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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
L is the likelihood of the fitted model
p is the number of parameters
N is the number of data points.
"""
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)
lowest_score = float('inf')
best_model = None
for n_components in range(self.min_n_components, self.max_n_components + 1):
try:
n_features = self.X.shape[1]
model = self.base_model(n_components)
# L is the likelihood of the fitted model
logL = model.score(self.X, self.lengths)
# N is the number of data points.
logN = np.log(len(self.X))
# https://discussions.udacity.com/t/number-of-parameters-bic-calculation/233235/17
# According to the formula, p(number of free parameters) is sum of these 4 terms:
# Transition probs are the transmat array- n* n
# Starting probabilities size n_components, but since they add up to 1.0, so it will be n - 1
# Number of means= n_components * n_features; Variances are the size of the covars array, s
# since we are using "diag" so it will be n_components * n_features
# So we will get the formula as n_components * n_components + 2 * n_components * n_features -1
p = np.power(n_components, 2) + 2 * n_components * n_features - 1
# compute BIC
BIC_score = -2 * logL + p * logN
# assign BIC_score to lowest_score if it is less than the lowest_score
lowest_score = min(BIC_score, lowest_score)
# assign current model to best_model if the lowest_score is the current BIC_score
best_model = model if lowest_score == BIC_score else best_model
except:
continue
return best_model
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
DIC = log(P(X(i)) - 1/(M-1)SUM(log(P(X(all but i))
'''
def select(self):
warnings.filterwarnings("ignore", category=DeprecationWarning)
# Initialize variables
best_score = float('-inf')
best_model = None
# Iterate through each component
for n_components in range(self.min_n_components, self.max_n_components + 1):
# Get the list of words
word_list = self.words.keys()
try:
scores = []
model = self.base_model(n_components)
# Iterate through each word in the list
for word in word_list:
# score all words that is not this_word
if word == self.this_word:
continue
# if word != self.this_word:
X_word, lengths_word = self.hwords[word]
scores.append(model.score(X_word, lengths_word))
# calculate score
current_score = model.score(self.X, self.lengths) - np.average(scores)
# update best_score and best_model
best_score = max(best_score, current_score)
best_model = model if best_score == current_score else best_model
except:
pass
return best_model
class SelectorCV(ModelSelector):
''' select best model based on average log Likelihood of cross-validation folds
'''
def select(self):
warnings.filterwarnings("ignore", category=DeprecationWarning)
# Initialize variables
best_score = float('-inf')
best_model = None
score_sum = 0
# By using the fit method during training, the Baum-Welch Expectation-Maximization (EM) algorithm is
# invoked iteratively to find the best estimate for the model for the number of hidden states
# specified from a group of sample sequences.
for n_components in range(self.min_n_components, self.max_n_components + 1):
try:
split_method = KFold(n_splits=min(3, len(self.sequences)))
logL_list = []
word_sequences = self.sequences
# Break the training set into "folds" and rotate which fold is left out of training
for cv_train_idx, cv_test_idx in split_method.split(word_sequences):
# In order to run hmmlearn training using the X,lengths tuples on the new folds,
# subsets must be combined based on the indices given for the folds.
# A helper utility has been provided in the asl_utils module named combine_sequences for this purpose.
X_train, lengths_train = combine_sequences(cv_train_idx, word_sequences)
X_test, lengths_test = combine_sequences(cv_test_idx, word_sequences)
# we train a single word using Gaussian hidden Markov models (HMM).
model = GaussianHMM(n_components=n_components, n_iter=1000).fit(X_train, lengths_train)
# The "left out" fold scored
logL = model.score(X_test, lengths_test)
logL_list.append(logL)
# compute average of logL and assign to best_score if it has a larger value than best_score
avg_score = np.average(logL_list)
best_score = max(avg_score, best_score)
# assign best_model to the current model if the current avg_score is the best_score
best_model = model if best_score == avg_score else best_model
except:
continue
return best_model