def _log_likelihood_triplet(self, counts_triplet, theta_triplet, alpha,
beta):
"""Compute the log likelihood of data for one triplet of annotators.
Input:
counts_triplet -- count data for one combination of annotators
theta_triplet -- theta parameters of the current triplet
"""
nclasses = self.nclasses
llhood = 0.
# loop over all possible agreement patterns
# 0=aaa, 1=aaA, 2=aAa, 3=Aaa, 4=Aa@
pattern_to_indices = _compatibility_tables(nclasses)
for pattern in range(5):
# P( A_ijk | T_ijk ) * P( T_ijk ) , or "alpha * theta triplet"
prob = self._prob_a_and_t(pattern, theta_triplet, alpha)
# P( V_ijk ! A_ijk) * P( A_ijk | T_ijk ) * P( T_ijk )
# = P( V_ijk | A, T, model)
prob *= beta[pattern]
# P( V_ijk | model ) = sum over A and T of conditional probability
indices = pattern_to_indices[pattern]
count_indices = _triplet_to_counts_index(indices, nclasses)
log_prob = ninf_to_num(np.log(prob))
llhood += (counts_triplet[count_indices] * log_prob).sum()
return llhood
def _log_likelihood_triplet(self, counts_triplet, theta_triplet,
alpha, beta):
"""Compute the log likelihood of data for one triplet of annotators.
Input:
counts_triplet -- count data for one combination of annotators
theta_triplet -- theta parameters of the current triplet
"""
nclasses = self.nclasses
llhood = 0.
# loop over all possible agreement patterns
# 0=aaa, 1=aaA, 2=aAa, 3=Aaa, 4=Aa@
pattern_to_indices = _compatibility_tables(nclasses)
for pattern in range(5):
# P( A_ijk | T_ijk ) * P( T_ijk ) , or "alpha * theta triplet"
prob = self._prob_a_and_t(pattern, theta_triplet, alpha)
# P( V_ijk ! A_ijk) * P( A_ijk | T_ijk ) * P( T_ijk )
# = P( V_ijk | A, T, model)
prob *= beta[pattern]
# P( V_ijk | model ) = sum over A and T of conditional probability
indices = pattern_to_indices[pattern]
count_indices = _triplet_to_counts_index(indices, nclasses)
log_prob = ninf_to_num(np.log(prob))
llhood += (counts_triplet[count_indices] * log_prob).sum()
return llhood
def _log_likelihood_triplet(self, counts_triplet, theta_triplet):
"""Compute the log likelihood of data for one triplet of annotators.
Input:
counts_triplet -- count data for one combination of annotators
theta_triplet -- theta parameters of the current triplet
"""
# log \prod_n P(v_{ijk}^{n} | params)
# = \sum_n log P(v_{ijk}^{n} | params)
# = \sum_v_{ijk} count(v_{ijk}) log P( v_{ijk} | params )
#
# where n is n-th annotation of triplet {ijk}]
# compute P( v_{ijk} | params )
pf = self._pattern_frequencies(theta_triplet)
log_pf = ninf_to_num(np.log(pf))
l = (counts_triplet * log_pf).sum()
return l
def _log_likelihood_triplet(self, counts_triplet, theta_triplet):
"""Compute the log likelihood of data for one triplet of annotators.
Input:
counts_triplet -- count data for one combination of annotators
theta_triplet -- theta parameters of the current triplet
"""
# log \prod_n P(v_{ijk}^{n} | params)
# = \sum_n log P(v_{ijk}^{n} | params)
# = \sum_v_{ijk} count(v_{ijk}) log P( v_{ijk} | params )
#
# where n is n-th annotation of triplet {ijk}]
# compute P( v_{ijk} | params )
pf = self._pattern_frequencies(theta_triplet)
log_pf = ninf_to_num(np.log(pf))
l = (counts_triplet * log_pf).sum()
return l
