):
"""Compute the covariance matrix between X and X2."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
if X2 is None:
FX2 = FX
else:
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
np.add(mdot(FX,self.Gi,FX2.T), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target)
@silence_errors
def _param_grad_helper(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is N x num_inducing x num_params)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
Lo = np.column_stack((self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
#dK_dlen
da_dlen = [-1./self.lengthscale**2,0.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = 1./2*Gint + self.lengthscale/2*dGint_dlen
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
#IPPprim2[0,0] = 2*(self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
#IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0])
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2))
r2,omega2,phi2 = dLa_dper2.T,Lo[:,0:1],dLp_dper2.T
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale/2*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)))
dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
target[0] += np.sum(dK_dvar*dL_dK)
target[1] += np.sum(dK_dlen*dL_dK)
target[2] += np.sum(dK_dper*dL_dK)
@silence_errors
def dKdiag_dtheta(self,dL_dKdiag,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
Lo = np.column_stack((self.basis_omega,self.basis_omega))
Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
r,omega,phi = self._cos_factorization(La,Lo,Lp)
Gint = self._int_computation( r,omega,phi, r,omega,phi)
Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX.T)
#dK_dlen
da_dlen = [-1./self.lengthscale**2,0.]
dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega))
r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
dGint_dlen = dGint_dlen + dGint_dlen.T
dG_dlen = 1./2*Gint + self.lengthscale/2*dGint_dlen
dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
#dK_dper
dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period))
dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period))
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2))
r2,omega2,phi2 = dLa_dper2.T,Lo[:,0:1],dLp_dper2.T
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
dGint_dper = dGint_dper + dGint_dper.T
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
dG_dper = 1./self.variance*(self.lengthscale/2*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)))
dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag)
target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag)
target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag)

101
GPy/kern/_src/prod_orthogonal.py
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@ -1,101 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
import numpy as np
import hashlib
#from scipy import integrate # This may not be necessary (Nicolas, 20th Feb)
class prod_orthogonal(Kernpart):
"""
Computes the product of 2 kernels
:param k1, k2: the kernels to multiply
:type k1, k2: Kernpart
:rtype: kernel object
"""
def __init__(self,k1,k2):
self.input_dim = k1.input_dim + k2.input_dim
self.num_params = k1.num_params + k2.num_params
self.name = k1.name + '<times>' + k2.name
self.k1 = k1
self.k2 = k2
self._X, self._X2, self._params = np.empty(shape=(3,1))
self._set_params(np.hstack((k1._get_params(),k2._get_params())))
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.k1._get_params(), self.k2._get_params()))
def _set_params(self,x):
"""set the value of the parameters."""
self.k1._set_params(x[:self.k1.num_params])
self.k2._set_params(x[self.k1.num_params:])
def _get_param_names(self):
"""return parameter names."""
return [self.k1.name + '_' + param_name for param_name in self.k1._get_param_names()] + [self.k2.name + '_' + param_name for param_name in self.k2._get_param_names()]
def K(self,X,X2,target):
self._K_computations(X,X2)
target += self._K1 * self._K2
def _param_grad_helper(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
self._K_computations(X,X2)
if X2 is None:
self.k1._param_grad_helper(dL_dK*self._K2, X[:,:self.k1.input_dim], None, target[:self.k1.num_params])
self.k2._param_grad_helper(dL_dK*self._K1, X[:,self.k1.input_dim:], None, target[self.k1.num_params:])
else:
self.k1._param_grad_helper(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target[:self.k1.num_params])
self.k2._param_grad_helper(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target[self.k1.num_params:])
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
target1 = np.zeros(X.shape[0])
target2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,:self.k1.input_dim],target1)
self.k2.Kdiag(X[:,self.k1.input_dim:],target2)
target += target1 * target2
def dKdiag_dtheta(self,dL_dKdiag,X,target):
K1 = np.zeros(X.shape[0])
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,:self.k1.input_dim],K1)
self.k2.Kdiag(X[:,self.k1.input_dim:],K2)
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,:self.k1.input_dim],target[:self.k1.num_params])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.k1.input_dim:],target[self.k1.num_params:])
def gradients_X(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
self._K_computations(X,X2)
self.k1.gradients_X(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target)
self.k2.gradients_X(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target)
def dKdiag_dX(self, dL_dKdiag, X, target):
K1 = np.zeros(X.shape[0])
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,0:self.k1.input_dim],K1)
self.k2.Kdiag(X[:,self.k1.input_dim:],K2)
self.k1.gradients_X(dL_dKdiag*K2, X[:,:self.k1.input_dim], target)
self.k2.gradients_X(dL_dKdiag*K1, X[:,self.k1.input_dim:], target)
def _K_computations(self,X,X2):
if not (np.array_equal(X,self._X) and np.array_equal(X2,self._X2) and np.array_equal(self._params , self._get_params())):
self._X = X.copy()
self._params == self._get_params().copy()
if X2 is None:
self._X2 = None
self._K1 = np.zeros((X.shape[0],X.shape[0]))
self._K2 = np.zeros((X.shape[0],X.shape[0]))
self.k1.K(X[:,:self.k1.input_dim],None,self._K1)
self.k2.K(X[:,self.k1.input_dim:],None,self._K2)
else:
self._X2 = X2.copy()
self._K1 = np.zeros((X.shape[0],X2.shape[0]))
self._K2 = np.zeros((X.shape[0],X2.shape[0]))
self.k1.K(X[:,:self.k1.input_dim],X2[:,:self.k1.input_dim],self._K1)
self.k2.K(X[:,self.k1.input_dim:],X2[:,self.k1.input_dim:],self._K2)

82
GPy/kern/_src/rational_quadratic.py
View file

@ -1,82 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import Kernpart
import numpy as np
class RationalQuadratic(Kernpart):
"""
rational quadratic kernel
.. math::
k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2 \ell^2} \\bigg)^{- \\alpha} \ \ \ \ \ \\text{ where } r^2 = (x-y)^2
:param input_dim: the number of input dimensions
:type input_dim: int (input_dim=1 is the only value currently supported)
:param variance: the variance :math:`\sigma^2`
:type variance: float
:param lengthscale: the lengthscale :math:`\ell`
:type lengthscale: float
:param power: the power :math:`\\alpha`
:type power: float
:rtype: Kernpart object
"""
def __init__(self,input_dim,variance=1.,lengthscale=1.,power=1.):
assert input_dim == 1, "For this kernel we assume input_dim=1"
self.input_dim = input_dim
self.num_params = 3
self.name = 'rat_quad'
self.variance = variance
self.lengthscale = lengthscale
self.power = power
def _get_params(self):
return np.hstack((self.variance,self.lengthscale,self.power))
def _set_params(self,x):
self.variance = x[0]
self.lengthscale = x[1]
self.power = x[2]
def _get_param_names(self):
return ['variance','lengthscale','power']
def K(self,X,X2,target):
if X2 is None: X2 = X
dist2 = np.square((X-X2.T)/self.lengthscale)
target += self.variance*(1 + dist2/2.)**(-self.power)
def Kdiag(self,X,target):
target += self.variance
def _param_grad_helper(self,dL_dK,X,X2,target):
if X2 is None: X2 = X
dist2 = np.square((X-X2.T)/self.lengthscale)
dvar = (1 + dist2/2.)**(-self.power)
dl = self.power * self.variance * dist2 / self.lengthscale * (1 + dist2/2.)**(-self.power-1)
dp = - self.variance * np.log(1 + dist2/2.) * (1 + dist2/2.)**(-self.power)
target[0] += np.sum(dvar*dL_dK)
target[1] += np.sum(dl*dL_dK)
target[2] += np.sum(dp*dL_dK)
def dKdiag_dtheta(self,dL_dKdiag,X,target):
target[0] += np.sum(dL_dKdiag)
# here self.lengthscale and self.power have no influence on Kdiag so target[1:] are unchanged
def gradients_X(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None:
dist2 = np.square((X-X.T)/self.lengthscale)
dX = -2.*self.variance*self.power * (X-X.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1)
else:
dist2 = np.square((X-X2.T)/self.lengthscale)
dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1)
target += np.sum(dL_dK*dX,1)[:,np.newaxis]
def dKdiag_dX(self,dL_dKdiag,X,target):
pass

