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Updated other likelihoods to give back logpdf and gradients for each link_f rather than summing on the inside

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Alan Saul 2015-03-09 10:27:21 +00:00
parent 48821a6b73
commit 233c5ee8b4
7 changed files with 22 additions and 42 deletions
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6
GPy/likelihoods/exponential.py
View file

@ -57,9 +57,8 @@ class Exponential(Likelihood):
:rtype: float
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
log_objective = np.log(link_f) - y*link_f
return np.sum(log_objective)
return log_objective
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
"""
@ -77,7 +76,6 @@ class Exponential(Likelihood):
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
grad = 1./link_f - y
#grad = y/(link_f**2) - 1./link_f
return grad
@ -103,7 +101,6 @@ class Exponential(Likelihood):
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
hess = -1./(link_f**2)
#hess = -2*y/(link_f**3) + 1/(link_f**2)
return hess
@ -123,7 +120,6 @@ class Exponential(Likelihood):
:returns: third derivative of likelihood evaluated at points f
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
d3lik_dlink3 = 2./(link_f**3)
#d3lik_dlink3 = 6*y/(link_f**4) - 2./(link_f**3)
return d3lik_dlink3

6
GPy/likelihoods/gamma.py
View file

@ -66,12 +66,11 @@ class Gamma(Likelihood):
:rtype: float
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
#alpha = self.gp_link.transf(gp)*self.beta
#return (1. - alpha)*np.log(obs) + self.beta*obs - alpha * np.log(self.beta) + np.log(special.gamma(alpha))
alpha = link_f*self.beta
log_objective = alpha*np.log(self.beta) - np.log(special.gamma(alpha)) + (alpha - 1)*np.log(y) - self.beta*y
return np.sum(log_objective)
return log_objective
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
"""
@ -90,7 +89,6 @@ class Gamma(Likelihood):
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
grad = self.beta*np.log(self.beta*y) - special.psi(self.beta*link_f)*self.beta
#old
#return -self.gp_link.dtransf_df(gp)*self.beta*np.log(obs) + special.psi(self.gp_link.transf(gp)*self.beta) * self.gp_link.dtransf_df(gp)*self.beta
@ -118,7 +116,6 @@ class Gamma(Likelihood):
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
hess = -special.polygamma(1, self.beta*link_f)*(self.beta**2)
#old
#return -self.gp_link.d2transf_df2(gp)*self.beta*np.log(obs) + special.polygamma(1,self.gp_link.transf(gp)*self.beta)*(self.gp_link.dtransf_df(gp)*self.beta)**2 + special.psi(self.gp_link.transf(gp)*self.beta)*self.gp_link.d2transf_df2(gp)*self.beta
@ -140,6 +137,5 @@ class Gamma(Likelihood):
:returns: third derivative of likelihood evaluated at points f
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
d3lik_dlink3 = -special.polygamma(2, self.beta*link_f)*(self.beta**3)
return d3lik_dlink3

28
GPy/likelihoods/gaussian.py
View file

@ -130,11 +130,10 @@ class Gaussian(Likelihood):
:returns: log likelihood evaluated for this point
:rtype: float
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
N = y.shape[0]
ln_det_cov = N*np.log(self.variance)
ln_det_cov = np.log(self.variance)
return -0.5*(np.sum((y-link_f)**2/self.variance) + ln_det_cov + N*np.log(2.*np.pi))
return -0.5*((y-link_f)**2/self.variance + ln_det_cov + np.log(2.*np.pi))
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
"""
@ -151,8 +150,7 @@ class Gaussian(Likelihood):
:returns: gradient of log likelihood evaluated at points link(f)
:rtype: Nx1 array
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
s2_i = (1.0/self.variance)
s2_i = 1.0/self.variance
grad = s2_i*y - s2_i*link_f
return grad
@ -178,9 +176,9 @@ class Gaussian(Likelihood):
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
N = y.shape[0]
hess = -(1.0/self.variance)*np.ones((N, 1))
D = link_f.shape[1]
hess = -(1.0/self.variance)*np.ones((N, D))
return hess
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
@ -198,9 +196,9 @@ class Gaussian(Likelihood):
:returns: third derivative of log likelihood evaluated at points link(f)
:rtype: Nx1 array
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
N = y.shape[0]
d3logpdf_dlink3 = np.zeros((N,1))
D = link_f.shape[1]
d3logpdf_dlink3 = np.zeros((N,D))
return d3logpdf_dlink3
def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
@ -218,12 +216,11 @@ class Gaussian(Likelihood):
:returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
:rtype: float
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
e = y - link_f
s_4 = 1.0/(self.variance**2)
N = y.shape[0]
dlik_dsigma = -0.5*N/self.variance + 0.5*s_4*np.sum(np.square(e))
return np.sum(dlik_dsigma) # Sure about this sum?
dlik_dsigma = -0.5/self.variance + 0.5*s_4*np.square(e)
return dlik_dsigma
def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
"""
@ -240,7 +237,6 @@ class Gaussian(Likelihood):
:returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
:rtype: Nx1 array
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
s_4 = 1.0/(self.variance**2)
dlik_grad_dsigma = -s_4*y + s_4*link_f
return dlik_grad_dsigma
@ -260,15 +256,15 @@ class Gaussian(Likelihood):
:returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
:rtype: Nx1 array
"""
assert np.asarray(link_f).shape == np.asarray(y).shape
s_4 = 1.0/(self.variance**2)
N = y.shape[0]
d2logpdf_dlink2_dvar = np.ones((N,1))*s_4
D = link_f.shape[1]
d2logpdf_dlink2_dvar = np.ones((N, D))*s_4
return d2logpdf_dlink2_dvar
def dlogpdf_link_dtheta(self, f, y, Y_metadata=None):
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata)
return np.asarray([[dlogpdf_dvar]])
return dlogpdf_dvar
def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None):
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata)

2
GPy/likelihoods/likelihood.py
View file

@ -425,7 +425,7 @@ class Likelihood(Parameterized):
return np.zeros([f.shape[0], 0])
def _laplace_gradients(self, f, y, Y_metadata=None):
dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata)
dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata).sum(axis=0)
dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, Y_metadata=Y_metadata)
d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, Y_metadata=Y_metadata)

3
GPy/likelihoods/poisson.py
View file

@ -105,7 +105,7 @@ class Poisson(Likelihood):
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
return -y/(link_f**2)
return -y/(link_f**2)
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
"""
@ -122,7 +122,6 @@ class Poisson(Likelihood):
:returns: third derivative of likelihood evaluated at points f
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
d3lik_dlink3 = 2*y/(link_f)**3
return d3lik_dlink3

13
GPy/likelihoods/student_t.py
View file

@ -86,7 +86,6 @@ class StudentT(Likelihood):
:rtype: float
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
#FIXME:
#Why does np.log(1 + (1/self.v)*((y-inv_link_f)**2)/self.sigma2) suppress the divide by zero?!
@ -97,7 +96,7 @@ class StudentT(Likelihood):
- 0.5*np.log(self.sigma2 * self.v * np.pi)
- 0.5*(self.v + 1)*np.log(1 + (1/np.float(self.v))*((e**2)/self.sigma2))
)
return np.sum(objective)
return objective
def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
"""
@ -115,7 +114,6 @@ class StudentT(Likelihood):
:rtype: Nx1 array
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
return grad
@ -141,7 +139,6 @@ class StudentT(Likelihood):
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
return hess
@ -161,7 +158,6 @@ class StudentT(Likelihood):
:returns: third derivative of likelihood evaluated at points f
:rtype: Nx1 array
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
d3lik_dlink3 = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) /
((e**2 + self.sigma2*self.v)**3)
@ -183,10 +179,9 @@ class StudentT(Likelihood):
:returns: derivative of likelihood evaluated at points f w.r.t variance parameter
:rtype: float
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
dlogpdf_dvar = self.v*(e**2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e**2))
return np.sum(dlogpdf_dvar)
return dlogpdf_dvar
def dlogpdf_dlink_dvar(self, inv_link_f, y, Y_metadata=None):
"""
@ -203,7 +198,6 @@ class StudentT(Likelihood):
:returns: derivative of likelihood evaluated at points f w.r.t variance parameter
:rtype: Nx1 array
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
dlogpdf_dlink_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
return dlogpdf_dlink_dvar
@ -223,7 +217,6 @@ class StudentT(Likelihood):
:returns: derivative of hessian evaluated at points f and f_j w.r.t variance parameter
:rtype: Nx1 array
"""
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
e = y - inv_link_f
d2logpdf_dlink2_dvar = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2)))
/ ((self.sigma2*self.v + (e**2))**3)
@ -246,7 +239,7 @@ class StudentT(Likelihood):
return np.hstack((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv))
def predictive_mean(self, mu, sigma, Y_metadata=None):
# The comment here confuses mean and median.
# The comment here confuses mean and median.
return self.gp_link.transf(mu) # only true if link is monotonic, which it is.
def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None):