def _update_distribution_and_lowerbound(self, m):
r"""
Find maximum likelihood estimate for the shape parameter
Messages from children appear in the lower bound as
.. math::
m_0 \cdot x + m_1 \cdot \log(\Gamma(x))
Take derivative, put it zero and solve:
.. math::
m_0 + m_1 \cdot d\log(\Gamma(x)) &= 0
\\
m_0 + m_1 \cdot \psi(x) &= 0
\\
x &= \psi^{-1}(-\frac{m_0}{m_1})
where :math:`\psi^{-1}` is the inverse digamma function.
"""
# Maximum likelihood estimate
x = misc.invpsi(-m[0] / m[1])
# Compute moments
self.u = self._moments.compute_fixed_moments(x)
return
def _update_distribution_and_lowerbound(self, m):
r"""
Find maximum likelihood estimate for the concentration parameter
"""
a = np.ones(self.D)
da = np.inf
logp = m[0] + self.regularization[0]
N = m[1] + self.regularization[1]
# Compute sufficient statistic
mean_logp = logp / N[...,None]
# It is difficult to estimate values lower than 0.02 because the
# Dirichlet distributed probability vector starts to give numerically
# zero random samples for lower values.
if np.any(np.isinf(mean_logp)):
raise ValueError(
"Cannot estimate DirichletConcentration because of infs. This "
"means that there are numerically zero probabilities in the "
"child Dirichlet node."
)
# Fixed-point iteration
while np.any(np.abs(da / a) > 1e-5):
a_new = misc.invpsi(
special.psi(np.sum(a, axis=-1, keepdims=True))
+ mean_logp
)
da = a_new - a
a = a_new
self.u = self._moments.compute_fixed_moments(a)
return
def _update_distribution_and_lowerbound(self, m):
r"""
Find maximum likelihood estimate for the shape parameter
Messages from children appear in the lower bound as
.. math::
m_0 \cdot x + m_1 \cdot \log(\Gamma(x))
Take derivative, put it zero and solve:
.. math::
m_0 + m_1 \cdot d\log(\Gamma(x)) &= 0
\\
m_0 + m_1 \cdot \psi(x) &= 0
\\
x &= \psi^{-1}(-\frac{m_0}{m_1})
where :math:`\psi^{-1}` is the inverse digamma function.
"""
# Maximum likelihood estimate
x = misc.invpsi(-m[0]/m[1])
# Compute moments
self.u = self._moments.compute_fixed_moments(x)
return
def _update_distribution_and_lowerbound(self, m):
r"""
Find maximum likelihood estimate for the concentration parameter
"""
a = np.ones(self.D)
da = np.inf
logp = m[0] + self.regularization[0]
N = m[1] + self.regularization[1]
# Compute sufficient statistic
mean_logp = logp / N[..., None]
# It is difficult to estimate values lower than 0.02 because the
# Dirichlet distributed probability vector starts to give numerically
# zero random samples for lower values.
if np.any(np.isinf(mean_logp)):
raise ValueError(
"Cannot estimate DirichletConcentration because of infs. This "
"means that there are numerically zero probabilities in the "
"child Dirichlet node.")
# Fixed-point iteration
while np.any(np.abs(da / a) > 1e-5):
a_new = misc.invpsi(
special.psi(np.sum(a, axis=-1, keepdims=True)) + mean_logp)
da = a_new - a
a = a_new
self.u = self._moments.compute_fixed_moments(a)
return