92
GPy/kern/_src/bias.py → GPy/kern/_src/static.py
View file

@ -7,11 +7,66 @@ from ...core.parameterization import Param
from ...core.parameterization.transformations import Logexp
import numpy as np
class Bias(Kern):
def __init__(self,input_dim,variance=1.,name=None):
class Static(Kern):
def __init__(self, input_dim, variance, name):
super(Static, self).__init__(input_dim, name)
self.variance = Param('variance', variance, Logexp())
self.add_parameters(self.variance)
def Kdiag(self, X):
ret = np.empty((X.shape[0],), dtype=np.float64)
ret[:] = self.variance
return ret
def gradients_X(self, dL_dK, X, X2, target):
return np.zeros(X.shape)
def gradients_X_diag(self, dL_dKdiag, X, target):
return np.zeros(X.shape)
def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
return np.zeros(Z.shape)
def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
return np.zeros(mu.shape), np.zeros(S.shape)
def psi0(self, Z, mu, S):
return self.Kdiag(mu)
def psi1(self, Z, mu, S, target):
return self.K(mu, Z)
def psi2(Z, mu, S):
K = self.K(mu, Z)
return K[:,:,None]*K[:,None,:] # NB. more efficient implementations on inherriting classes
class White(Static):
def __init__(self, input_dim, variance=1., name='white'):
super(White, self).__init__(input_dim, name)
def K(self, X, X2=None):
if X2 is None:
return np.eye(X.shape[0])*self.variance
else:
return np.zeros((X.shape[0], X2.shape[0]))
def psi2(self, Z, mu, S, target):
return np.zeros((mu.shape[0], Z.shape[0], Z.shape[0]), dtype=np.float64)
def update_gradients_full(self, dL_dK, X):
self.variance.gradient = np.trace(dL_dK)
def update_gradients_diag(self, dL_dKdiag, X):
self.variance.gradient = dL_dKdiag.sum()
def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
self.variance.gradient = np.trace(dL_dKmm) + dL_dpsi0.sum()
class Bias(Static):
def __init__(self, input_dim, variance=1., name='bias'):
super(Bias, self).__init__(input_dim, name)
self.variance = Param("variance", variance, Logexp())
self.add_parameter(self.variance)
def K(self, X, X2=None):
shape = (X.shape[0], X.shape[0] if X2 is None else X2.shape[0])
@ -19,33 +74,11 @@ class Bias(Kern):
ret[:] = self.variance
return ret
def Kdiag(self,X):
ret = np.empty((X.shape[0],), dtype=np.float64)
ret[:] = self.variance
return ret
def update_gradients_full(self, dL_dK, X, X2=None):
self.variance.gradient = dL_dK.sum()
def update_gradients_diag(self, dL_dKdiag, X):
self.variance.gradient = dL_dKdiag.sum()
def gradients_X(self, dL_dK,X, X2):
return np.zeros(X.shape)
def gradients_X_diag(self,dL_dKdiag,X):
return np.zeros(X.shape)
#---------------------------------------#
# PSI statistics #
#---------------------------------------#
def psi0(self, Z, mu, S):
return self.Kdiag(mu)
def psi1(self, Z, mu, S, target):
return self.K(mu, S)
self.variance.gradient = dL_dK.sum()
def psi2(self, Z, mu, S, target):
ret = np.empty((mu.shape[0], Z.shape[0], Z.shape[0]), dtype=np.float64)
@ -55,8 +88,3 @@ class Bias(Kern):
def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
self.variance.gradient = dL_dKmm.sum() + dL_dpsi0.sum() + dL_dpsi1.sum() + 2.*self.variance*dL_dpsi2.sum()
def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
return np.zeros(Z.shape)
def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
return np.zeros(mu.shape), np.zeros(S.shape)

