import numpy as np
import pandas as pd
from asl_data import AslDb


asl = AslDb() # initializes the database
asl.df.head() # displays the first five rows of the asl database, indexed by video and frame

asl.df.ix[98,1]  # look at the data available for an individual frame

"""
Explanation: Artificial Intelligence Engineer Nanodegree - Probabilistic Models
Project: Sign Language Recognition System

Introduction
Part 1 Feature Selection
Tutorial
Features Submission
Features Unittest


Part 2 Train the models
Tutorial
Model Selection Score Submission
Model Score Unittest


Part 3 Build a Recognizer
Tutorial
Recognizer Submission
Recognizer Unittest


Part 4 (OPTIONAL) Improve the WER with Language Models

<a id='intro'></a>
Introduction
The overall goal of this project is to build a word recognizer for American Sign Language video sequences, demonstrating the power of probabalistic models.  In particular, this project employs  hidden Markov models (HMM's) to analyze a series of measurements taken from videos of American Sign Language (ASL) collected for research (see the RWTH-BOSTON-104 Database).  In this video, the right-hand x and y locations are plotted as the speaker signs the sentence.

The raw data, train, and test sets are pre-defined.  You will derive a variety of feature sets (explored in Part 1), as well as implement three different model selection criterion to determine the optimal number of hidden states for each word model (explored in Part 2). Finally, in Part 3 you will implement the recognizer and compare the effects the different combinations of feature sets and model selection criteria.  
At the end of each Part, complete the submission cells with implementations, answer all questions, and pass the unit tests.  Then submit the completed notebook for review!
<a id='part1_tutorial'></a>
PART 1: Data
Features Tutorial
Load the initial database
A data handler designed for this database is provided in the student codebase as the AslDb class in the asl_data module.  This handler creates the initial pandas dataframe from the corpus of data included in the data directory as well as dictionaries suitable for extracting data in a format friendly to the hmmlearn library.  We'll use those to create models in Part 2.
To start, let's set up the initial database and select an example set of features for the training set.  At the end of Part 1, you will create additional feature sets for experimentation.
End of explanation
"""


asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']
asl.df.head()  # the new feature 'grnd-ry' is now in the frames dictionary

"""
Explanation: The frame represented by video 98, frame 1 is shown here:

Feature selection for training the model
The objective of feature selection when training a model is to choose the most relevant variables while keeping the model as simple as possible, thus reducing training time.  We can use the raw features already provided or derive our own and add columns to the pandas dataframe asl.df for selection. As an example, in the next cell a feature named 'grnd-ry' is added. This feature is the difference between the right-hand y value and the nose y value, which serves as the "ground" right y value.
End of explanation
"""


from asl_utils import test_features_tryit
# TODO add df columns for 'grnd-rx', 'grnd-ly', 'grnd-lx' representing differences between hand and nose locations
asl.df['grnd-rx'] = asl.df['right-x'] - asl.df['nose-x']
asl.df['grnd-ly'] = asl.df['left-y'] - asl.df['nose-y']
asl.df['grnd-lx'] = asl.df['left-x'] - asl.df['nose-x']

# test the code
test_features_tryit(asl)

# collect the features into a list
features_ground = ['grnd-rx','grnd-ry','grnd-lx','grnd-ly']
 #show a single set of features for a given (video, frame) tuple
[asl.df.ix[98,1][v] for v in features_ground]

"""
Explanation: Try it!
End of explanation
"""


training = asl.build_training(features_ground)
print("Training words: {}".format(training.words))

"""
Explanation: Build the training set
Now that we have a feature list defined, we can pass that list to the build_training method to collect the features for all the words in the training set.  Each word in the training set has multiple examples from various videos.  Below we can see the unique words that have been loaded into the training set:
End of explanation
"""


training.get_word_Xlengths('CHOCOLATE')

"""
Explanation: The training data in training is an object of class WordsData defined in the asl_data module.  in addition to the words list, data can be accessed with the get_all_sequences, get_all_Xlengths, get_word_sequences, and get_word_Xlengths methods. We need the get_word_Xlengths method to train multiple sequences with the hmmlearn library.  In the following example, notice that there are two lists; the first is a concatenation of all the sequences(the X portion) and the second is a list of the sequence lengths(the Lengths portion).
End of explanation
"""


df_means = asl.df.groupby('speaker').mean()
df_means

"""
Explanation: More feature sets
So far we have a simple feature set that is enough to get started modeling.  However, we might get better results if we manipulate the raw values a bit more, so we will go ahead and set up some other options now for experimentation later.  For example, we could normalize each speaker's range of motion with grouped statistics using Pandas stats functions and pandas groupby.  Below is an example for finding the means of all speaker subgroups.
End of explanation
"""


asl.df['left-x-mean']= asl.df['speaker'].map(df_means['left-x'])
asl.df.head()

