def logLikelihood(self,X,y,noise=None,alpha=None,variance=None,mu=None,gradient=False):
if alpha is None:
alpha=self.alpha
if variance is None:
variance=self.variance
if mu is None:
mu=self.mu
if noise is None:
K=self.A(X,alpha=alpha,variance=variance)
else:
K=self.A(X,alpha=alpha,variance=variance,noise=noise)
y2=y-mu
N=X.shape[0]
try:
L=np.linalg.cholesky(K)
alp=inverseComp(L,y2)
logLike=-0.5*np.dot(y2,alp)-np.sum(np.log(np.diag(L)))-0.5*N*np.log(2.0*np.pi)
if gradient==False:
return logLike
gradient=np.zeros(self.dimension+2)
###0 to n-1, gradient respect to alpha
###n, gradient respect to log(variance)
###n+1,gradient respect to mu
temp=np.dot(alp[:,None],alp[None,:])
K2=self.A(X,alpha=alpha,variance=variance)
for i in range(self.dimension):
derivative=np.zeros((N,N))
derivative=K2*(-0.5*(alpha[i]**2)*((X[:,i][:,None]-X[:,i][None,:])**2))
temp3=inverseComp(L,derivative)
gradient[i]=0.5*np.trace(np.dot(temp,derivative)-temp3)
der=self.K(X,alpha=alpha,variance=variance)
temp3=inverseComp(L,der)
gradient[self.dimension]=0.5*np.trace(np.dot(temp,der)-temp3)
der=np.ones((N,N))
temp3=inverseComp(L,der)
gradient[self.dimension+1]=0.5*np.trace(np.dot(temp,der)-temp3)
return logLike,gradient
except:
L=np.linalg.inv(K)
det=np.linalg.det(L)
logLike=-0.5*np.dot(y2,np.dot(L,y2))-0.5*N*np.log(2*np.pi)-0.5*np.log(det)
if gradient==False:
return logLike
gradient=np.zeros(self.dimension+2)
alp=np.dot(L,y2)
temp=np.dot(alp[:,None],alp.T[None,:])
K2=self.A(X,alpha=alpha,variance=variance)
for i in range(self.dimension):
derivative=np.zeros((N,N))
derivative=K2*(-1.0*alpha[i]*((X[:,i][:,None]-X[:,i][None,:])**2))
temp2=np.dot(temp-L,derivative)
gradient[i]=0.5*np.trace(temp2)
temp2=np.dot(temp-L,K2)
gradient[self.dimension]=0.5*np.trace(temp2)
der=np.ones((N,N))
temp2=np.dot(temp-L,der)
gradient[self.dimension+1]=0.5*np.trace(temp2)
return logLike,gradient
def logLikelihood(self,X,y,noise=None,alpha=None,variance=None,mu=None,gradient=False):
"""
Computes the log-likelihood and its gradient. The gradient is respect to log(var)
and log(alpha**2).
Args:
-X: Matrix with the training data.
-y: Output of the training data.
-noise: Noise of the outputs.
-alpha: Hyperparameters of the kernel
-variance: Hyperparameter of the kernel.
-mu: Mean parameter of the GP.
-gradient: True if we want the gradient; False otherwise.
"""
if alpha is None:
alpha=self.alpha
if variance is None:
variance=self.variance
if mu is None:
mu=self.mu
if noise is None:
K=self.A(X,alpha=alpha,variance=variance)
else:
K=self.A(X,alpha=alpha,variance=variance,noise=noise)
y2=y-mu
N=X.shape[0]
try:
L=np.linalg.cholesky(K)
alp=inverseComp(L,y2)
logLike=-0.5*np.dot(y2,alp)-np.sum(np.log(np.diag(L)))-0.5*N*np.log(2.0*np.pi)
if gradient==False:
return logLike
gradient=np.zeros(self.dimension+2)
temp=np.dot(alp[:,None],alp[None,:])
K2=self.A(X,alpha=alpha,variance=variance)
for i in range(self.dimension):
derivative=np.zeros((N,N))
derivative=K2*(-(0.5/(self.scaleAlpha**2))*(alpha[i]**2)*((X[:,i][:,None]-X[:,i][None,:])**2))
temp3=inverseComp(L,derivative)
gradient[i]=0.5*np.trace(np.dot(temp,derivative)-temp3)
der=self.K(X,alpha=alpha,variance=variance)
temp3=inverseComp(L,der)
gradient[self.dimension]=0.5*np.trace(np.dot(temp,der)-temp3)
der=np.ones((N,N))
temp3=inverseComp(L,der)
gradient[self.dimension+1]=0.5*np.trace(np.dot(temp,der)-temp3)
return logLike,gradient
except:
print "no"
L=np.linalg.inv(K)
det=np.linalg.det(K)
logLike=-0.5*np.dot(y2,np.dot(L,y2))-0.5*N*np.log(2*np.pi)-0.5*np.log(det)
if gradient==False:
return logLike
gradient=np.zeros(self.dimension+2)
alp=np.dot(L,y2)
temp=np.dot(alp[:,None],alp.T[None,:])
K2=self.A(X,alpha=alpha,variance=variance)
for i in range(self.dimension):
derivative=np.zeros((N,N))
derivative=K2*(-(0.5/(self.scaleAlpha**2))*(alpha[i]**2)*((X[:,i][:,None]-X[:,i][None,:])**2))
temp2=np.dot(temp-L,derivative)
gradient[i]=0.5*np.trace(temp2)
temp2=np.dot(temp-L,K2)
gradient[self.dimension]=0.5*np.trace(temp2)
der=np.ones((N,N))
temp2=np.dot(temp-L,der)
gradient[self.dimension+1]=0.5*np.trace(temp2)
return logLike,gradient