136
GPy/kern/_src/stationary.py
View file

@ -32,6 +32,13 @@ class Stationary(Kern):
assert self.variance.size==1
self.add_parameters(self.variance, self.lengthscale)
def K_of_r(self, r):
raise NotImplementedError, "implement the covaraiance functino and a fn of r to use this class"
def K(self, X, X2=None):
r = self._scaled_dist(X, X2)
return self.K_of_r(r)
def _dist(self, X, X2):
if X2 is None:
X2 = X
@ -50,11 +57,11 @@ class Stationary(Kern):
self.lengthscale.gradient = 0.
def update_gradients_full(self, dL_dK, X, X2=None):
K = self.K(X, X2)
self.variance.gradient = np.sum(K * dL_dK)/self.variance
r = self._scaled_dist(X, X2)
K = self.K_of_r(r)
rinv = self._inv_dist(X, X2)
dL_dr = self.dK_dr(X, X2) * dL_dK
dL_dr = self.dK_dr(r) * dL_dK
x_xl3 = np.square(self._dist(X, X2)) / self.lengthscale**3
if self.ARD:
@ -62,6 +69,8 @@ class Stationary(Kern):
else:
self.lengthscale.gradient = -((dL_dr*rinv)[:,:,None]*x_xl3).sum()
self.variance.gradient = np.sum(K * dL_dK)/self.variance
def _inv_dist(self, X, X2=None):
dist = self._scaled_dist(X, X2)
if X2 is None:
@ -72,7 +81,8 @@ class Stationary(Kern):
return 1./np.where(dist != 0., dist, np.inf)
def gradients_X(self, dL_dK, X, X2=None):
dL_dr = self.dK_dr(X, X2) * dL_dK
r = self._scaled_dist(X, X2)
dL_dr = self.dK_dr(r) * dL_dK
invdist = self._inv_dist(X, X2)
ret = np.sum((invdist*dL_dr)[:,:,None]*self._dist(X, X2),1)/self.lengthscale**2
if X2 is None:
@ -82,19 +92,65 @@ class Stationary(Kern):
def gradients_X_diag(self, dL_dKdiag, X):
return np.zeros(X.shape)
def add(self, other, tensor=False):
if not tensor:
return StatAdd(self, other)
else:
return super(Stationary, self).add(other, tensor)
def prod(self, other, tensor=False):
if not tensor:
return StatProd(self, other)
else:
return super(Stationary, self).prod(other, tensor)
class StatAdd(Stationary):
"""
Addition of two Stationary kernels on the same space is still stationary.
If you need to add two (stationary) kernels on separate spaces, use the generic add class.
"""
def __init__(self, k1, k2):
assert isinstance(k1, Stationary)
assert isinstance(k2, Stationary)
self.k1, self.k2 = k1, k2
self.add_parameters(k1, k2)
def K_of_r(self, r):
return self.k1.K(r) + self.k2.K(r)
def dK_dr(self, r):
return self.k1.dK_dr + self.k2.dK_dr(r)
class StatProd(Stationary):
"""
Product of two Stationary kernels on the same space is still stationary.
If you need to multiply two (stationary) kernels on separate spaces, use the generic Prod class.
"""
def __init__(self, k1, k2):
assert isinstance(k1, Stationary)
assert isinstance(k2, Stationary)
self.k1, self.k2 = k1, k2
self.add_parameters(k1, k2)
def K_of_r(self, r):
return self.k1.K(r) * self.k2.K(r)
def dK_dr(self, r):
return self.k1.dK_dr(r) * self.k2.K_of_r(r) + self.k2.dK_dr(r) * self.k1.K_of_r(r)
class Exponential(Stationary):
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='Exponential'):
super(Exponential, self).__init__(input_dim, variance, lengthscale, ARD, name)
