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
'''
component_probabilities = list()
for component in range(self.num_components):
# prob = weigth * geo(x)
component_probability = self.mixture_weights[
component] + self.component_distributions[component].log_prob(
observation)
component_probabilities.append(component_probability)
# marginal_probabilities:
observation_probability = log_add_list(component_probabilities)
self.log_likelihood += observation_probability
for component in range(self.num_components):
# component/total
norm_comp_prob = component_probabilities[
component] - observation_probability
self.expected_component_counts[component] = log_add(
self.expected_component_counts[component], norm_comp_prob)
# we take care if observation is 0, we have to define: prob * value = -inf
if observation == 0:
self.expected_observation_counts[component] = log_add(
self.expected_observation_counts[component], -float("inf"))
else:
self.expected_observation_counts[component] = log_add(
self.expected_observation_counts[component],
norm_comp_prob + log(observation))
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)))
param_list = list()
weight_list = list()
for component in range(self.num_components):
# calculate new weight (= expected component counts / total number of datapoints)
new_weight = exp( self.expected_component_counts[component] - sum_obs_counts )
weight_list.append(new_weight)
# for each component, calculate denominator of geometric MLE-function (= expected component counts * expected observation counts )
# see (https://www.projectrhea.org/rhea/index.php/MLE_Examples:_Exponential_and_Geometric_Distributions_Old_Kiwi)
nSigmaX = log_add(self.expected_component_counts[component], self.expected_observation_counts[component])
# calculate new parameter value
new_param = exp(self.expected_component_counts[component] - nSigmaX)
param_list.append(new_param)
for component in range(self.num_components):
# update weights
self.mixture_weights[component] = weight_list[component]
# update parameters
self.component_distributions[component] = GeometricDistribution(param_list[component])
# reset counters
self.expected_component_counts[component] = -float("inf")
self.expected_observation_counts[component] = -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)))
weight_list = list()
param_list = list()
for component in range(self.num_components):
new_weight = exp(self.expected_component_counts[component] -
sum_obs_counts)
weight_list.append(new_weight)
noemer = log_add(self.expected_component_counts[component],
self.expected_observation_counts[component])
new_param = exp(self.expected_component_counts[component] - noemer)
param_list.append(new_param)
for component in range(self.num_components):
self.mixture_weights[component] = weight_list[
component] #add float
self.component_distributions[component] = GeometricDistribution(
param_list[component])
self.expected_component_counts[component] = -float("inf")
self.expected_observation_counts[component] = -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 (x_i)
'''
likelihood_list = list()
for component in range(self.num_components):
# Prior (= weights)
log_prior = self.mixture_weights[component]
# Calculate log-likelihood of one datapoint for each component
log_likelihood = log_prior + self.component_distributions[component].log_prob(observation)
# store result in list
likelihood_list.append(log_likelihood)
# log sum of likelihood over all components (for this datapoint)
marginal_likelihood = log_add_list(likelihood_list)
# Calculate total likelihood of data for this iteration ( = sum of marginal log likelihoods over all datapoints)
self.log_likelihood += marginal_likelihood
for component in range(self.num_components):
# Calculate posterior for current datapoint
posterior = likelihood_list[component] - marginal_likelihood
# Calculate weight of each component ( = cumulative log-addition of posteriors for all datapoints)
self.expected_component_counts[component] = log_add(self.expected_component_counts[component], posterior)
# Update expected observation counts
# Skip if value == 0 (i.e., zero-values won't add anything and will crash log-function)
if observation == 0:
continue
# calculate expected observation count of current datapoint for each component
value_count_log = log(observation) + posterior
# add to total observation count of each component
self.expected_observation_counts[component] = log_add(self.expected_observation_counts[component], value_count_log)
def e_step(self, observation):
'''Perform the E-step on a single observation. 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
'''
#TODO: Implement this. Make sure to update the log-likelihood during the E-step.
naive_posterior_list = list()
loglikelihood_list = list()
for component in range(self.num_components):
# prior component weight
log_prior = self.mixture_weights[component]
# calculate likelihood of the observation given that component
prob_geo_obs = self.component_distributions[component].log_prob(
observation)
likelihood_obs = prob_geo_obs + log_prior
loglikelihood_list.append(likelihood_obs)
# sum of the posteriors of that observation for the three components
marginal_posterior = log_add_list(
loglikelihood_list) # sum of logprobs becomes log_add
# likelihood_obs_total = sum(loglikelihood_list)
self.log_likelihood += marginal_posterior
for component in range(self.num_components):
posterior = loglikelihood_list[component] - marginal_posterior
self.expected_component_counts[component] = log_add(
self.expected_component_counts[component], posterior)
observation_count = observation * exp(posterior)
if observation_count == 0.0:
continue
else:
log_observation_count = log(observation_count)
self.expected_observation_counts[component] = log_add(
self.expected_observation_counts[component],
log_observation_count)
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)))
# updating mixture weights and mixture components
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
'''
# computing the new log_likelihood
log_like = []
for i in range(self.num_components):
# we can take the logprob of observation from the GeometricDistribution object. mixture weights are logs already.
log_like.append(
self.mixture_weights[i] +
self.component_distributions[i].log_prob(observation))
log_like_nr = log_add_list(log_like)
self.log_likelihood += log_like_nr
# compute expected component counts and expected observation counts, account for special case where observation = 0
for i in range(self.num_components):
# normalising the component probability
normalised = log_like[i] - log_like_nr
self.expected_component_counts[i] = log_add(
self.expected_component_counts[i], normalised)
# if the observation is 0, we have to account for that (otherwise we take log(0))
if observation != 0:
self.expected_observation_counts[i] = log_add(
self.expected_observation_counts[i],
normalised + log(observation))
else:
self.expected_observation_counts[i] = log_add(
self.expected_observation_counts[i], -float('inf'))