def _moments_match_analytical(self,data_i,tau_i,v_i):
"""
Moments match of the marginal approximation in EP algorithm
:param i: number of observation (int)
:param tau_i: precision of the cavity distribution (float)
:param v_i: mean/variance of the cavity distribution (float)
"""
if data_i == 1:
sign = 1.
elif data_i == 0:
sign = -1
else:
raise ValueError("bad value for Bernouilli observation (0,1)")
if isinstance(self.gp_link,gp_transformations.Probit):
z = sign*v_i/np.sqrt(tau_i**2 + tau_i)
Z_hat = std_norm_cdf(z)
phi = std_norm_pdf(z)
mu_hat = v_i/tau_i + sign*phi/(Z_hat*np.sqrt(tau_i**2 + tau_i))
sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
elif isinstance(self.gp_link,gp_transformations.Heaviside):
a = sign*v_i/np.sqrt(tau_i)
Z_hat = std_norm_cdf(a)
N = std_norm_pdf(a)
mu_hat = v_i/tau_i + sign*N/Z_hat/np.sqrt(tau_i)
sigma2_hat = (1. - a*N/Z_hat - np.square(N/Z_hat))/tau_i
if np.any(np.isnan([Z_hat, mu_hat, sigma2_hat])):
stop
else:
raise ValueError("Exact moment matching not available for link {}".format(self.gp_link.gp_transformations.__name__))
return Z_hat, mu_hat, sigma2_hat
def dtransf_df(self, z):
if type(z) == type(np.ones(1)):
z_shape = np.shape(z)
z = np.reshape(z, (1, -1))[0]
output = np.array(map(lambda z_in: std_norm_pdf(self.copula(z_in)) * self.dcopula_dz(z_in), z))
output = np.reshape(output, z_shape)
else:
output = std_norm_pdf(self.copula(z)) * self.dcopula_dz(z)
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def dtransf_df(self, z):
if type(z) == type(np.ones(1)):
z_shape = np.shape(z)
z = np.reshape(z, (1, -1))[0]
output = np.array(
map(
lambda z_in: std_norm_pdf(self.copula(z_in)) * self.
dcopula_dz(z_in), z))
output = np.reshape(output, z_shape)
else:
output = std_norm_pdf(self.copula(z)) * self.dcopula_dz(z)
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def dcopula_dk(self, z):
output = self.marginal.dquantile_dcdf(std_norm_cdf(
z / np.sqrt(self.k))) * (std_norm_pdf(
z / np.sqrt(self.k))) * -0.5 * z * (self.k**(-1.5))
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def pdf(self, f):
input = (f - self.mu_vec) / (self.sigma_vec)
output = np.dot(
self.k_vec,
np.reshape(std_norm_pdf(input) / self.sigma_vec, (1, -1))[0])
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def dcdf_dtheta(self, f):
# FIXME: Limit to only mu_vec at the moment.
input = (f - self.mu_vec) / (self.sigma_vec)
output = -1. * std_norm_pdf(input) / (self.sigma_vec * self.k_vec)
output = np.reshape(output, (1, -1))[0]
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def dcdf_dtheta(self, f):
# FIXME: Limit to only mu_vec at the moment.
input = (f - self.mu_vec)/(self.sigma_vec)
output = -1. * std_norm_pdf(input)/(self.sigma_vec * self.k_vec)
output = np.reshape(output, (1, -1))[0]
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def dcopula_dz(self, z):
output = self.marginal.dquantile_dcdf(std_norm_cdf(z)) * std_norm_pdf(z)
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def d3transf_df3(self,f):
shiftedf = (f-self.offset)*self.scale
return (safe_square(shiftedf)-1.)*std_norm_pdf(shiftedf)
def d2transf_df2(self,shiftedf):
shiftedf = (f-self.offset)*self.scale
return -f * std_norm_pdf(shiftedf)
def dtransf_df(self,f):
shiftedf = (f-self.offset)*self.scale
return std_norm_pdf(shiftedf)
def d2transf_df2(self,f):
#FIXME
return -f * std_norm_pdf(f)
def dtransf_df(self,f):
return std_norm_pdf(f)
def dtransf_dk(self, z):
''' f being z'''
output = std_norm_pdf(self.copula(z)) * self.dcopula_dk(z)
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def pdf(self, f):
output = std_norm_pdf((f - self.mu) / self.sigma) / self.sigma
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def dcopula_dk(self, z):
output = self.marginal.dquantile_dcdf(std_norm_cdf(z/np.sqrt(self.k))) * (std_norm_pdf(z/np.sqrt(self.k))) * -0.5 * z * (self.k ** (-1.5))
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def pdf(self, f):
output = std_norm_pdf((f - self.mu)/self.sigma)/self.sigma
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def pdf(self, f):
input = (f - self.mu_vec)/(self.sigma_vec)
output = np.dot(self.k_vec, np.reshape(std_norm_pdf(input)/self.sigma_vec, (1, -1))[0])
assert not(np.isnan(output).any()), 'function returns NaN'
assert not(np.isinf(output).any()), 'function returns inf'
return output
def dtransf_dk(self, z):
''' f being z'''
output = std_norm_pdf(self.copula(z)) * self.dcopula_dk(z)
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
def dcopula_dz(self, z):
output = self.marginal.dquantile_dcdf(
std_norm_cdf(z)) * std_norm_pdf(z)
assert not (np.isnan(output).any()), 'function returns NaN'
assert not (np.isinf(output).any()), 'function returns inf'
return output