def K(self, X, X2=None):
dist = self._scaled_dist(X, X2)
return self.variance * np.exp(-0.5 * dist)
def dK_dr(self, X, X2):
return -0.5*self.K(X, X2)
def dK_dr(self, r):
return -0.5*self.K_of_r(r)
class Matern32(Stationary):
"""
@ -109,13 +165,11 @@ class Matern32(Stationary):
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='Mat32'):
super(Matern32, self).__init__(input_dim, variance, lengthscale, ARD, name)
def K(self, X, X2=None):
dist = self._scaled_dist(X, X2)
return self.variance * (1. + np.sqrt(3.) * dist) * np.exp(-np.sqrt(3.) * dist)
def K_of_r(self, r):
return self.variance * (1. + np.sqrt(3.) * r) * np.exp(-np.sqrt(3.) * r)
def dK_dr(self, X, X2):
dist = self._scaled_dist(X, X2)
return -3.*self.variance*dist*np.exp(-np.sqrt(3.)*dist)
def dK_dr(self,r):
return -3.*self.variance*r*np.exp(-np.sqrt(3.)*r)
def Gram_matrix(self, F, F1, F2, lower, upper):
"""
@ -153,12 +207,10 @@ class Matern52(Stationary):
k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} }
"""
def K(self, X, X2=None):
r = self._scaled_dist(X, X2)
def K_of_r(self, r):
return self.variance*(1+np.sqrt(5.)*r+5./3*r**2)*np.exp(-np.sqrt(5.)*r)
def dK_dr(self, X, X2):
r = self._scaled_dist(X, X2)
def dK_dr(self, r):
return self.variance*(10./3*r -5.*r -5.*np.sqrt(5.)/3*r**2)*np.exp(-np.sqrt(5.)*r)
def Gram_matrix(self,F,F1,F2,F3,lower,upper):
@ -193,19 +245,55 @@ class Matern52(Stationary):
return(1./self.variance* (G_coef*G + orig + orig2))
class ExpQuad(Stationary):
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='ExpQuad'):
super(ExpQuad, self).__init__(input_dim, variance, lengthscale, ARD, name)
def K(self, X, X2=None):
r = self._scaled_dist(X, X2)
def K_of_r(self, r):
return self.variance * np.exp(-0.5 * r**2)
def dK_dr(self, X, X2):
dist = self._scaled_dist(X, X2)
return -dist*self.K(X, X2)
def dK_dr(self, r):
return -r*self.K_of_r(r)
class Cosine(Stationary):
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='Cosine'):
super(Cosine, self).__init__(input_dim, variance, lengthscale, ARD, name)
def K_of_r(self, r)
return self.variance * np.cos(r)
def dK_dr(self, r):
return -self.variance * np.sin(r)
class RatQuad(Stationary):
"""
Rational Quadratic Kernel
.. math::
k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \\alpha}
"""
def __init__(self, input_dim, variance=1., lengthscale=None, power=2., ARD=False, name='ExpQuad'):
super(RatQuad, self).__init__(input_dim, variance, lengthscale, ARD, name)
self.power = Param('power', power, Logexp())
self.add_parameters(self.power)
def K_of_r(self, r)
return self.variance*(1. + r**2/2.)**(-self.power)
def dK_dr(self, r):
return -self.variance*self.power*r*(1. + r**2/2)**(-self.power - 1.)
def update_gradients_full(self, dL_dK, X, X2=None):
super(RatQuad, self).update_gradients_full(dL_dK, X, X2)
r = self._scaled_dist(X, X2)
r2 = r**2
dpow = -2.**self.power*(r2 + 2.)**(-self.power)*np.log(0.5*(r2+2.))
self.power.gradient = np.sum(dL_dK*dpow)

