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Changed LOO implementation for Eq 30 instead of 37

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Alan Saul 2015-04-14 16:27:58 +01:00
parent b6761c21d7
commit ab5f359103
2 changed files with 20 additions and 8 deletions
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22
GPy/inference/latent_function_inference/laplace.py
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@ -57,9 +57,20 @@ class Laplace(LatentFunctionInference):
K_Wi_i, _, _, Ki_W_i = self._compute_B_statistics(K, W, likelihood.log_concave) K_Wi_i, _, _, Ki_W_i = self._compute_B_statistics(K, W, likelihood.log_concave)
#Eq 37 W = np.diagflat(W)
posterior_cav_var = 1./(1./np.diag(Ki_W_i) - 1./np.diag(W))[:, None]
posterior_cav_mean = f_hat - posterior_cav_var*logpdf_dfhat #Eq 14, and 16
var_site = 1./np.diag(W)[:, None]
mu_site = f_hat + var_site*logpdf_dfhat
prec_site = 1./var_site
#Eq 19
marginal_cov = Ki_W_i
marginal_mu = marginal_cov.dot(np.diagflat(prec_site)).dot(mu_site)
marginal_var = np.diag(marginal_cov)[:, None]
#Eq 30 with using site parameters instead of Gaussian site parameters
#(var_site instead of sigma^{2} )
posterior_cav_var = 1./(1./marginal_var - 1./var_site)
posterior_cav_mean = posterior_cav_var*((1./marginal_var)*marginal_mu - (1./var_site)*Y)
flat_y = Y.flatten() flat_y = Y.flatten()
flat_mu = posterior_cav_mean.flatten() flat_mu = posterior_cav_mean.flatten()
@ -90,12 +101,13 @@ class Laplace(LatentFunctionInference):
def integral_generator(yi, mi, vi, yi_m): def integral_generator(yi, mi, vi, yi_m):
def f(fi_star): def f(fi_star):
#More stable in the log space #More stable in the log space
return np.exp(likelihood.logpdf(fi_star, yi, yi_m) p_fi = np.exp(likelihood.logpdf(fi_star, yi, yi_m)
- 0.5*np.log(2*np.pi*vi) - 0.5*np.log(2*np.pi*vi)
- 0.5*np.square(mi-fi_star)/vi) - 0.5*np.square(mi-fi_star)/vi)
return p_fi
return f return f
#Eq 25 #Eq 30
p_ystar, _ = zip(*[quad(integral_generator(y, m, v, yi_m), -np.inf, np.inf) p_ystar, _ = zip(*[quad(integral_generator(y, m, v, yi_m), -np.inf, np.inf)
for y, m, v, yi_m in zipped_values]) for y, m, v, yi_m in zipped_values])
p_ystar = np.array(p_ystar).reshape(-1, 1) p_ystar = np.array(p_ystar).reshape(-1, 1)

6
GPy/likelihoods/likelihood.py
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@ -539,9 +539,9 @@ class Likelihood(Parameterized):
#Parameters are stacked vertically. Must be listed in same order as 'get_param_names' #Parameters are stacked vertically. Must be listed in same order as 'get_param_names'
# ensure we have gradients for every parameter we want to optimize # ensure we have gradients for every parameter we want to optimize
assert dlogpdf_dtheta.shape[0] == self.size #f, d x num_param array assert dlogpdf_dtheta.shape[0] == self.size #num_param array x f, d
assert dlogpdf_df_dtheta.shape[0] == self.size #f x d x num_param matrix or just f x num_param assert dlogpdf_df_dtheta.shape[0] == self.size #num_param x f x d x matrix or just num_param x f
assert d2logpdf_df2_dtheta.shape[0] == self.size #f x num_param matrix or f x d x num_param matrix, f x f x num_param or f x f x d x num_param assert d2logpdf_df2_dtheta.shape[0] == self.size #num_param x f matrix or num_param x f x d x matrix, num_param x f x f or num_param x f x f x d
return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta