def m_step(self):
'''Perform the M-step. This step updates
self.mixture_weights
self.component_distributions
'''
# test if the sum of the summed expected_component_counts is roughly equal to the total amount of observations
sum_obs_counts = log_add_list(self.expected_component_counts.values())
print("Sum of expected component counts: {}".format(exp(sum_obs_counts)))
def m_step(self):
'''Perform the M-step. This step updates
self.mixture_weights
self.component_distributions
'''
# test if the sum of the summed expected_component_counts is roughly equal to the total amount of observations
sum_obs_counts = log_add_list(self.expected_component_counts.values())
print("Sum of expected component counts: {}".format(exp(sum_obs_counts)))
def m_step(self):
'''Perform the M-step. This step updates
self.mixture_weights
self.component_distributions
'''
sum_obs_counts = log_add_list(self.expected_component_counts.values())
for i in range(self.num_components):
self.mixture_weights[i] = self.expected_component_counts[i] - sum_obs_counts
self.component_distributions[i] = GeometricDistribution(exp(self.expected_component_counts[i] - (log_add(self.expected_component_counts[i], self.expected_observation_counts[i]))))
self.expected_component_counts[i] = -float("inf")
self.expected_observation_counts[i] = -float("inf")
def m_step(self):
'''Perform the M-step. This step updates
self.mixture_weights
self.component_distributions
'''
# test if the sum of the summed expected_component_counts is roughly equal to the total amount of observations
sum_obs_counts = log_add_list(self.expected_component_counts.values())
print("Sum of expected component counts: {}".format(exp(sum_obs_counts)))
for i in range(self.num_components):
self.mixture_weights[i] = self.expected_component_counts[i] - sum_obs_counts
self.component_distributions[i] = GeometricDistribution(exp(self.expected_component_counts[i] - (log_add(self.expected_component_counts[i], self.expected_observation_counts[i]))))
self.expected_component_counts[i] = -float("inf")
self.expected_observation_counts[i] = -float("inf")
def e_step(self, observation):
'''Perform the E-step on a single obervation. That is, compute the posterior of mixture components
and add the expected occurrence of each component to the running totals
self.log_likelihood ,
self.expected_component_counts , and
self.expected_observation_counts
:param observation: The observation
'''
# Compute the joint probabilities p(x, c)
joint_logprobs = list()
for component in range(self.num_components):
comp_dist = self.component_distributions[component]
logprob = self.mixture_weights[component] + comp_dist.log_prob(observation)
joint_logprobs.append(logprob)
# Marginal probability p(x) = p(x, c_1) + ... + p(x, c_n)
marginal_logprob = log_add_list(joint_logprobs)
# Update log likelihood: log p(x_1, x_2, ...) = log p(x_1) + log p(x_2) + ...
self.log_likelihood += marginal_logprob
# Responsibilities are the posteriors p(c | x) = p(x, c) / p(x)
# So log p(c | x) = log p(x, c) - log p(x)
logresponsibilities = list()
for component in range(self.num_components):
dist = self.component_distributions[component]
logresp = joint_logprobs[component] - marginal_logprob
logresponsibilities.append(logresp)
# Update the expected component count and expected observation counts
for component in range(self.num_components):
# log( expected observation counts )
logresp = logresponsibilities[component]
self.expected_component_counts[component] = log_add(self.expected_component_counts[component], logresp)
# Compute the log( expected observation counts)
# log (exp obs count)
# = log( exp_obs_count + val * exp(logresp))
# = log( exp_obs_count + exp( log(val) + logresp ) )
# = log_add( log(exp_obs_count), log(val) + logresp )
if observation > 0:
exp_obs = self.expected_observation_counts[component]
self.expected_observation_counts[component] = log_add(exp_obs, log(observation) + logresp)
def m_step(self):
'''Perform the M-step. This step updates
self.mixture_weights
self.component_distributions
'''
# test if the sum of the summed expected_component_counts is roughly equal to the total amount of observations
sum_obs_counts = log_add_list(self.expected_component_counts.values())
print("Sum of expected component counts: {}".format(exp(sum_obs_counts)))
# TODO: Implement this.
# TODO: Make sure to reset the data structures you use for counting after you have
# TODO: updated all parameters, namely self.expected_component_counts and self.expected_observation_counts
for component in range(self.num_components):
# log_new_weight
# = log( exp( log_exp_count ) / exp( sum_obs_counts ) ) )
# = log( exp( log_exp_count )) - log( exp(sum_obs_counts) )
# = log_exp_count - sum_obs_counts
log_exp_count = self.expected_component_counts[component]
self.mixture_weights[component] = log_exp_count - sum_obs_counts
# log_new_param
# = log( exp( log_exp_count) / (exp(log_exp_count) + exp(log_exp_sum)))
# = log_exp_count - (log( exp(log_exp_count) + exp(log_exp_sum) )
# = log_exp_count - log_add( log_exp_count + log_exp_sum )
log_exp_sum = self.expected_observation_counts[component]
logparam = log_exp_count - log_add(log_exp_count, log_exp_sum)
self.component_distributions[component] = GeometricDistribution(exp(logparam))
# Reset
for component in range(self.num_components):
self.expected_component_counts[component] = -float("inf")
self.expected_observation_counts[component] = -float("inf")