def _post_sample(self,
f_mean,
f_var=None,
expectedlog=False,
K_star=None,
v=None,
u=None):
if v is None:
v = self.pref_v
if u is None:
u = self.pref_u
if np.isscalar(f_mean):
N = 1
else:
N = f_mean.shape[0]
# since we don't have f_cov
if K_star is not None and self.use_svi:
#sample the inducing points because we don't have full covariance matrix. In this case, f_cov should be Ks_nm
f_samples = mvn.rvs(mean=self.um_minus_mu0.flatten(),
cov=self.uS,
size=1000).T
f_samples = K_star.dot(self.invK_mm).dot(f_samples) + f_mean
elif K_star is not None:
f_samples = mvn.rvs(mean=f_mean.flatten(), cov=K_star, size=1000).T
else:
f_samples = np.random.normal(loc=f_mean,
scale=np.sqrt(f_var),
size=(N, 1000))
# g_f = (f_samples[v, :] - f_samples[u, :]) / np.sqrt(2)
# phi = norm.cdf(g_f) # the probability of the actual observation, which takes g_f as a parameter. In the
if N == 1:
phi = self.forward_model(f_samples, v=[0], u=[0])
else:
phi = self.forward_model(f_samples, v=v, u=u)
phi = temper_extreme_probs(phi)
if expectedlog:
phi = np.log(phi)
notphi = np.log(1 - phi)
else:
notphi = 1 - phi
m_post = np.mean(phi, axis=1)[:, np.newaxis]
not_m_post = np.mean(notphi, axis=1)[:, np.newaxis]
v_post = np.var(phi, axis=1)[:, np.newaxis]
v_post = temper_extreme_probs(v_post, zero_only=True)
v_post[
m_post * (1 - not_m_post) <=
1e-7] = 1e-8 # fixes extreme values to sensible values. Don't think this is needed and can lower variance?
return m_post, not_m_post, v_post
def _post_rough(self, f_mean, f_cov=None, pref_v=None, pref_u=None):
'''
When making predictions, we want to predict the probability of each listed preference pair.
Use a solution given by applying the forward model to the mean of the latent function --
ignore the uncertainty in f itself, considering only the uncertainty due to the noise sigma.
'''
if pref_v is None:
pref_v = self.pref_v
if pref_u is None:
pref_u = self.pref_u
# to remedy this. However, previously the maths seemed to show it wasn't needed at all?
if f_cov is None:
m_post = self.forward_model(f_mean,
None,
v=pref_v,
u=pref_u,
return_g_f=False)
else:
# since we subtract the two f-values, the correlations between them are flipped, hence the '-' in the last
# two covariance terms here.
m_post = self.forward_model(
f_mean,
f_cov[pref_v, pref_v] + f_cov[pref_u, pref_u] -
f_cov[pref_v, pref_u] - f_cov[pref_u, pref_v],
v=pref_v,
u=pref_u,
return_g_f=False)
m_post = temper_extreme_probs(m_post)
not_m_post = 1 - m_post
return m_post, not_m_post,
def _logpt(self):
rho = pref_likelihood(self.obs_f, v=self.pref_v, u=self.pref_u)
rho = temper_extreme_probs(rho)
return np.log(rho), np.log(1 - rho)