# Import libraries necessary for this project
import numpy as np
import pandas as pd
from sklearn.cross_validation import ShuffleSplit

# Import supplementary visualizations code visuals.py
import visuals as vs

# Pretty display for notebooks
%matplotlib inline

# Load the Boston housing dataset
data = pd.read_csv('housing.csv')
prices = data['MEDV']
features = data.drop('MEDV', axis = 1)
    
# Success
print "Boston housing dataset has {} data points with {} variables each.".format(*data.shape)

"""
Explanation: Machine Learning Engineer Nanodegree
Model Evaluation & Validation
Project: Predicting Boston Housing Prices
Welcome to the first project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and you will need to implement additional functionality to successfully complete this project. You will not need to modify the included code beyond what is requested. Sections that begin with 'Implementation' in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.  

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.

Getting Started
In this project, you will evaluate the performance and predictive power of a model that has been trained and tested on data collected from homes in suburbs of Boston, Massachusetts. A model trained on this data that is seen as a good fit could then be used to make certain predictions about a home — in particular, its monetary value. This model would prove to be invaluable for someone like a real estate agent who could make use of such information on a daily basis.
The dataset for this project originates from the UCI Machine Learning Repository. The Boston housing data was collected in 1978 and each of the 506 entries represent aggregated data about 14 features for homes from various suburbs in Boston, Massachusetts. For the purposes of this project, the following preprocessing steps have been made to the dataset:
- 16 data points have an 'MEDV' value of 50.0. These data points likely contain missing or censored values and have been removed.
- 1 data point has an 'RM' value of 8.78. This data point can be considered an outlier and has been removed.
- The features 'RM', 'LSTAT', 'PTRATIO', and 'MEDV' are essential. The remaining non-relevant features have been excluded.
- The feature 'MEDV' has been multiplicatively scaled to account for 35 years of market inflation.
Run the code cell below to load the Boston housing dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported.
End of explanation
"""


# TODO: Minimum price of the data
minimum_price = np.amin(prices)

# TODO: Maximum price of the data
maximum_price = np.amax(prices)

# TODO: Mean price of the data
mean_price = np.mean(prices)

# TODO: Median price of the data
median_price = np.median(prices)

# TODO: Standard deviation of prices of the data
std_price = np.std(prices)

# Show the calculated statistics
print "Statistics for Boston housing dataset:\n"
print "Minimum price: ${:,.2f}".format(minimum_price)
print "Maximum price: ${:,.2f}".format(maximum_price)
print "Mean price: ${:,.2f}".format(mean_price)
print "Median price ${:,.2f}".format(median_price)
print "Standard deviation of prices: ${:,.2f}".format(std_price)

"""
Explanation: Data Exploration
In this first section of this project, you will make a cursory investigation about the Boston housing data and provide your observations. Familiarizing yourself with the data through an explorative process is a fundamental practice to help you better understand and justify your results.
Since the main goal of this project is to construct a working model which has the capability of predicting the value of houses, we will need to separate the dataset into features and the target variable. The features, 'RM', 'LSTAT', and 'PTRATIO', give us quantitative information about each data point. The target variable, 'MEDV', will be the variable we seek to predict. These are stored in features and prices, respectively.
Implementation: Calculate Statistics
For your very first coding implementation, you will calculate descriptive statistics about the Boston housing prices. Since numpy has already been imported for you, use this library to perform the necessary calculations. These statistics will be extremely important later on to analyze various prediction results from the constructed model.
In the code cell below, you will need to implement the following:
- Calculate the minimum, maximum, mean, median, and standard deviation of 'MEDV', which is stored in prices.
  - Store each calculation in their respective variable.
End of explanation
"""


# TODO: Import 'r2_score'
from sklearn.metrics import r2_score

def performance_metric(y_true, y_predict):
    """ Calculates and returns the performance score between 
        true and predicted values based on the metric chosen. """
    
    # TODO: Calculate the performance score between 'y_true' and 'y_predict'
    score = r2_score(y_true, y_predict)
    
    # Return the score
    return score

"""
Explanation: Question 1 - Feature Observation
As a reminder, we are using three features from the Boston housing dataset: 'RM', 'LSTAT', and 'PTRATIO'. For each data point (neighborhood):
- 'RM' is the average number of rooms among homes in the neighborhood.
- 'LSTAT' is the percentage of homeowners in the neighborhood considered "lower class" (working poor).
- 'PTRATIO' is the ratio of students to teachers in primary and secondary schools in the neighborhood.
Using your intuition, for each of the three features above, do you think that an increase in the value of that feature would lead to an increase in the value of 'MEDV' or a decrease in the value of 'MEDV'? Justify your answer for each.
Hint: Would you expect a home that has an 'RM' value of 6 be worth more or less than a home that has an 'RM' value of 7?
Answer: The influence of each variable can be directly or inversely influential. For example, intuitively the bigger RM shows that is a richer neighborhood and, consequently, has a bigger price for square meter. When there is a bigger LSTAT you may be led to think that the house is in a poorer and cheaper square meter. About the PTRATIO can tell that there is more children in the school and is a good sign or that is a property of lower class neighborhood, and I do not know, intuitively, if it is from an expensive or cheaper house.

Developing a Model
In this second section of the project, you will develop the tools and techniques necessary for a model to make a prediction. Being able to make accurate evaluations of each model's performance through the use of these tools and techniques helps to greatly reinforce the confidence in your predictions.
Implementation: Define a Performance Metric
It is difficult to measure the quality of a given model without quantifying its performance over training and testing. This is typically done using some type of performance metric, whether it is through calculating some type of error, the goodness of fit, or some other useful measurement. For this project, you will be calculating the coefficient of determination, R<sup>2</sup>, to quantify your model's performance. The coefficient of determination for a model is a useful statistic in regression analysis, as it often describes how "good" that model is at making predictions. 
The values for R<sup>2</sup> range from 0 to 1, which captures the percentage of squared correlation between the predicted and actual values of the target variable. A model with an R<sup>2</sup> of 0 is no better than a model that always predicts the mean of the target variable, whereas a model with an R<sup>2</sup> of 1 perfectly predicts the target variable. Any value between 0 and 1 indicates what percentage of the target variable, using this model, can be explained by the features. A model can be given a negative R<sup>2</sup> as well, which indicates that the model is arbitrarily worse than one that always predicts the mean of the target variable.
For the performance_metric function in the code cell below, you will need to implement the following:
- Use r2_score from sklearn.metrics to perform a performance calculation between y_true and y_predict.
- Assign the performance score to the score variable.
End of explanation
"""


# Calculate the performance of this model
score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])
print "Model has a coefficient of determination, R^2, of {:.3f}.".format(score)

"""
Explanation: Question 2 - Goodness of Fit
Assume that a dataset contains five data points and a model made the following predictions for the target variable:
| True Value | Prediction |
| :-------------: | :--------: |
| 3.0 | 2.5 |
| -0.5 | 0.0 |
| 2.0 | 2.1 |
| 7.0 | 7.8 |
| 4.2 | 5.3 |
Would you consider this model to have successfully captured the variation of the target variable? Why or why not? 
Run the code cell below to use the performance_metric function and calculate this model's coefficient of determination.
End of explanation
"""


# TODO: Import 'train_test_split'
from sklearn.cross_validation import train_test_split

# TODO: Shuffle and split the data into training and testing subsets
X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.20, random_state=73816383)

# Success
print "Training and testing split was successful."

"""
Explanation: Answer: 0.923. Looks like the model can represent the data well, once the Rˆ2 was close to 1 (100%). But not necessarily a high Rˆ2 means the model has a good fit. Checking the residual plots could help to determine if this is a good model.
Implementation: Shuffle and Split Data
Your next implementation requires that you take the Boston housing dataset and split the data into training and testing subsets. Typically, the data is also shuffled into a random order when creating the training and testing subsets to remove any bias in the ordering of the dataset.
For the code cell below, you will need to implement the following:
- Use train_test_split from sklearn.cross_validation to shuffle and split the features and prices data into training and testing sets.
  - Split the data into 80% training and 20% testing.
  - Set the random_state for train_test_split to a value of your choice. This ensures results are consistent.
- Assign the train and testing splits to X_train, X_test, y_train, and y_test.
End of explanation
"""


# Produce learning curves for varying training set sizes and maximum depths
vs.ModelLearning(features, prices)

"""
Explanation: Question 3 - Training and Testing
What is the benefit to splitting a dataset into some ratio of training and testing subsets for a learning algorithm?
Hint: What could go wrong with not having a way to test your model?
Answer:  The purpose of training data is to discover the relationships while the test data is used to evaluate how much these relationships keeps itself to others data. The test set can be used to obtain to analyse important properties such as accuracy, sensitivity, and others. It the test isn't applyed the model can have the bias or variance not discovered.

Analyzing Model Performance
In this third section of the project, you'll take a look at several models' learning and testing performances 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 performance. 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.
Learning Curves
The following code cell produces four graphs for a decision tree model with different maximum depths. Each graph visualizes the learning curves of the model for both training and testing as the size of the training set is increased. Note that the shaded region of a learning curve denotes the uncertainty of that curve (measured as the standard deviation). The model is scored on both the training and testing sets using R<sup>2</sup>, the coefficient of determination.  
Run the code cell below and use these graphs to answer the following question.
End of explanation
"""


vs.ModelComplexity(X_train, y_train)

"""
Explanation: Question 4 - Learning the Data
Choose one of the graphs above and state the maximum depth for the model. What happens to the score of the training curve as more training points are added? What about the testing curve? Would having more training points benefit the model?
Hint: Are the learning curves converging to particular scores?
Answer:  max_depth = 3. If the training set has small number of points, the the training curve will be close to 1, because the overfitting. As training set increase, the training curve score decreases and converge to something like 0.8. The testing curve starts with 0 because model will predict a small number of points and can not generalize. With bigger training set, the test curve start to increase and go to something like 0.8 too. About having more training is benefit to the model isn't true, because with 50 or more training point the testing curve score don't change much. Apparently the model has a good generalization.
Complexity Curves
The following code cell produces a graph for a decision tree model that has been trained and validated on the training data using different maximum depths. The graph produces two complexity curves — one for training and one for validation. Similar to the learning curves, the shaded regions of both the complexity curves denote the uncertainty in those curves, and the model is scored on both the training and validation sets using the performance_metric function.  
Run the code cell below and use this graph to answer the following two questions.
End of explanation
"""


# TODO: Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'
from sklearn.metrics import make_scorer
from sklearn.tree import DecisionTreeRegressor
from sklearn.model_selection import GridSearchCV

def fit_model(X, y):
    """ Performs grid search over the 'max_depth' parameter for a 
        decision tree regressor trained on the input data [X, y]. """
    
    # Create cross-validation sets from the training data
    cv_sets = ShuffleSplit(X.shape[0], n_iter = 10, test_size = 0.20, random_state = 0)

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

    # TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10
    params = {'max_depth':list(range(1,11))}

    # TODO: Transform 'performance_metric' into a scoring function using 'make_scorer' 
    scoring_fnc = make_scorer(performance_metric)

    # TODO: Create the grid search object
    grid = GridSearchCV(regressor, params, scoring = scoring_fnc, cv = cv_sets)

    # Fit the grid search object to the data to compute the optimal model
    grid = grid.fit(X, y)

    # Return the optimal model after fitting the data
    return grid.best_estimator_

"""
Explanation: Question 5 - Bias-Variance Tradeoff
When the model is trained with a maximum depth of 1, does the model suffer from high bias or from high variance? How about when the model is trained with a maximum depth of 10? What visual cues in the graph justify your conclusions?
Hint: How do you know when a model is suffering from high bias or high variance?
Answer:  At max_depth = 1 the model suffer from high bias. Both training and test score are low in graph. When it is equal 10 the model suffer with high variance and overfitting the training set. In this case the training score is much greater then test score and almost 1. The graph show the distance between the curves and how they distanced themselves. You know when a model if suffering from high bias or high variance when both have low score or when the training score is much better and test score is low.
Question 6 - Best-Guess Optimal Model
Which maximum depth do you think results in a model that best generalizes to unseen data? What intuition lead you to this answer?
Answer:  The best depth is very close, or equal to 4. Is when the Validation Score is maximum and the training score isn't overfitting. The value in depth 5 is very similar to the dept 4, but the training score is greater.

Evaluating Model Performance
In this final section of the project, you will construct a model and make a prediction on the client's feature set using an optimized model from fit_model.
Question 7 - Grid Search
What is the grid search technique and how it can be applied to optimize a learning algorithm?
Answer:  Grid Search is a technique to find good set of parameters (or candidate) to the model. It is simply the way to search exhaustively through parameters space. It must be guided by some performance or fitness function. Normally this function is the cross-validation. Grid Search can be used in Machine Learning, since the bounds and discretization may be setted, manually or not.
Question 8 - Cross-Validation
What is the k-fold cross-validation training technique? What benefit does this technique provide for grid search when optimizing a model?
Hint: Much like the reasoning behind having a testing set, what could go wrong with using grid search without a cross-validated set?
Answer:  k-fold cross-validation is a technique of model validation where the set is partitioned, randomly, into k subsets with same size. In theses subsets, one of them is used to validate and the others for testing. This process is repetead k-1 times to each subset be used to validation. Then the average error across the k testing sets is computed.
This technique has the advantage of use all data for both testing and training and each one of them is used once to validation.
Using Grid Search without cross-validate can be biased, once the bound is manually setted and the parameters candidate aren't tested and compared to possible others candidates.
Implementation: Fitting a Model
Your final implementation requires that you bring everything together and train a model using the decision tree algorithm. To ensure that you are producing an optimized model, you will train the model using the grid search technique to optimize the 'max_depth' parameter for the decision tree. The 'max_depth' parameter can be thought of as how many questions the decision tree algorithm is allowed to ask about the data before making a prediction. Decision trees are part of a class of algorithms called supervised learning algorithms.
In addition, you will find your implementation is using ShuffleSplit() for an alternative form of cross-validation (see the 'cv_sets' variable). While it is not the K-Fold cross-validation technique you describe in Question 8, this type of cross-validation technique is just as useful!. The ShuffleSplit() implementation below will create 10 ('n_iter') shuffled sets, and for each shuffle, 20% ('test_size') of the data will be used as the validation set. While you're working on your implementation, think about the contrasts and similarities it has to the K-fold cross-validation technique.
For the fit_model function in the code cell below, you will need to implement the following:
- Use DecisionTreeRegressor from sklearn.tree to create a decision tree regressor object.
  - Assign this object to the 'regressor' variable.
- Create a dictionary for 'max_depth' with the values from 1 to 10, and assign this to the 'params' variable.
- Use make_scorer from sklearn.metrics to create a scoring function object.
  - Pass the performance_metric function as a parameter to the object.
  - Assign this scoring function to the 'scoring_fnc' variable.
- Use GridSearchCV from sklearn.grid_search to create a grid search object.
  - Pass the variables 'regressor', 'params', 'scoring_fnc', and 'cv_sets' as parameters to the object. 
  - Assign the GridSearchCV object to the 'grid' variable.
End of explanation
"""


# Fit the training data to the model using grid search
reg = fit_model(X_train, y_train)

# Produce the value for 'max_depth'
print "Parameter 'max_depth' is {} for the optimal model.".format(reg.get_params()['max_depth'])

"""
Explanation: Making Predictions
Once a model has been trained on a given set of data, it can now be used to make predictions on new sets of input data. In the case of a decision tree regressor, the model has learned what the best questions to ask about the input data are, and can respond with a prediction for the target variable. You can use these predictions to gain information about data where the value of the target variable is unknown — such as data the model was not trained on.
Question 9 - Optimal Model
What maximum depth does the optimal model have? How does this result compare to your guess in Question 6?  
Run the code block below to fit the decision tree regressor to the training data and produce an optimal model.
End of explanation
"""


# Produce a matrix for client data
client_data = [[5, 17, 15], # Client 1
               [4, 32, 22], # Client 2
               [8, 3, 12]]  # Client 3

# Show predictions
for i, price in enumerate(reg.predict(client_data)):
    print "Predicted selling price for Client {}'s home: ${:,.2f}".format(i+1, price)
print "---"
print zip(X_train.columns, reg.feature_importances_)

"""
Explanation: Answer: Parameter 'max_depth' is 4 for the optimal model. This answer was similiar the visual analysis made in Question 6.
Question 10 - Predicting Selling Prices
Imagine that you were a real estate agent in the Boston area looking to use this model to help price homes owned by your clients that they wish to sell. You have collected the following information from three of your clients:
| Feature | Client 1 | Client 2 | Client 3 |
| :---: | :---: | :---: | :---: |
| Total number of rooms in home | 5 rooms | 4 rooms | 8 rooms |
| Neighborhood poverty level (as %) | 17% | 32% | 3% |
| Student-teacher ratio of nearby schools | 15-to-1 | 22-to-1 | 12-to-1 |
What price would you recommend each client sell his/her home at? Do these prices seem reasonable given the values for the respective features?
Hint: Use the statistics you calculated in the Data Exploration section to help justify your response.  
Run the code block below to have your optimized model make predictions for each client's home.
End of explanation
"""


vs.PredictTrials(features, prices, fit_model, client_data)

"""
Explanation: Answer:  The prices for Clients 1, 2 and 3 was, respectively, USD 409,752.00, USD 235,117.65 and USD 892,850.00.
As we thougt intuitively, the Number of Rooms has a directly influence (i.e. more rooms make the price increase). The LSTAT has a inverse effect, and as smaller this percentage, bigger the price.
All three variables follow the sequence: The house with more rooms has the bigger price, the 2nd in rooms number has the 2nd bigger price, and the 3rd in rooms number has the 3rd price. This is inversely true with the two other variables. 
After all, seems that the number of rooms has the bigger influence in the price.
Sensitivity
An optimal model is not necessarily a robust model. Sometimes, a model is either too complex or too simple to sufficiently generalize to new data. Sometimes, a model could use a learning algorithm that is not appropriate for the structure of the data given. Other times, the data itself could be too noisy or contain too few samples to allow a model to adequately capture the target variable — i.e., the model is underfitted. Run the code cell below to run the fit_model function ten times with different training and testing sets to see how the prediction for a specific client changes with the data it's trained on.
End of explanation
"""


