def estimate_mixture_params(EmissionParameters, curr_counts_orig, curr_nr_of_counts_orig, curr_state, rand_sample_size, max_nr_iter, nr_of_iter=20, stop_crit=1.0, nr_of_init=10, verbosity=1):
'''
This function estimates thedirichlet multinomial mixture parameters
'''
#1) Copy old parameters and use it as initialisation for the first iteration
alphas_list = []
mixtures_list = []
lls_list = []
curr_counts = deepcopy(curr_counts_orig)
curr_nr_of_counts = deepcopy(curr_nr_of_counts_orig)
if len(curr_counts.shape) == 1:
curr_counts = np.expand_dims(curr_counts, axis=1)
if np.sum(np.sum(curr_counts, axis=0) > 0) > 0:
curr_nr_of_counts = curr_nr_of_counts[:, np.sum(curr_counts, axis=0) >0]
curr_counts = curr_counts[:, np.sum(curr_counts, axis=0) >0]
#Test for fitting distributions only on diag events
curr_nr_of_counts = curr_nr_of_counts[:, np.sum(curr_counts, axis=0) > 10]
curr_counts = curr_counts[:, np.sum(curr_counts, axis=0) > 10]
tracks_per_rep = EmissionParameters['Diag_event_params']['alpha'][curr_state].shape[0]
NrOfReplicates = curr_counts.shape[0] / tracks_per_rep
noncon = np.sum(curr_counts[[tracks_per_rep - 1 + (tracks_per_rep * i) for i in range(NrOfReplicates)],:], axis=0)
conv = np.sum(curr_counts, axis=0) - noncon
ratio = conv / np.float64(conv + noncon)
rat_ix = ((ratio > 0.05) * (ratio < 0.95)) > 0
rat_ix = ((ratio < 0.95)) > 0
curr_nr_of_counts = curr_nr_of_counts[:, rat_ix]
curr_counts = curr_counts[:, rat_ix]
#end test
if len(curr_counts.shape) == 1:
curr_counts = np.expand_dims(curr_counts, axis=1)
#Save old lls mixtures and alphas
mixtures = deepcopy(EmissionParameters['Diag_event_params']['mix_comp'][curr_state])
OldAlpha = deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state])
#pdb.set_trace()
scored_counts = score_counts(curr_counts, curr_state, EmissionParameters)
scored_counts += np.tile(np.log(mixtures[:, np.newaxis]), (1, scored_counts.shape[1]))
ll = np.sum(np.sum(logsumexp(scored_counts, axis=0) + np.log(curr_nr_of_counts)))
alphas_list.append(deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state]))
mixtures_list.append(deepcopy(EmissionParameters['Diag_event_params']['mix_comp'][curr_state]))
lls_list.append(ll)
for curr_init in range(nr_of_init):
#compute the curr mixture, ll and alpha
#initialiste the parameters
old_ll = 0
if curr_init == 0:
OldAlpha = deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state])
mixtures = deepcopy(mixtures)
else:
OldAlpha = np.random.uniform(low=0.0001, high=0.1, size=OldAlpha.shape)
for i in range(OldAlpha.shape[1]):
OldAlpha[np.random.randint(OldAlpha.shape[0]-1), i] = np.random.random() * 10.0
OldAlpha[-2, i] = np.random.random() * 1.0
OldAlpha[-1, i] = np.random.random() * 10.0
mixtures = np.random.uniform(low=0.0001, high=1.0, size=mixtures.shape)
mixtures /= np.sum(mixtures)
if EmissionParameters['Diag_event_params']['nr_mix_comp'] == 1:
#Case that only one mixture component is given
EmissionParameters['Diag_event_params']['alpha'][curr_state][:, 0] = diag_event_model.estimate_multinomial_parameters(curr_counts, curr_nr_of_counts, EmissionParameters, OldAlpha[:])
#compute ll
scored_counts = score_counts(curr_counts, curr_state, EmissionParameters)
scored_counts += np.tile(np.log(mixtures[:, np.newaxis]), (1, scored_counts.shape[1]))
ll = np.sum(np.sum(logsumexp(scored_counts, axis=0) + np.log(curr_nr_of_counts)))
alphas_list.append(deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state]))
mixtures_list.append(deepcopy(EmissionParameters['Diag_event_params']['mix_comp'][curr_state]))
lls_list.append(ll)
else:
zero_ix = []
for iter_nr in range(max_nr_iter):
print('em-iteration ' + str(iter_nr))
scored_counts = score_counts(curr_counts, curr_state, EmissionParameters)
scored_counts += np.tile(np.log(mixtures[:, np.newaxis]), (1, scored_counts.shape[1]))
# 2) Compute the mixture components
#compute the normalisation factor
normalised_likelihood = logsumexp(scored_counts, axis=0)
old_ll = ll
ll = np.sum(np.sum(logsumexp(scored_counts, axis=0) + np.log(curr_nr_of_counts)))
if np.abs(old_ll - ll) < stop_crit:
#Check if convergence has been reached
if len(zero_ix) == 0:
break
normalised_scores = scored_counts - np.tile(normalised_likelihood, (scored_counts.shape[0], 1))
un_norm_mixtures = logsumexp(normalised_scores, b=np.tile(curr_nr_of_counts, (scored_counts.shape[0], 1)), axis = 1)
mixtures = np.exp(un_norm_mixtures - logsumexp(un_norm_mixtures))
# 3) Compute for eachcount the most likely mixture component
curr_weights = np.exp(normalised_scores)
curr_weights = (curr_weights == np.tile(np.max(curr_weights, axis=0), (curr_weights.shape[0], 1))) *1.0
zero_mix = np.sum(curr_weights,axis=1) == 0
zero_ix = np.where(zero_mix)[0].tolist()
EmissionParameters['Diag_event_params']['mix_comp'][curr_state] = mixtures
#Get number of positions that are used. (In case there are fewer entries that rand_sample_size in counts)
rand_size = min(rand_sample_size, curr_counts.shape[1])
for i in zero_ix:
random_ix = np.random.choice(curr_counts.shape[1], rand_size, p=(curr_nr_of_counts[0, :] / np.float(np.sum(curr_nr_of_counts[0, :]))))
curr_counts = np.hstack([curr_counts, curr_counts[:, random_ix]])
curr_nr_of_counts = np.hstack([curr_nr_of_counts, np.ones((1, rand_size))])
temp_array = np.zeros((normalised_scores.shape[0], rand_size))
temp_array[i, :] = i
normalised_scores = np.hstack([normalised_scores, temp_array])
temp_array = np.zeros((curr_weights.shape[0], rand_size))
temp_array[i, :] = 1
curr_weights = np.hstack([curr_weights, temp_array])
# 4) Compute the dirichlet-multinomial parameters
for curr_mix_comp in range(EmissionParameters['Diag_event_params']['nr_mix_comp']):
local_counts = curr_counts
local_nr_counts = curr_nr_of_counts * curr_weights[curr_mix_comp, :]
local_counts = local_counts[:, local_nr_counts[0, :] > 0]
local_nr_counts = local_nr_counts[0, local_nr_counts[0, :] > 0]
if len(local_counts.shape) == 1:
local_counts = np.expand_dims(local_counts, axis=1)
curr_alpha = diag_event_model.estimate_multinomial_parameters(local_counts, local_nr_counts, EmissionParameters, OldAlpha[:, curr_mix_comp])
if curr_mix_comp in zero_ix:
OldAlpha[:, curr_mix_comp] = np.random.uniform(low=0.0001, high=0.1, size=OldAlpha[:, curr_mix_comp].shape)
OldAlpha[np.random.randint(OldAlpha.shape[0]), curr_mix_comp] = np.random.random() * 10.0
OldAlpha[-2, curr_mix_comp] = np.random.random() * 1.0
OldAlpha[-1, curr_mix_comp] = np.random.random() * 10.0
else:
OldAlpha[:, curr_mix_comp] = curr_alpha
if (len(zero_ix) > 0) and (iter_nr + 2 < max_nr_iter):
#Treat the case where some mixtures have prob zero
mixtures[zero_ix] = np.mean(mixtures)
mixtures /= np.sum(mixtures)
EmissionParameters['Diag_event_params']['mix_comp'][curr_state] = deepcopy(mixtures)
EmissionParameters['Diag_event_params']['alpha'][curr_state] = deepcopy(OldAlpha)
# Check if convergence has been achieved.
alphas_list.append(deepcopy(OldAlpha))
mixtures[zero_ix] = np.min(mixtures[mixtures > 0])
mixtures /= np.sum(mixtures)
mixtures_list.append(deepcopy(mixtures))
lls_list.append(ll)
#select which alpha had the highest ll
max_ll_pos = np.argmax(np.array(lls_list))
alpha = alphas_list[max_ll_pos]
mixtures = mixtures_list[max_ll_pos]
return alpha, mixtures
def Parallel_estimate_single_mixture_params(args):
'''
This function estimates thedirichlet multinomial mixture parameters
'''
stop_crit, rand_sample_size, max_nr_iter, curr_init, EmissionParameters, curr_state, curr_counts, curr_nr_of_counts = args
#compute the curr mixture, ll and alpha
#initialiste the parameters
old_ll = 0
ll = -10
OldAlpha = deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state])
mixtures = deepcopy(EmissionParameters['Diag_event_params']['mix_comp'][curr_state])
if curr_init > 0:
OldAlpha = np.random.uniform(low=0.0001, high=0.1, size=OldAlpha.shape)
for i in range(OldAlpha.shape[1]):
OldAlpha[np.random.randint(OldAlpha.shape[0]-1), i] = np.random.random() * 10.0
OldAlpha[-2, i] = np.random.random() * 1.0
OldAlpha[-1, i] = np.random.random() * 10.0
mixtures = np.random.uniform(low=0.0001, high=1.0, size=mixtures.shape)
mixtures /= np.sum(mixtures)
if EmissionParameters['Diag_event_params']['nr_mix_comp'] == 1:
#Case that only one mixture component is given
EmissionParameters['Diag_event_params']['alpha'][curr_state][:, 0] = diag_event_model.estimate_multinomial_parameters(curr_counts, curr_nr_of_counts, EmissionParameters, OldAlpha[:])
#compute ll
scored_counts = score_counts(curr_counts, curr_state, EmissionParameters)
scored_counts += np.tile(np.log(mixtures[:, np.newaxis]), (1, scored_counts.shape[1]))
ll = np.sum(np.sum(logsumexp(scored_counts, axis=0) + np.log(curr_nr_of_counts)))
OldAlpha = deepcopy(EmissionParameters['Diag_event_params']['alpha'][curr_state])
mixtures = deepcopy(EmissionParameters['Diag_event_params']['mix_comp'][curr_state])
else:
zero_ix = []
for iter_nr in range(max_nr_iter):
print('em-iteration ' + str(iter_nr))
scored_counts = score_counts(curr_counts, curr_state, EmissionParameters)
scored_counts += np.tile(np.log(mixtures[:, np.newaxis]), (1, scored_counts.shape[1]))
# 2) Compute the mixture components
#compute the normalisation factor
normalised_likelihood = logsumexp(scored_counts, axis=0)
old_ll = ll
ll = np.sum(np.sum(logsumexp(scored_counts, axis=0) + np.log(curr_nr_of_counts)))
if np.abs(old_ll - ll) < stop_crit:
if len(zero_ix) == 0:
break
normalised_scores = scored_counts - np.tile(normalised_likelihood, (scored_counts.shape[0], 1))
un_norm_mixtures = logsumexp(normalised_scores, b=np.tile(curr_nr_of_counts, (scored_counts.shape[0], 1)), axis = 1)
mixtures = np.exp(un_norm_mixtures - logsumexp(un_norm_mixtures))
# 3) Compute for eachcount the most likely mixture component
curr_weights = np.exp(normalised_scores)
curr_weights = (curr_weights == np.tile(np.max(curr_weights, axis=0), (curr_weights.shape[0], 1))) *1.0
zero_mix = np.sum(curr_weights,axis=1) == 0
zero_ix = np.where(zero_mix)[0].tolist()
EmissionParameters['Diag_event_params']['mix_comp'][curr_state] = mixtures
#Get number of positions that are used. (In case there are fewer entries that rand_sample_size in counts)
rand_size = min(rand_sample_size, curr_counts.shape[1])
for i in zero_ix:
random_ix = np.random.choice(curr_counts.shape[1], rand_size, p=(curr_nr_of_counts[0, :] / np.float(np.sum(curr_nr_of_counts[0, :]))))
curr_counts = np.hstack([curr_counts, curr_counts[:, random_ix]])
curr_nr_of_counts = np.hstack([curr_nr_of_counts, np.ones((1, rand_size))])
temp_array = np.zeros((normalised_scores.shape[0], rand_size))
temp_array[i, :] = i
normalised_scores = np.hstack([normalised_scores, temp_array])
temp_array = np.zeros((curr_weights.shape[0], rand_size))
temp_array[i, :] = 1
curr_weights = np.hstack([curr_weights, temp_array])
# 4) Compute the dirichlet-multinomial parameters
for curr_mix_comp in range(EmissionParameters['Diag_event_params']['nr_mix_comp']):
local_counts = curr_counts
local_nr_counts = curr_nr_of_counts * curr_weights[curr_mix_comp, :]
local_counts = local_counts[:, local_nr_counts[0, :] > 0]
local_nr_counts = local_nr_counts[0, local_nr_counts[0, :] > 0]
if len(local_counts.shape) == 1:
local_counts = np.expand_dims(local_counts, axis=1)
curr_alpha = diag_event_model.estimate_multinomial_parameters(local_counts, local_nr_counts, EmissionParameters, OldAlpha[:, curr_mix_comp])
if curr_mix_comp in zero_ix:
OldAlpha[:, curr_mix_comp] = np.random.uniform(low=0.0001, high=0.1, size=OldAlpha[:, curr_mix_comp].shape)
OldAlpha[np.random.randint(OldAlpha.shape[0]), curr_mix_comp] = np.random.random() * 10.0
OldAlpha[-2, curr_mix_comp] = np.random.random() * 1.0
OldAlpha[-1, curr_mix_comp] = np.random.random() * 10.0
else:
OldAlpha[:, curr_mix_comp] = curr_alpha
if (len(zero_ix) > 0) and (iter_nr + 2 < max_nr_iter):
#Treat the case where some mixtures have prob zero
mixtures[zero_ix] = np.mean(mixtures)
mixtures /= np.sum(mixtures)
EmissionParameters['Diag_event_params']['mix_comp'][curr_state] = deepcopy(mixtures)
EmissionParameters['Diag_event_params']['alpha'][curr_state] = deepcopy(OldAlpha)
# Check if convergence has been achieved.
mixtures[zero_ix] = np.min(mixtures[mixtures > 0])
mixtures /= np.sum(mixtures)
return [deepcopy(OldAlpha), mixtures, ll]