"""
Explanation: To select a mean that matches by speaker, use the pandas map method:
End of explanation
"""


from asl_utils import test_std_tryit
# TODO Create a dataframe named `df_std` with standard deviations grouped by speaker
df_std = asl.df.groupby('speaker').std()

# test the code
test_std_tryit(df_std)

"""
Explanation: Try it!
End of explanation
"""


# TODO add features for normalized by speaker values of left, right, x, y
# Name these 'norm-rx', 'norm-ry', 'norm-lx', and 'norm-ly'
# using Z-score scaling (X-Xmean)/Xstd

columns = ['right-x','right-y','left-x','left-y']
features_norm = ['norm-rx','norm-ry', 'norm-lx','norm-ly']
for i,f in enumerate(features_norm):
    means = asl.df['speaker'].map(df_means[columns[i]])
    standards = asl.df['speaker'].map(df_std[columns[i]])
    asl.df[f]=(asl.df[columns[i]] - means) / standards

# TODO add features for polar coordinate values where the nose is the origin
# Name these 'polar-rr', 'polar-rtheta', 'polar-lr', and 'polar-ltheta'
# Note that 'polar-rr' and 'polar-rtheta' refer to the radius and angle

features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']
columns = [['grnd-rx','grnd-ry'],['grnd-lx','grnd-ly']]

def radius(x, y):
    return np.sqrt(x ** 2 + y ** 2)

def theta(x, y):
    return np.arctan2(x, y)

for i, f in enumerate(features_polar):
    if i % 2 == 0:
        asl.df[f] = radius(asl.df[features_ground[i]],
                          asl.df[features_ground[i + 1]])
    else:
        asl.df[f] = theta(asl.df[features_ground[i - 1]],
                         asl.df[features_ground[i]])

# TODO add features for left, right, x, y differences by one time step, i.e. the "delta" values discussed in the lecture
# Name these 'delta-rx', 'delta-ry', 'delta-lx', and 'delta-ly'

features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']
columns = ['right-x','right-y','left-x','left-y']
for i,f in enumerate(features_delta):
    asl.df[f] = asl.df[columns[i]].diff().fillna(0.0)

# TODO add features of your own design, which may be a combination of the above or something else
# Name these whatever you would like

# TODO define a list named 'features_custom' for building the training set

custom_features = ['norm-delta-rx', 'norm-delta-ry', 'norm-delta-lx', 'norm-delta-ly']
columns = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']
df_new_means = asl.df.groupby('speaker').mean()
df_new_std = asl.df.groupby('speaker').std()
for i,f in enumerate(custom_features):
    means = asl.df['speaker'].map(df_new_means[columns[i]])
    standards = asl.df['speaker'].map(df_new_std[columns[i]])
    asl.df[f]=((asl.df[columns[i]] - means) / standards)+ asl.df[features_delta[i]]

"""
Explanation: <a id='part1_submission'></a>
Features Implementation Submission
Implement four feature sets and answer the question that follows.
- normalized Cartesian coordinates
    - use mean and standard deviation statistics and the standard score equation to account for speakers with different heights and arm length


polar coordinates

calculate polar coordinates with Cartesian to polar equations
use the np.arctan2 function and swap the x and y axes to move the $0$ to $2\pi$ discontinuity to 12 o'clock instead of 3 o'clock;  in other words, the normal break in radians value from $0$ to $2\pi$ occurs directly to the left of the speaker's nose, which may be in the signing area and interfere with results.  By swapping the x and y axes, that discontinuity move to directly above the speaker's head, an area not generally used in signing.