78
GPy/kern/_src/white.py
View file

@ -1,78 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kern import Kern
import numpy as np
from ...core.parameterization import Param
from ...core.parameterization.transformations import Logexp
class White(Kern):
"""
White noise kernel.
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance:
:type variance: float
"""
def __init__(self,input_dim,variance=1., name='white'):
super(White, self).__init__(input_dim, name)
self.input_dim = input_dim
self.variance = Param('variance', variance, Logexp())
self.add_parameters(self.variance)
def K(self, X, X2=None):
if X2 is None:
return np.eye(X.shape[0])*self.variance
else:
return np.zeros((X.shape[0], X2.shape[0]))
def Kdiag(self,X):
ret = np.ones(X.shape[0])
ret[:] = self.variance
return ret
def update_gradients_full(self, dL_dK, X):
self.variance.gradient = np.trace(dL_dK)
def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
self.variance.gradient = np.trace(dL_dKmm) + np.sum(dL_dKdiag)
def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
raise NotImplementedError
def gradients_X(self,dL_dK,X,X2):
return np.zeros_like(X)
def psi0(self,Z,mu,S,target):
pass # target += self.variance
def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
pass # target += dL_dpsi0.sum()
def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S):
pass
def psi1(self,Z,mu,S,target):
pass
def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,target):
pass
def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target):
pass
def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S):
pass
def psi2(self,Z,mu,S,target):
pass
def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target):
pass
def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target):
pass
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
pass

9
GPy/plotting/matplot_dep/models_plots.py
View file

@ -57,8 +57,10 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
fig = pb.figure(num=fignum)
ax = fig.add_subplot(111)
X, Y, Z = param_to_array(model.X, model.Y, model.Z)
if model.has_uncertain_inputs(): X_variance = param_to_array(model.q.variance)
X, Y = param_to_array(model.X, model.Y)
if hasattr(model, 'has_uncertain_inputs') and model.has_uncertain_inputs(): X_variance = model.X_variance
if hasattr(model, 'Z'): Z = param_to_array(model.Z)
#work out what the inputs are for plotting (1D or 2D)
fixed_dims = np.array([i for i,v in fixed_inputs])
@ -68,8 +70,7 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
if len(free_dims) == 1:
#define the frame on which to plot
resolution = resolution or 200
Xnew, xmin, xmax = x_frame1D(X[:,free_dims], plot_limits=plot_limits)
Xnew, xmin, xmax = x_frame1D(X[:,free_dims], plot_limits=plot_limits, resolution=resolution or 200)
Xgrid = np.empty((Xnew.shape[0],model.input_dim))
Xgrid[:,free_dims] = Xnew
for i,v in fixed_inputs:

