from lab2_proto import *
from lab2_tools import *
from prondict import prondict
import matplotlib.pyplot as plt
data = np.load('lab2_data.npz')['data']
one_speaker_model = np.load('lab2_models_onespkr.npz')
all_model = np.load('lab2_models_all.npz')
example = np.load('lab2_example.npz')["example"]
example.shape = (1, )
example = example[0]
# load one model
isolated = {}
for digit in prondict.keys():
isolated[digit] = ['sil'] + prondict[digit] + ['sil']
phoneHMMs = np.load('lab2_models_onespkr.npz')['phoneHMMs'].item()
wordHMMs = {}
for key in isolated.keys():
wordHMMs[key] = concatHMMs(phoneHMMs, isolated[key])
# log_multivariate_normal_density_diag(X, means, covars):
# test correctness
if False:
result = log_multivariate_normal_density_diag(example["lmfcc"],
wordHMMs['o']["means"],
wordHMMs['o']["covars"])
def main():
np.seterr(divide='ignore') # Suppress divide by zero warning
example = np.load('lab2_example.npz', allow_pickle=True)['example'].item()
phone_hmms = np.load('lab2_models_all.npz',
allow_pickle=True)['phoneHMMs'].item()
# Concatenate all digit hmms
word_hmms = {}
for digit in prondict.keys():
word_hmms[digit] = concatHMMs(phone_hmms,
['sil'] + prondict[digit] + ['sil'])
data = np.load('lab2_data.npz', allow_pickle=True)['data']
best_model = {}
acc_count = 0
print("Running Forward algorithm...")
for idx, dt in tqdm(enumerate(data)): # Iterate over data samples
maxloglik = None
for digit in word_hmms.keys(): # Iterate over hmms
obsloglik = log_multivariate_normal_density_diag(
dt['lmfcc'], word_hmms[digit]['means'],
word_hmms[digit]['covars'])
logalpha = forward(obsloglik,
np.log(word_hmms[digit]['startprob']),
np.log(word_hmms[digit]['transmat']))
loglik = logsumexp(logalpha[-1])
if maxloglik is None or maxloglik < loglik: # If better likelihood found
best_model[idx] = digit # Set most probable model
maxloglik = loglik # Update max log likelihood
if dt['digit'] == best_model[idx]:
acc_count += 1
# print("The best model for utterance " + str(idx) + " was hmm: " + str(best_model[idx]))
# print("The real digit of utterance " + str(idx) + " was digit: " + str(dt['digit']) + "\n")
print("The accuracy of the predictions has been: " +
str(np.round(acc_count / len(data) * 100, 2)) + "%")
np.seterr(divide='ignore') # Suppress divide by zero warning
logalpha = forward(example['obsloglik'],
np.log(word_hmms['o']['startprob']),
np.log(word_hmms['o']['transmat']))
vloglik, vpath = viterbi(example['obsloglik'],
np.log(word_hmms['o']['startprob']),
np.log(word_hmms['o']['transmat']))
plt.pcolormesh(logalpha.T)
plt.plot(vpath.T, color="red")
plt.show()
best_model = {}
acc_count = 0
print("Running Viterbi algorithm...")
for idx, dt in tqdm(enumerate(data)): # Iterate over data samples
maxloglik = None
for digit in word_hmms.keys(): # Iterate over hmms
obsloglik = log_multivariate_normal_density_diag(
dt['lmfcc'], word_hmms[digit]['means'],
word_hmms[digit]['covars'])
vloglik, vpath = viterbi(obsloglik,
np.log(word_hmms[digit]['startprob']),
np.log(word_hmms[digit]['transmat']))
if maxloglik is None or maxloglik < vloglik: # If better likelihood found
best_model[idx] = digit # Set most probable model
maxloglik = vloglik # Update max log likelihood
if dt['digit'] == best_model[idx]:
acc_count += 1
# print("The best model for utterance " + str(idx) + " was hmm: " + str(best_model[idx]))
# print("The real digit of utterance " + str(idx) + " was digit: " + str(dt['digit']) + "\n")
print("The accuracy of the predictions has been: " +
str(np.round(acc_count / len(data) * 100, 2)) + "%")
# Baum-Welch algorithm
best_loglik = None
best_model = None
for digit in word_hmms.keys(): # Iterate over hmms
print("Trying model " + str(digit))
means = word_hmms[digit]['means']
covars = word_hmms[digit]['covars']
obsloglik = log_multivariate_normal_density_diag(
data[10]['lmfcc'], means, covars)
vloglik = 0
newloglik = viterbi(obsloglik, np.log(word_hmms[digit]['startprob']),
np.log(word_hmms[digit]['transmat']))[0]
it = 0
while it < 20 and abs(newloglik - vloglik) > 1.0:
vloglik = newloglik # Update value of log-likelihood
forward_prob = forward(obsloglik,
np.log(word_hmms[digit]['startprob']),
np.log(word_hmms[digit]['transmat']))
backward_prob = backward(obsloglik,
np.log(word_hmms[digit]['transmat']))
log_gamma = statePosteriors(forward_prob, backward_prob)
means, covars = updateMeanAndVar(data[10]['lmfcc'], log_gamma)
obsloglik = log_multivariate_normal_density_diag(
data[10]['lmfcc'], means, covars)
newloglik = viterbi(obsloglik,
np.log(word_hmms[digit]['startprob']),
np.log(word_hmms[digit]['transmat']))[0]
it += 1 # Update number of iterations
print("Log-likelihood: " + str(newloglik) +
". Number of iterations until convergence: " + str(it))
if best_loglik is None or newloglik > best_loglik:
best_loglik = newloglik
best_model = digit
print("The best log-likelihood is: " + str(best_loglik) +
". It corresponds to the model " + str(best_model))
def maintask(task):
data = np.load('lab2_data.npz')['data']
phoneHMMs = np.load('lab2_models_onespkr.npz')['phoneHMMs'].item()
phoneHMMs_all = np.load('lab2_models_all.npz')['phoneHMMs'].item()
if task == '4':
hmm1 = phoneHMMs['ah']
hmm2 = phoneHMMs['ao']
twohmm = concatTwoHMMs(hmm1, hmm2)
"""5 HMM Likelihood and Recognition"""
example = np.load('lab2_example.npz')['example'].item()
isolated = {}
for digit in prondict.keys():
isolated[digit] = ['sil'] + prondict[digit] + ['sil']
wordHMMs = {}
wordHMMs_all = {}
for digit in prondict.keys():
wordHMMs[digit] = concatHMMs(phoneHMMs, isolated[digit])
# for 11 digits
for digit in prondict.keys():
wordHMMs_all[digit] = concatHMMs(phoneHMMs_all, isolated[digit])
# example
lpr = log_multivariate_normal_density_diag(example['lmfcc'],
wordHMMs['o']['means'],
wordHMMs['o']['covars'])
diff = example['obsloglik'] - lpr # 0
# same digit 'o'
lpr_o = log_multivariate_normal_density_diag(data[22]['lmfcc'],
wordHMMs_all['o']['means'],
wordHMMs_all['o']['covars'])
if task == '5.1':
plt.figure()
plt.subplot(2, 1, 1)
plt.pcolormesh(lpr.T)
plt.title('example "o" ')
plt.colorbar()
plt.subplot(2, 1, 2)
plt.pcolormesh(lpr_o.T)
plt.title('test "o" from data22')
plt.colorbar()
plt.show()
"""
5.2
"""
lalpha = forward(lpr, np.log(wordHMMs['o']['startprob']),
np.log(wordHMMs['o']['transmat']))
diff1 = example['logalpha'] - lalpha # 0
# log-likelihood
loglike = logsumexp(lalpha[-1])
diff0 = example['loglik'] - loglike # 0
# score all the 44 utterances in the data array with each of the 11 HMM
# models in wordHMMs.
scores_1 = np.zeros((44, 11))
scores_2 = np.zeros((44, 11))
labels_ori = []
labels_pre = []
labels_pre2 = []
keys = list(prondict.keys())
acc_1 = 0
acc_2 = 0
if task == '5.2':
for i in range(44):
for j, key in enumerate(keys):
lpr = log_multivariate_normal_density_diag(
data[i]['lmfcc'], wordHMMs_all[key]['means'],
wordHMMs_all[key]['covars'])
alpha = forward(lpr, np.log(wordHMMs_all[key]['startprob']),
np.log(wordHMMs_all[key]['transmat']))
scores_2[i, j] = logsumexp(alpha[-1])
lpr_1 = log_multivariate_normal_density_diag(
data[i]['lmfcc'], wordHMMs[key]['means'],
wordHMMs[key]['covars'])
alpha_1 = forward(lpr_1, np.log(wordHMMs[key]['startprob']),
np.log(wordHMMs[key]['transmat']))
scores_1[i, j] = logsumexp(alpha_1[-1])
ori = data[i]['digit']
pre_1 = keys[int(np.argmax(scores_1[i, :]))]
pre_2 = keys[int(np.argmax(scores_2[i, :]))]
#labels_ori.append(ori)
labels_pre.append(pre_1)
labels_pre2.append(pre_2)
if ori == pre_1:
acc_1 += 1
if ori == pre_2:
acc_2 += 1
print(
"Accuracy(trained on all speakers): {0}; Accuracy(trained on one speaker):{1} "
.format(acc_2, acc_1))
print(labels_pre, labels_pre2)
"""
5.3 Viterbi
"""
viterbi_loglik, viterbi_path = viterbi(lpr,
np.log(wordHMMs['o']['startprob']),
np.log(wordHMMs['o']['transmat']))
if task == '5.3':
plt.pcolormesh(lalpha.T)
plt.plot(viterbi_path, 'r')
plt.title(
'alpha array overlaid with best path obtained by Viterbi decoding '
)
plt.colorbar()
plt.show()
diff3 = example['vloglik'] - viterbi_loglik.T # 0
# Score all 44 utterances in the data with each of the 11 HMM models in wordHMMs
for i in range(44):
for j, key in enumerate(keys):
lpr = log_multivariate_normal_density_diag(
data[i]['lmfcc'], wordHMMs_all[key]['means'],
wordHMMs_all[key]['covars'])
viterbi_2, viterbi_path_2 = viterbi(
lpr, np.log(wordHMMs_all[key]['startprob']),
np.log(wordHMMs_all[key]['transmat']))
scores_2[i, j] = viterbi_2
lpr_1 = log_multivariate_normal_density_diag(
data[i]['lmfcc'], wordHMMs[key]['means'],
wordHMMs[key]['covars'])
viterbi_1, viterbi_path_1 = viterbi(
lpr_1, np.log(wordHMMs[key]['startprob']),
np.log(wordHMMs[key]['transmat']))
scores_1[i, j] = viterbi_1
ori = data[i]['digit']
pre_1 = keys[int(np.argmax(scores_1[i, :]))]
pre_2 = keys[int(np.argmax(scores_2[i, :]))]
#labels_ori.append(ori)
labels_pre.append(pre_1)
labels_pre2.append(pre_2)
if ori == pre_1:
acc_1 += 1
if ori == pre_2:
acc_2 += 1
print(
"Accuracy(trained on all speakers): {0}; Accuracy(trained on one speaker):{1} "
.format(acc_2, acc_1))
print(labels_pre, labels_pre2)
"""
5.4
"""
lbeta = backward(lpr, np.log(wordHMMs['o']['startprob']),
np.log(wordHMMs['o']['transmat']))
diff2 = example['logbeta'] - lbeta
# log-likelihood
loglike = logsumexp(lbeta[0])
diff4 = example['loglik'] - loglike # 0
if task == '5.4':
plt.figure()
plt.subplot(1, 3, 1)
plt.pcolormesh(lbeta)
plt.title('log-beta')
plt.subplot(1, 3, 2)
plt.pcolormesh(example['logbeta'])
plt.title('example')
plt.subplot(1, 3, 3)
plt.pcolormesh(example['logalpha'])
plt.title('log-alpha')
plt.show()
"""6 HMM Retraining(emission probability distributions)"""
"""
6.1
"""
lgamma = statePosteriors(lalpha, lbeta)
N = lgamma.shape[0]
K = 9
lgamma_gmm = np.zeros((N, K))
total = log_multivariate_normal_density_diag(example['lmfcc'],
wordHMMs['o']['means'],
wordHMMs['o']['covars'])
if task == '6.1':
print('HMM posteriors')
print('each time step sum along state axis',
np.sum(np.exp(lgamma), axis=1)) #=1
print('each state sum along time axis',
np.sum(np.exp(lgamma) / 71, axis=0))
print('sum over both states and time steps',
np.sum(np.sum(
np.exp(lgamma)))) # =length of obs sequence/time steps
print('length of observation sequence', lalpha.shape[0])
print('GMM posteriors')
# for k in range(K):
#lgamma_gmm[:, k] = 1 / K * total[:, k] / np.sum(total[:, k])
gmm = mixture.GaussianMixture(n_components=9)
gmm.fit(example['lmfcc'])
gmm_post = gmm.predict_proba(example['lmfcc'])
plt.subplot(2, 1, 1)
plt.pcolormesh(gmm_post.T)
plt.title('GMM posteriors')
plt.colorbar()
plt.subplot(2, 1, 2)
plt.pcolormesh(lgamma.T)
plt.title('HMM posteriors')
plt.colorbar()
plt.show()
"""6.2"""
if task == '6.2':
plt.figure()
L = {}
for d in prondict:
# initialization
log_pi = np.log(wordHMMs_all[d]['startprob'])
log_tr = np.log(wordHMMs_all[d]['transmat'])
means = wordHMMs_all[d]['means']
covars = wordHMMs_all[d]['covars']
l = []
# repitation:
for i in range(20):
lpr = log_multivariate_normal_density_diag(
data[10]['lmfcc'], means, covars)
# Expectation
lalpha = forward(lpr, log_pi, log_tr)
lbeta = backward(lpr, log_pi, log_tr)
log_gamma = statePosteriors(lalpha, lbeta)
# Maximization
means, covars = updateMeanAndVar(data[10]['lmfcc'], log_gamma)
# Estimate likelihood
log_like = logsumexp(lalpha[-1])
if i > 2 and log_like - l[-1] < 0.1:
l.append(log_like)
L[d] = l
break
else:
l.append(log_like)
L[d] = l
plt.plot(l, label=d)
plt.legend()
plt.title('log-likelihood (data[10] with different wordHMMs)')
plt.show()