delta difference

as described in Thad's lecture, use the difference in values between one frame and the next frames as features
pandas diff method and fillna method will be helpful for this one



custom features

These are your own design; combine techniques used above or come up with something else entirely. We look forward to seeing what you come up with! 
Some ideas to get you started:
normalize using a feature scaling equation
normalize the polar coordinates
adding additional deltas
End of explanation
"""


import unittest
# import numpy as np

class TestFeatures(unittest.TestCase):

    def test_features_ground(self):
        sample = (asl.df.ix[98, 1][features_ground]).tolist()
        self.assertEqual(sample, [9, 113, -12, 119])

    def test_features_norm(self):
        sample = (asl.df.ix[98, 1][features_norm]).tolist()
        np.testing.assert_almost_equal(sample, [ 1.153,  1.663, -0.891,  0.742], 3)

    def test_features_polar(self):
        sample = (asl.df.ix[98,1][features_polar]).tolist()
        np.testing.assert_almost_equal(sample, [113.3578, 0.0794, 119.603, -0.1005], 3)

    def test_features_delta(self):
        sample = (asl.df.ix[98, 0][features_delta]).tolist()
        self.assertEqual(sample, [0, 0, 0, 0])
        sample = (asl.df.ix[98, 18][features_delta]).tolist()
        self.assertTrue(sample in [[-16, -5, -2, 4], [-14, -9, 0, 0]], "Sample value found was {}".format(sample))
                         
suite = unittest.TestLoader().loadTestsFromModule(TestFeatures())
unittest.TextTestRunner().run(suite)

"""
Explanation: Question 1:  What custom features did you choose for the features_custom set and why?
Answer 1:  The custom features choosen is the addition of normalized polar coordinates with the delta values. Polar coordinates are used to make the nose the origin of the frame and all the frame points orbit around it. Normalization is used as the gaussian fit normal distribution very well. The delta values show the change in the positions with time and help measure up the probabilities and gaussian size.
<a id='part1_test'></a>
Features Unit Testing
Run the following unit tests as a sanity check on the defined "ground", "norm", "polar", and 'delta"
feature sets.  The test simply looks for some valid values but is not exhaustive.  However, the project should not be submitted if these tests don't pass.
End of explanation
"""


import warnings
from hmmlearn.hmm import GaussianHMM

def train_a_word(word, num_hidden_states, features):
    
    warnings.filterwarnings("ignore", category=DeprecationWarning)
    training = asl.build_training(features)  
    X, lengths = training.get_word_Xlengths(word)
    model = GaussianHMM(n_components=num_hidden_states, n_iter=1000).fit(X, lengths)
    logL = model.score(X, lengths)
    return model, logL

demoword = 'BOOK'
model, logL = train_a_word(demoword, 3, features_ground)
print("Number of states trained in model for {} is {}".format(demoword, model.n_components))
print("logL = {}".format(logL))

"""
Explanation: <a id='part2_tutorial'></a>
PART 2: Model Selection
Model Selection Tutorial
The objective of Model Selection is to tune the number of states for each word HMM prior to testing on unseen data.  In this section you will explore three methods: 
- Log likelihood using cross-validation folds (CV)
- Bayesian Information Criterion (BIC)
- Discriminative Information Criterion (DIC) 
Train a single word
Now that we have built a training set with sequence data, we can "train" models for each word.  As a simple starting example, we train a single word using Gaussian hidden Markov models (HMM).   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 seequences. For this example, we assume the correct number of hidden states is 3, but that is just a guess.  How do we know what the "best" number of states for training is?  We will need to find some model selection technique to choose the best parameter.
End of explanation
"""


def show_model_stats(word, model):
    print("Number of states trained in model for {} is {}".format(word, model.n_components))    
    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])    
    for i in range(model.n_components):  # for each hidden state
        print("hidden state #{}".format(i))
        print("mean = ", model.means_[i])
        print("variance = ", variance[i])
        print()
    
show_model_stats(demoword, model)

"""
Explanation: The HMM model has been trained and information can be pulled from the model, including means and variances for each feature and hidden state.  The log likelihood for any individual sample or group of samples can also be calculated with the score method.
End of explanation
"""


my_testword = 'CHOCOLATE'
model, logL = train_a_word(my_testword, 3, features_ground) # Experiment here with different parameters
show_model_stats(my_testword, model)
print("logL = {}".format(logL))

"""
Explanation: Try it!
Experiment by changing the feature set, word, and/or num_hidden_states values in the next cell to see changes in values.
End of explanation
"""


%matplotlib inline

import math
from matplotlib import (cm, pyplot as plt, mlab)

def visualize(word, model):
    """ visualize the input model for a particular word """
    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])
    figures = []
    for parm_idx in range(len(model.means_[0])):
        xmin = int(min(model.means_[:,parm_idx]) - max(variance[:,parm_idx]))
        xmax = int(max(model.means_[:,parm_idx]) + max(variance[:,parm_idx]))
        fig, axs = plt.subplots(model.n_components, sharex=True, sharey=False)
        colours = cm.rainbow(np.linspace(0, 1, model.n_components))
        for i, (ax, colour) in enumerate(zip(axs, colours)):
            x = np.linspace(xmin, xmax, 100)
            mu = model.means_[i,parm_idx]
            sigma = math.sqrt(np.diag(model.covars_[i])[parm_idx])
            ax.plot(x, mlab.normpdf(x, mu, sigma), c=colour)
            ax.set_title("{} feature {} hidden state #{}".format(word, parm_idx, i))

            ax.grid(True)
        figures.append(plt)
    for p in figures:
        p.show()
        
visualize(my_testword, model)

"""
Explanation: Visualize the hidden states
We can plot the means and variances for each state and feature.  Try varying the number of states trained for the HMM model and examine the variances.  Are there some models that are "better" than others?  How can you tell?  We would like to hear what you think in the classroom online.
End of explanation
"""


from my_model_selectors import SelectorConstant

training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1
word = 'VEGETABLE' # Experiment here with different words
model = SelectorConstant(training.get_all_sequences(), training.get_all_Xlengths(), word, n_constant=3).select()
print("Number of states trained in model for {} is {}".format(word, model.n_components))

"""
Explanation: ModelSelector class
Review the ModelSelector class from the codebase found in the my_model_selectors.py module.  It is designed to be a strategy pattern for choosing different model selectors.  For the project submission in this section, subclass SelectorModel to implement the following model selectors.  In other words, you will write your own classes/functions in the my_model_selectors.py module and run them from this notebook:

SelectorCV:  Log likelihood with CV
SelectorBIC: BIC 
SelectorDIC: DIC

You will train each word in the training set with a range of values for the number of hidden states, and then score these alternatives with the model selector, choosing the "best" according to each strategy. The simple case of training with a constant value for n_components can be called using the provided SelectorConstant subclass as follow:
End of explanation
"""


from sklearn.model_selection import KFold

training = asl.build_training(features_ground) # Experiment here with different feature sets
word = 'VEGETABLE' # Experiment here with different words
word_sequences = training.get_word_sequences(word)
split_method = KFold()
for cv_train_idx, cv_test_idx in split_method.split(word_sequences):
    print("Train fold indices:{} Test fold indices:{}".format(cv_train_idx, cv_test_idx))  # view indices of the folds

"""
Explanation: Cross-validation folds
If we simply score the model with the Log Likelihood calculated from the feature sequences it has been trained on, we should expect that more complex models will have higher likelihoods. However, that doesn't tell us which would have a better likelihood score on unseen data.  The model will likely be overfit as complexity is added.  To estimate which topology model is better using only the training data, we can compare scores using cross-validation.  One technique for cross-validation is to break the training set into "folds" and rotate which fold is left out of training.  The "left out" fold scored.  This gives us a proxy method of finding the best model to use on "unseen data". In the following example, a set of word sequences is broken into three folds using the scikit-learn Kfold class object. When you implement SelectorCV, you will use this technique.
End of explanation
"""


words_to_train = ['FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']
import timeit

# TODO: Implement SelectorCV in my_model_selector.py
from my_model_selectors import SelectorCV

training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1
sequences = training.get_all_sequences()
Xlengths = training.get_all_Xlengths()
for word in words_to_train:
    start = timeit.default_timer()
    model = SelectorCV(sequences, Xlengths, word, 
                    min_n_components=2, max_n_components=15, random_state = 14).select()
    end = timeit.default_timer()-start
    if model is not None:
        print("Training complete for {} with {} states with time {} seconds".format(word, model.n_components, end))
    else:
        print("Training failed for {}".format(word))

# TODO: Implement SelectorBIC in module my_model_selectors.py
from my_model_selectors import SelectorBIC

training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1
sequences = training.get_all_sequences()
Xlengths = training.get_all_Xlengths()
for word in words_to_train:
    start = timeit.default_timer()
    model = SelectorBIC(sequences, Xlengths, word, 
                    min_n_components=2, max_n_components=15, random_state = 14).select()
    end = timeit.default_timer()-start
    if model is not None:
        print("Training complete for {} with {} states with time {} seconds".format(word, model.n_components, end))
    else:
        print("Training failed for {}".format(word))