66
GPy/testing/likelihood_tests.py
View file

@ -10,6 +10,7 @@ from functools import partial
#np.random.seed(300)
#np.random.seed(7)
np.seterr(divide='raise')
def dparam_partial(inst_func, *args):
"""
If we have a instance method that needs to be called but that doesn't
@ -149,9 +150,9 @@ class TestNoiseModels(object):
noise_models = {"Student_t_default": {
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [self.var],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
#"constraints": [("t_noise", constrain_positive), ("deg_free", partial(constrain_fixed, value=5))]
},
"laplace": True
@ -159,66 +160,66 @@ class TestNoiseModels(object):
"Student_t_1_var": {
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [1.0],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Student_t_small_deg_free": {
"model": GPy.likelihoods.StudentT(deg_free=1.5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [self.var],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Student_t_small_var": {
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"vals": [0.0001],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"names": [".*t_noise"],
"vals": [0.001],
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Student_t_large_var": {
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [10.0],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Student_t_approx_gauss": {
"model": GPy.likelihoods.StudentT(deg_free=1000, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [self.var],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Student_t_log": {
"model": GPy.likelihoods.StudentT(gp_link=link_functions.Log(), deg_free=5, sigma2=self.var),
"grad_params": {
"names": ["t_noise"],
"names": [".*t_noise"],
"vals": [self.var],
"constraints": [("t_noise", constrain_positive), ("deg_free", constrain_fixed)]
"constraints": [(".*t_noise", constrain_positive), (".*deg_free", constrain_fixed)]
},
"laplace": True
},
"Gaussian_default": {
"model": GPy.likelihoods.Gaussian(variance=self.var),
"grad_params": {
"names": ["variance"],
"names": [".*variance"],
"vals": [self.var],
"constraints": [("variance", constrain_positive)]
"constraints": [(".*variance", constrain_positive)]
},
"laplace": True,
"ep": True
"ep": False # FIXME: Should be True when we have it working again
},
#"Gaussian_log": {
#"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log(), variance=self.var, D=self.D, N=self.N),
@ -252,7 +253,7 @@ class TestNoiseModels(object):
"link_f_constraints": [partial(constrain_bounded, lower=0, upper=1)],
"laplace": True,
"Y": self.binary_Y,
"ep": True
"ep": False # FIXME: Should be True when we have it working again
},
#"Exponential_default": {
#"model": GPy.likelihoods.exponential(),
@ -515,10 +516,10 @@ class TestNoiseModels(object):
#Normalize
Y = Y/Y.max()
white_var = 1e-6
kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
laplace_likelihood = GPy.inference.latent_function_inference.Laplace()
m = GPy.core.GP(X.copy(), Y.copy(), kernel, likelihood=model, inference_method=laplace_likelihood)
m['white'].constrain_fixed(white_var)
m['.*white'].constrain_fixed(white_var)
#Set constraints
for constrain_param, constraint in constraints:
@ -541,9 +542,6 @@ class TestNoiseModels(object):
#NOTE this test appears to be stochastic for some likelihoods (student t?)
# appears to all be working in test mode right now...
if not m.checkgrad():
import ipdb; ipdb.set_trace() # XXX BREAKPOINT
assert m.checkgrad(step=step)
###########
@ -555,10 +553,10 @@ class TestNoiseModels(object):
#Normalize
Y = Y/Y.max()
white_var = 1e-6
kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
ep_inf = GPy.inference.latent_function_inference.EP()
m = GPy.core.GP(X.copy(), Y.copy(), kernel=kernel, likelihood=model, inference_method=ep_inf)
m['white'].constrain_fixed(white_var)
m['.*white'].constrain_fixed(white_var)
for param_num in range(len(param_names)):
name = param_names[param_num]
@ -634,26 +632,24 @@ class LaplaceTests(unittest.TestCase):
Y = Y/Y.max()
#Yc = Y.copy()
#Yc[75:80] += 1
kernel1 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
kernel1 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
#FIXME: Make sure you can copy kernels when params is fixed
#kernel2 = kernel1.copy()
kernel2 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
kernel2 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
gauss_distr1 = GPy.likelihoods.Gaussian(variance=initial_var_guess)
exact_inf = GPy.inference.latent_function_inference.ExactGaussianInference()
m1 = GPy.core.GP(X, Y.copy(), kernel=kernel1, likelihood=gauss_distr1, inference_method=exact_inf)
m1['white'].constrain_fixed(1e-6)
m1['variance'] = initial_var_guess
m1['variance'].constrain_bounded(1e-4, 10)
m1['rbf'].constrain_bounded(1e-4, 10)
m1['.*white'].constrain_fixed(1e-6)
m1['.*rbf.variance'] = initial_var_guess
m1['.*rbf.variance'].constrain_bounded(1e-4, 10)
m1.randomize()
gauss_distr2 = GPy.likelihoods.Gaussian(variance=initial_var_guess)
laplace_inf = GPy.inference.latent_function_inference.Laplace()
m2 = GPy.core.GP(X, Y.copy(), kernel=kernel2, likelihood=gauss_distr2, inference_method=laplace_inf)
m2['white'].constrain_fixed(1e-6)
m2['rbf'].constrain_bounded(1e-4, 10)
m2['variance'].constrain_bounded(1e-4, 10)
m2['.*white'].constrain_fixed(1e-6)
m2['.*rbf.variance'].constrain_bounded(1e-4, 10)
m2.randomize()
if debug: