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my_model_selectors.py
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my_model_selectors.py
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import math
import statistics
import warnings
import numpy as np
from hmmlearn.hmm import GaussianHMM
from sklearn.model_selection import KFold
from asl_utils import combine_sequences
class ModelSelector(object):
'''
base class for model selection (strategy design pattern)
'''
def __init__(self, all_word_sequences: dict, all_word_Xlengths: dict, this_word: str,
n_constant=3,
min_n_components=2, max_n_components=10,
random_state=14, verbose=False):
self.words = all_word_sequences
self.hwords = all_word_Xlengths
self.sequences = all_word_sequences[this_word]
self.X, self.lengths = all_word_Xlengths[this_word]
self.this_word = this_word
self.n_constant = n_constant
self.min_n_components = min_n_components
self.max_n_components = max_n_components
self.random_state = random_state
self.verbose = verbose
def select(self):
raise NotImplementedError
def base_model(self, num_states):
# with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=DeprecationWarning)
# warnings.filterwarnings("ignore", category=RuntimeWarning)
try:
hmm_model = GaussianHMM(n_components=num_states, covariance_type="diag", n_iter=1000,
random_state=self.random_state, verbose=False).fit(self.X, self.lengths)
if self.verbose:
print("model created for {} with {} states".format(self.this_word, num_states))
return hmm_model
except:
if self.verbose:
print("failure on {} with {} states".format(self.this_word, num_states))
return None
class SelectorConstant(ModelSelector):
""" select the model with value self.n_constant
"""
def select(self):
""" select based on n_constant value
:return: GaussianHMM object
"""
best_num_components = self.n_constant
return self.base_model(best_num_components)
class SelectorBIC(ModelSelector):
""" select the model with the lowest Bayesian Information Criterion(BIC) score
http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf
Bayesian information criteria: BIC = -2 * logL + p * logN
"""
def select(self):
""" select the best model for self.this_word based on
BIC score for n between self.min_n_components and self.max_n_components
:return: GaussianHMM object
"""
warnings.filterwarnings("ignore", category=DeprecationWarning)
# TODO implement model selection based on BIC scores
BIC = [] #track the BIC
hidden_states = [] #track the number of hidden_states
n = len(self.sequences) #number of sequences
for num_hidden_states in range(self.min_n_components, self.max_n_components + 1): #for each possible number of hidden states
try: #if the hmmlearn library can train or score the model
hmm_model = self.base_model(num_states = num_hidden_states)
logL = hmm_model.score(self.X, self.lengths)
#each state has mean and Var for each of the features:
#2 * num_hidden_states * num_features
#Initial state occupation probabilities: num_hidden_states - 1
#Transition probabilities: num_hidden_states * (num_hidden_states - 1)
#https://discussions.udacity.com/t/number-of-parameters-bic-calculation/233235/12
#https://discussions.udacity.com/t/number-of-parameters-bic-calculation/233235/17
p = num_hidden_states * (num_hidden_states - 1) + num_hidden_states - 1 + 2 * num_hidden_states * hmm_model.n_features
BIC.append(-2 * logL + p * math.log(n))
hidden_states.append(num_hidden_states)
except: #if the hmmlearn library cannot train or score the model
pass
#now see which number of hidden states gave the smallest BIC
try:
optimal_num_hidden_states = hidden_states[BIC.index(min(BIC))]
optimal_hmm_model = GaussianHMM(n_components = optimal_num_hidden_states, covariance_type="diag", n_iter=1000,
random_state = self.random_state, verbose = False).fit(self.X, self.lengths)
return optimal_hmm_model
except ValueError: #if the hmmlearn library cannot train a single model for all possible number of hidden states
pass
class SelectorDIC(ModelSelector):
''' select best model based on Discriminative Information Criterion
Biem, Alain. "A model selection criterion for classification: Application to hmm topology optimization."