# TODO: Implement SelectorDIC in module my_model_selectors.py
from my_model_selectors import SelectorDIC

training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1
sequences = training.get_all_sequences()
Xlengths = training.get_all_Xlengths()
for word in words_to_train:
    start = timeit.default_timer()
    model = SelectorDIC(sequences, Xlengths, word, 
                    min_n_components=2, max_n_components=15, random_state = 14).select()
    end = timeit.default_timer()-start
    if model is not None:
        print("Training complete for {} with {} states with time {} seconds".format(word, model.n_components, end))
    else:
        print("Training failed for {}".format(word))

"""
Explanation: Tip: 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.
Scoring models with other criterion
Scoring model topologies with BIC balances fit and complexity within the training set for each word.  In the BIC equation, a penalty term penalizes complexity to avoid overfitting, so that it is not necessary to also use cross-validation in the selection process.  There are a number of references on the internet for this criterion.  These slides include a formula you may find helpful for your implementation.
The advantages of scoring model topologies with DIC over BIC are presented by Alain Biem in this reference (also found here).  DIC scores the discriminant ability of a training set for one word against competing words.  Instead of a penalty term for complexity, it provides a penalty if model liklihoods for non-matching words are too similar to model likelihoods for the correct word in the word set.
<a id='part2_submission'></a>
Model Selection Implementation Submission
Implement SelectorCV, SelectorBIC, and SelectorDIC classes in the my_model_selectors.py module.  Run the selectors on the following five words. Then answer the questions about your results.
Tip: The hmmlearn library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration.
End of explanation
"""


from asl_test_model_selectors import TestSelectors
suite = unittest.TestLoader().loadTestsFromModule(TestSelectors())
unittest.TextTestRunner().run(suite)

"""
Explanation: Question 2:  Compare and contrast the possible advantages and disadvantages of the various model selectors implemented.
Answer 2: 
SelectorBIC (lowest Baysian Information Criterion(BIC) score)
Advantage : It penalizes the complexity of the model where complexity refers to the number of parameters in the model.
Disadvantage: The above approximation is only valid for sample size n {\displaystyle n} n much larger than the number k where k of parameters in the model and BIC cannot handle complex collections of models as in the variable selection (or feature selection) problem in high-dimension.
SelectorDIC (Discriminative Information Criterion)
Advantage : DIC is easily calculated from the samples generated by a Markov chain Monte Carlo simulation. BIC require calculating the likelihood
Disdvantage : DIC equation is derived under the assumption that the specified parametric family of probability distributions that generate futuire observations encompasses the true model. This assumption does not always hold. -The observed data are both used to construct the posterior distribution and to evaluate the estimated models. DIC therfore tends to select over-fitted models.
SelectorCV (average log Likelihood of cross-validation folds):
Advantage : High Accuracy given large amount of training data and the knowledge that the unseen data does not deviate much from the seen data. of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once
Disdvantage : When the training data set is small, the model will overfit -If the training data set is small and the unseen data deviates significantly from the training data set, accuracy will be low. -Calculation of the folds introduces increased time and space complexity.
<a id='part2_test'></a>
Model Selector Unit Testing
Run the following unit tests as a sanity check on the implemented model selectors.  The test simply looks for valid interfaces  but is not exhaustive. However, the project should not be submitted if these tests don't pass.
End of explanation
"""


# autoreload for automatically reloading changes made in my_model_selectors and my_recognizer
%load_ext autoreload
%autoreload 2

from my_model_selectors import SelectorConstant

def train_all_words(features, model_selector):
    training = asl.build_training(features)  # Experiment here with different feature sets defined in part 1
    sequences = training.get_all_sequences()
    Xlengths = training.get_all_Xlengths()
    model_dict = {}
    for word in training.words:
        model = model_selector(sequences, Xlengths, word, 
                        n_constant=3).select()
        model_dict[word]=model
    return model_dict

models = train_all_words(features_ground, SelectorConstant)
print("Number of word models returned = {}".format(len(models)))

"""
Explanation: <a id='part3_tutorial'></a>
PART 3: Recognizer
The objective of this section is to "put it all together".  Using the four feature sets created and the three model selectors, you will experiment with the models and present your results.  Instead of training only five specific words as in the previous section, train the entire set with a feature set and model selector strategy.  
Recognizer Tutorial
Train the full training set
The following example trains the entire set with the example features_ground and SelectorConstant features and model selector.  Use this pattern for you experimentation and final submission cells.
End of explanation
"""


test_set = asl.build_test(features_ground)
print("Number of test set items: {}".format(test_set.num_items))
print("Number of test set sentences: {}".format(len(test_set.sentences_index)))

"""
Explanation: Load the test set
The build_test method in ASLdb is similar to the build_training method already presented, but there are a few differences:
- the object is type SinglesData 
- the internal dictionary keys are the index of the test word rather than the word itself
- the getter methods are get_all_sequences, get_all_Xlengths, get_item_sequences and get_item_Xlengths
End of explanation
"""


# TODO implement the recognize method in my_recognizer
from my_recognizer import recognize
from asl_utils import show_errors

# TODO Choose a feature set and model selector
features = custom_features # change as needed
model_selector = SelectorCV # change as needed

# TODO Recognize the test set and display the result with the show_errors method
models = train_all_words(features, model_selector)
test_set = asl.build_test(features)
probabilities, guesses = recognize(models, test_set)
show_errors(guesses, test_set)

# TODO Choose a feature set and model selector
features = custom_features # change as needed
model_selector = SelectorBIC # change as needed

# TODO Recognize the test set and display the result with the show_errors method
models = train_all_words(features, model_selector)
test_set = asl.build_test(features)
probabilities, guesses = recognize(models, test_set)
show_errors(guesses, test_set)

# TODO Choose a feature set and model selector
features = custom_features # change as needed
model_selector = SelectorDIC # change as needed

# TODO Recognize the test set and display the result with the show_errors method
models = train_all_words(features, model_selector)
test_set = asl.build_test(features)
probabilities, guesses = recognize(models, test_set)
show_errors(guesses, test_set)

"""
Explanation: <a id='part3_submission'></a>
Recognizer Implementation Submission
For the final project submission, students must implement a recognizer following guidance in the my_recognizer.py module.  Experiment with the four feature sets and the three model selection methods (that's 12 possible combinations). You can add and remove cells for experimentation or run the recognizers locally in some other way during your experiments, but retain the results for your discussion.  For submission, you will provide code cells of only three interesting combinations for your discussion (see questions below). At least one of these should produce a word error rate of less than 60%, i.e. WER < 0.60 . 
Tip: The hmmlearn library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration.
End of explanation
"""


from asl_test_recognizer import TestRecognize
suite = unittest.TestLoader().loadTestsFromModule(TestRecognize())
unittest.TextTestRunner().run(suite)

"""
Explanation: Question 3:  Summarize the error results from three combinations of features and model selectors.  What was the "best" combination and why?  What additional information might we use to improve our WER?  For more insight on improving WER, take a look at the introduction to Part 4.
Answer 3: Using the custom_features, but with different model_selector.
SelectorCV  WER = 0.651685393258427
SelectorBIC WER = 0.5898876404494382
SelectorDIC WER = 0.6179775280898876
Custom features are expected to provide an appropriate dataset with all the objects orbiting around nose and the normalisation makes the data fit for gaussian models. By varying the choice of model, BIC appears to give the "best" combination. This is because BIC has a strict penalization based on the the number of components and hence provides a inference for the model.
There are multiple techniques which we can use to improve WER, such as assigning higher probability to real and frequently observed sentences, use the shanon visualisation method, or use n gram models with generalisation by zeros. In addition, we can use less context data to avoid overfitting and use interpolation of probabilities to compensate.
<a id='part3_test'></a>
Recognizer Unit Tests
Run the following unit tests as a sanity check on the defined recognizer.  The test simply looks for some valid values but is not exhaustive. However, the project should not be submitted if these tests don't pass.
End of explanation
"""


# create a DataFrame of log likelihoods for the test word items
df_probs = pd.DataFrame(data=probabilities)
df_probs.head()

"""
Explanation: <a id='part4_info'></a>
PART 4: (OPTIONAL)  Improve the WER with Language Models
We've squeezed just about as much as we can out of the model and still only get about 50% of the words right! Surely we can do better than that.  Probability to the rescue again in the form of statistical language models (SLM).  The basic idea is that each word has some probability of occurrence within the set, and some probability that it is adjacent to specific other words. We can use that additional information to make better choices.
Additional reading and resources

Introduction to N-grams (Stanford Jurafsky slides)
Speech Recognition Techniques for a Sign Language Recognition System, Philippe Dreuw et al see the improved results of applying LM on this data!
SLM data for this ASL dataset

Optional challenge
The recognizer you implemented in Part 3 is equivalent to a "0-gram" SLM.  Improve the WER with the SLM data provided with the data set in the link above using "1-gram", "2-gram", and/or "3-gram" statistics. The probabilities data you've already calculated will be useful and can be turned into a pandas DataFrame if desired (see next cell).
Good luck!  Share your results with the class!
End of explanation
"""


