# Importing a few necessary libraries
import numpy as np
import matplotlib.pyplot as pl
from sklearn import datasets
from sklearn.tree import DecisionTreeRegressor

# Make matplotlib show our plots inline (nicely formatted in the notebook)
%matplotlib inline

# Create our client's feature set for which we will be predicting a selling price
CLIENT_FEATURES = [[11.95, 0.00, 18.100, 0, 0.6590, 5.6090, 90.00, 1.385, 24, 680.0, 20.20, 332.09, 12.13]]

# Load the Boston Housing dataset into the city_data variable
city_data = datasets.load_boston()

# Initialize the housing prices and housing features
housing_prices = city_data.target
housing_features = city_data.data

print "Boston Housing dataset loaded successfully!"

"""
Explanation: Machine Learning Engineer Nanodegree
Model Evaluation & Validation
Project 1: Predicting Boston Housing Prices
Welcome to the first project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been written. You will need to implement additional functionality to successfully answer all of the questions for this project. Unless it is requested, do not modify any of the code that has already been included. In this template code, there are four sections which you must complete to successfully produce a prediction with your model. Each section where you will write code is preceded by a STEP X header with comments describing what must be done. Please read the instructions carefully!
In addition to implementing code, there will be questions that you must answer that relate to the project and your implementation. Each section where you will answer a question is preceded by a QUESTION X header. Be sure that you have carefully read each question and provide thorough answers in the text boxes that begin with "Answer:". Your project submission will be evaluated based on your answers to each of the questions.  
A description of the dataset can be found here, which is provided by the UCI Machine Learning Repository.
Getting Started
To familiarize yourself with an iPython Notebook, try double clicking on this cell. You will notice that the text changes so that all the formatting is removed. This allows you to make edits to the block of text you see here. This block of text (and mostly anything that's not code) is written using Markdown, which is a way to format text using headers, links, italics, and many other options! Whether you're editing a Markdown text block or a code block (like the one below), you can use the keyboard shortcut Shift + Enter or Shift + Return to execute the code or text block. In this case, it will show the formatted text.
Let's start by setting up some code we will need to get the rest of the project up and running. Use the keyboard shortcut mentioned above on the following code block to execute it. Alternatively, depending on your iPython Notebook program, you can press the Play button in the hotbar. You'll know the code block executes successfully if the message "Boston Housing dataset loaded successfully!" is printed.
End of explanation
"""


# Number of houses in the dataset
total_houses = housing_features.shape[0]

# Number of features in the dataset
total_features = housing_features.shape[1]

# Minimum housing value in the dataset
minimum_price = housing_prices.min()

# Maximum housing value in the dataset
maximum_price = housing_prices.max()

# Mean house value of the dataset
mean_price = housing_prices.mean()

# Median house value of the dataset
median_price = np.median(housing_prices)

# Standard deviation of housing values of the dataset
std_dev = housing_prices.std()

# Show the calculated statistics
print "Boston Housing dataset statistics (in $1000's):\n"
print "Total number of houses:", total_houses
print "Total number of features:", total_features
print "Minimum house price:", minimum_price
print "Maximum house price:", maximum_price
print "Mean house price: {0:.3f}".format(mean_price)
print "Median house price:", median_price
print "Standard deviation of house price: {0:.3f}".format(std_dev)

"""
Explanation: Statistical Analysis and Data Exploration
In this first section of the project, you will quickly investigate a few basic statistics about the dataset you are working with. In addition, you'll look at the client's feature set in CLIENT_FEATURES and see how this particular sample relates to the features of the dataset. Familiarizing yourself with the data through an explorative process is a fundamental practice to help you better understand your results.
Step 1
In the code block below, use the imported numpy library to calculate the requested statistics. You will need to replace each None you find with the appropriate numpy coding for the proper statistic to be printed. Be sure to execute the code block each time to test if your implementation is working successfully. The print statements will show the statistics you calculate!
End of explanation
"""


print CLIENT_FEATURES

"""
Explanation: Question 1
As a reminder, you can view a description of the Boston Housing dataset here, where you can find the different features under Attribute Information. The MEDV attribute relates to the values stored in our housing_prices variable, so we do not consider that a feature of the data.
Of the features available for each data point, choose three that you feel are significant and give a brief description for each of what they measure.
Remember, you can double click the text box below to add your answer!
Answer: 
1. CRIM: per capita crime rate by town, indicating surrounding security environment.
2. RM: average number of rooms per dwelling, indicating the level of the house.
3. PTRATIO: pupil-teacher ratio by town, indicating the primary education quality.
Question 2
Using your client's feature set CLIENT_FEATURES, which values correspond with the features you've chosen above?
Hint:  Run the code block below to see the client's data.
End of explanation
"""