Document Analysis and Recognition, 2003. Proceedings. Seventh International Conference on. IEEE, 2003.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf
https://pdfs.semanticscholar.org/ed3d/7c4a5f607201f3848d4c02dd9ba17c791fc2.pdf
DIC = log(P(X(i)) - 1/(M-1)SUM(log(P(X(all but i))
'''
def select(self):
warnings.filterwarnings("ignore", category=DeprecationWarning)
# TODO implement model selection based on DIC scores
DIC = [] #track the DIC
hidden_states = [] #track the number of hidden_states
rest_words = list(self.words) #list
rest_words.remove(self.this_word)
for num_hidden_states in range(self.min_n_components, self.max_n_components + 1): #for each possible number of hidden states
try: #if the hmmlearn library can train or score the model
rest_logL = 0
hmm_model = self.base_model(num_states = num_hidden_states)
logL = hmm_model.score(self.X, self.lengths)
rest_num_scorable_words = 0
for word in rest_words:
X, lengths = self.hwords[word]
try: #if the hmmlearn library can score the model
rest_logL = rest_logL + hmm_model.score(X, lengths)
rest_num_scorable_words = rest_num_scorable_words + 1
except: #if the hmmlearn library cannot score the model
print('{0} is not scorable!'.format(word))
DIC.append(logL - rest_logL / rest_num_scorable_words)
hidden_states.append(num_hidden_states)
except: #if the hmmlearn library cannot train or score the model
pass
#now see which number of hidden states gave the largest DIC
try:
optimal_num_hidden_states = hidden_states[DIC.index(max(DIC))]
optimal_hmm_model = GaussianHMM(n_components = optimal_num_hidden_states, covariance_type="diag", n_iter=1000,
random_state = self.random_state, verbose = False).fit(self.X, self.lengths)
return optimal_hmm_model
except ValueError: #if the hmmlearn library cannot train a single model for all possible number of hidden states
pass
class SelectorCV(ModelSelector):
''' select best model based on average log Likelihood of cross-validation folds
'''
def select(self):
warnings.filterwarnings("ignore", category=DeprecationWarning)
# TODO implement model selection using CV
likelihoods = [] #track the likelihoods
hidden_states = [] #track the number of hidden_states
k = len(self.sequences) #number of sequences
k = min(k, 5) #if k<=5, do leave-one-out cross-validation; otherwise, do 5-fold cross-validation
for num_hidden_states in range(self.min_n_components, self.max_n_components + 1): #for each possible number of hidden states
try: #if the hmmlearn library can train or score the model
if k > 1: #only then do cross-validation
ave_logL = 0
split_method = KFold(n_splits = k)
for training_idx, testing_idx in split_method.split(self.sequences):
training_X, training_lengths = combine_sequences(training_idx, self.sequences) #list, list
training_X = np.asarray(training_X)
testing_X, testing_lengths = combine_sequences(testing_idx, self.sequences) #list, list
testing_X = np.asarray(testing_X)
hmm_model = GaussianHMM(n_components = num_hidden_states, covariance_type="diag", n_iter=1000,
random_state = self.random_state, verbose = False).fit(training_X, training_lengths)
logL = hmm_model.score(testing_X, testing_lengths)
ave_logL = ave_logL + logL
ave_logL = ave_logL / k
else:
hmm_model = GaussianHMM(n_components = num_hidden_states, covariance_type="diag", n_iter=1000,
random_state = self.random_state, verbose = False).fit(self.X, self.lengths)
ave_logL = hmm_model.score(self.X, self.lengths)
likelihoods.append(ave_logL)
hidden_states.append(num_hidden_states)
except: #if the hmmlearn library cannot train or score the model
pass
#now see which number of hidden states gave the largest likelihood
try:
optimal_num_hidden_states = hidden_states[likelihoods.index(max(likelihoods))]
optimal_hmm_model = GaussianHMM(n_components = optimal_num_hidden_states, covariance_type="diag", n_iter=1000,
random_state = self.random_state, verbose = False).fit(self.X, self.lengths)
return optimal_hmm_model
except ValueError: #if the hmmlearn library cannot train a single model for all possible number of hidden states
pass