# Put any import statements you need for this code block here
from sklearn.cross_validation import train_test_split


def shuffle_split_data(X, y):
    """ Shuffles and splits data into 70% training and 30% testing subsets,
        then returns the training and testing subsets. """

    # Shuffle and split the data
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0)


    # Return the training and testing data subsets
    return X_train, y_train, X_test, y_test


# Test shuffle_split_data
try:
    X_train, y_train, X_test, y_test = shuffle_split_data(housing_features, housing_prices)
    print "Successfully shuffled and split the data!"
except:
    print "Something went wrong with shuffling and splitting the data."

"""
Explanation: Answer: 
1. CRIM: 11.95
2. RM: 5.609
3. PTRATIO: 20.2
Evaluating Model Performance
In this second section of the project, you will begin to develop the tools necessary for a model to make a prediction. Being able to accurately evaluate each model's performance through the use of these tools helps to greatly reinforce the confidence in your predictions.
Step 2
In the code block below, you will need to implement code so that the shuffle_split_data function does the following:
- Randomly shuffle the input data X and target labels (housing values) y.
- Split the data into training and testing subsets, holding 30% of the data for testing.
If you use any functions not already acessible from the imported libraries above, remember to include your import statement below as well! 
Ensure that you have executed the code block once you are done. You'll know the shuffle_split_data function is working if the statement "Successfully shuffled and split the data!" is printed.
End of explanation
"""


# Put any import statements you need for this code block here
from sklearn.metrics import mean_squared_error

def performance_metric(y_true, y_predict):
    """ Calculates and returns the total error between true and predicted values
        based on a performance metric chosen by the student. """

    error = mean_squared_error(y_true, y_predict)
    return error


# Test performance_metric
try:
    total_error = performance_metric(y_train, y_train)
    print "Successfully performed a metric calculation!"
except:
    print "Something went wrong with performing a metric calculation."

"""
Explanation: Question 3
Why do we split the data into training and testing subsets for our model?
Answer:  because if we train and test a model on the same data, it will get a perfect score but would fail to predict anthing useful on other unseen data, i.e. overfitting. To avoid it, it's a common practice to split the data into training and testing subsets.
Step 3
In the code block below, you will need to implement code so that the performance_metric function does the following:
- Perform a total error calculation between the true values of the y labels y_true and the predicted values of the y labels y_predict.
You will need to first choose an appropriate performance metric for this problem. See the sklearn metrics documentation to view a list of available metric functions. Hint:  Look at the question below to see a list of the metrics that were covered in the supporting course for this project.
Once you have determined which metric you will use, remember to include the necessary import statement as well!
Ensure that you have executed the code block once you are done. You'll know the performance_metric function is working if the statement "Successfully performed a metric calculation!" is printed.
End of explanation
"""


# Put any import statements you need for this code block
from sklearn.tree import DecisionTreeRegressor
from sklearn.metrics import mean_squared_error, make_scorer
from sklearn.grid_search import GridSearchCV

def fit_model(X, y):
    """ Tunes a decision tree regressor model using GridSearchCV on the input data X 
        and target labels y and returns this optimal model. """

    # Create a decision tree regressor object
    regressor = DecisionTreeRegressor()

    # Set up the parameters we wish to tune
    parameters = {'max_depth':(1,2,3,4,5,6,7,8,9,10)}

    # Make an appropriate scoring function
    scoring_function = make_scorer(mean_squared_error, greater_is_better=False)

    # Make the GridSearchCV object
    reg = GridSearchCV(regressor, param_grid=parameters, scoring=scoring_function)

    # Fit the learner to the data to obtain the optimal model with tuned parameters
    reg.fit(X, y)

    # Return the optimal model
    return reg.best_estimator_


# Test fit_model on entire dataset
try:
    reg = fit_model(housing_features, housing_prices)
    print "Successfully fit a model!"
except:
    print "Something went wrong with fitting a model."

"""
Explanation: Question 4
Which performance metric below did you find was most appropriate for predicting housing prices and analyzing the total error. Why?
- Accuracy
- Precision
- Recall
- F1 Score
- Mean Squared Error (MSE)
- Mean Absolute Error (MAE)
Answer:   
Mean Squared Error (MSE).  
First the house price is an continuous value, so this is a regression problem and the first four metrics are not suitable.    MSE has a nice mathematical proerties and it's easier to compute.Besides, when analyzing the total error, the error weights in MSE is proportional to the square size of the error, while in MAE the weights are proportional to the size of the error, So MSE magnifies errors which makes sense for a price prediction model.
Step 4 (Final Step)
In the code block below, you will need to implement code so that the fit_model function does the following:
- Create a scoring function using the same performance metric as in Step 3. See the sklearn make_scorer documentation.
- Build a GridSearchCV object using regressor, parameters, and scoring_function. See the sklearn documentation on GridSearchCV.
When building the scoring function and GridSearchCV object, be sure that you read the parameters documentation thoroughly. It is not always the case that a default parameter for a function is the appropriate setting for the problem you are working on.
Since you are using sklearn functions, remember to include the necessary import statements below as well!
Ensure that you have executed the code block once you are done. You'll know the fit_model function is working if the statement "Successfully fit a model to the data!" is printed.
End of explanation
"""


def learning_curves(X_train, y_train, X_test, y_test):
    """ Calculates the performance of several models with varying sizes of training data.
        The learning and testing error rates for each model are then plotted. """
    
    print "Creating learning curve graphs for max_depths of 1, 3, 6, and 10. . ."
    
    # Create the figure window
    fig = pl.figure(figsize=(10,8))

    # We will vary the training set size so that we have 50 different sizes
    sizes = np.rint(np.linspace(1, len(X_train), 50)).astype(int)
    train_err = np.zeros(len(sizes))
    test_err = np.zeros(len(sizes))

    # Create four different models based on max_depth
    for k, depth in enumerate([1,3,6,10]):
        
        for i, s in enumerate(sizes):
            
            # Setup a decision tree regressor so that it learns a tree with max_depth = depth
            regressor = DecisionTreeRegressor(max_depth = depth)
            
            # Fit the learner to the training data
            regressor.fit(X_train[:s], y_train[:s])

            # Find the performance on the training set
            train_err[i] = performance_metric(y_train[:s], regressor.predict(X_train[:s]))
            
            # Find the performance on the testing set
            test_err[i] = performance_metric(y_test, regressor.predict(X_test))

        # Subplot the learning curve graph
        ax = fig.add_subplot(2, 2, k+1)
        ax.plot(sizes, test_err, lw = 2, label = 'Testing Error')
        ax.plot(sizes, train_err, lw = 2, label = 'Training Error')
        ax.legend()
        ax.set_title('max_depth = %s'%(depth))
        ax.set_xlabel('Number of Data Points in Training Set')
        ax.set_ylabel('Total Error')
        ax.set_xlim([0, len(X_train)])
    
    # Visual aesthetics
    fig.suptitle('Decision Tree Regressor Learning Performances', fontsize=18, y=1.03)
    fig.tight_layout()
    fig.show()

def model_complexity(X_train, y_train, X_test, y_test):
    """ Calculates the performance of the model as model complexity increases.
        The learning and testing errors rates are then plotted. """
    
    print "Creating a model complexity graph. . . "

    # We will vary the max_depth of a decision tree model from 1 to 14
    max_depth = np.arange(1, 14)
    train_err = np.zeros(len(max_depth))
    test_err = np.zeros(len(max_depth))

    for i, d in enumerate(max_depth):
        # Setup a Decision Tree Regressor so that it learns a tree with depth d
        regressor = DecisionTreeRegressor(max_depth = d)

        # Fit the learner to the training data
        regressor.fit(X_train, y_train)

        # Find the performance on the training set
        train_err[i] = performance_metric(y_train, regressor.predict(X_train))

        # Find the performance on the testing set
        test_err[i] = performance_metric(y_test, regressor.predict(X_test))

    # Plot the model complexity graph
    pl.figure(figsize=(7, 5))
    pl.title('Decision Tree Regressor Complexity Performance')
    pl.plot(max_depth, test_err, lw=2, label = 'Testing Error')
    pl.plot(max_depth, train_err, lw=2, label = 'Training Error')
    pl.legend()
    pl.xlabel('Maximum Depth')
    pl.ylabel('Total Error')
    pl.show()

"""
Explanation: Question 5
What is the grid search algorithm and when is it applicable?
Answer:   
The grid search algorithm exhaustively generates candidates from a grid of parameter values specified with the param_grid parameter. All the possible combinations of parameter values are evaluated and the best combination is retained.  
When an objective metric or score function is chosen and the parameter space is reasonably small, it's applicable.
Question 6
What is cross-validation, and how is it performed on a model? Why would cross-validation be helpful when using grid search?
Answer:    
Cross-validation is a model validation technique for assessing how the results of a statistical analysis will generalized to an independent data set.  
It is recommended to shuffle the input samples prior to cross-validation in order to randomize any localized patterns found in the input samples. One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, multiple rounds of cross-validation are performed using different partitions, and the validation results are averaged over the rounds. 
Though cross validation with grid search would increase training time but would increase the model's robustness, and the hyper-parameters are optimized properly without being tied to a specific training or test sets. So it can derive a more accurate estimate of model prediction performance.
Checkpoint!
You have now successfully completed your last code implementation section. Pat yourself on the back! All of your functions written above will be executed in the remaining sections below, and questions will be asked about various results for you to analyze. To prepare the Analysis and Prediction sections, you will need to intialize the two functions below. Remember, there's no need to implement any more code, so sit back and execute the code blocks! Some code comments are provided if you find yourself interested in the functionality.
End of explanation
"""


learning_curves(X_train, y_train, X_test, y_test)

"""
Explanation: Analyzing Model Performance
In this third section of the project, you'll take a look at several models' learning and testing error rates on various subsets of training data. Additionally, you'll investigate one particular algorithm with an increasing max_depth parameter on the full training set to observe how model complexity affects learning and testing errors. Graphing your model's performance based on varying criteria can be beneficial in the analysis process, such as visualizing behavior that may not have been apparent from the results alone.
End of explanation
"""


model_complexity(X_train, y_train, X_test, y_test)

"""
Explanation: Question 7
Choose one of the learning curve graphs that are created above. What is the max depth for the chosen model? As the size of the training set increases, what happens to the training error? What happens to the testing error?
Answer:   
The third graph is chosen, and max_depth = 6.  
As the size of the training set increases, the training error increases, but the testing error decreases dramatically when the number of the data points < 50 and then levels off.
Question 8
Look at the learning curve graphs for the model with a max depth of 1 and a max depth of 10. When the model is using the full training set, does it suffer from high bias or high variance when the max depth is 1? What about when the max depth is 10?
Answer:   
When the model is using the full training set, for the max depth is 1, two error curves converge into a high error value, which means it suffers from high bias; for the max depth is 10, the training curve remains a quite low value but the difference between the training and hihg testing curves is a huge gap, which indicating that it suffers from high variance.
End of explanation
"""


print "Final model has an optimal max_depth parameter of", reg.get_params()['max_depth']

"""
Explanation: Question 9
From the model complexity graph above, describe the training and testing errors as the max depth increases. Based on your interpretation of the graph, which max depth results in a model that best generalizes the dataset? Why?
Answer:   
As the max depth increases, the training and testing errors decreases which means lower bias, but the difference between training and testing errors increases which indicates higher variance, i.e. Bias-Variance Tradeoff.  
So the optimum max depth would be ~5, where the testing error is low and the model remains its simplicity.
Model Prediction
In this final section of the project, you will make a prediction on the client's feature set using an optimized model from fit_model. When applying grid search along with cross-validation to optimize your model, it would typically be performed and validated on a training set and subsequently evaluated on a dedicated test set. In this project, the optimization below is performed on the entire dataset (as opposed to the training set you made above) due to the many outliers in the data. Using the entire dataset for training provides for a less volatile prediction at the expense of not testing your model's performance. 
To answer the following questions, it is recommended that you run the code blocks several times and use the median or mean value of the results.
Question 10
Using grid search on the entire dataset, what is the optimal max_depth parameter for your model? How does this result compare to your intial intuition?
Hint:  Run the code block below to see the max depth produced by your optimized model.
End of explanation
"""


sale_price = reg.predict(CLIENT_FEATURES)
print "Predicted value of client's home: {0:.3f}".format(sale_price[0])

"""
Explanation: Answer:   
After testing several times, the result max_depth changes from 4 to 6, so the optimal amx_depth parameter for the model shall be 5. This is the same as I expected.
Question 11
With your parameter-tuned model, what is the best selling price for your client's home? How does this selling price compare to the basic statistics you calculated on the dataset?  
Hint:  Run the code block below to have your parameter-tuned model make a prediction on the client's home.
End of explanation
"""


