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

# 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 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 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.min(prices)

# TODO: Maximum price of the data
maximum_price = np.max(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:  
1. 'RM' should be positively correlated with 'MEDV' as we expect the price to go up with the number of rooms available.
2. 'LSTAT' should be negatively correlated with 'MEDV' as the lower class neighbourhood would like to settle in place of lower prices.
3. 'PTRATIO' should be negatively correlated with 'MEDV' as higher student/teacher ratio generally points to lower school fees and hence the neighbourhood rates should be lower.  

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 always fails to predict 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 no better than one that naively 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=0.2, random_state = 15)

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

"""
Explanation: Answer: Yes the model captures the target variable quite well (as shown by the high R2 value). 
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:  To evaluate the performance of the model (on the new data), we need a data set. If we use the same data points for training the model and then evaluating it, the result may not reflect the actual model performance on the new data. So we need separate test data set. Best way is to split available data set to exclusive training and test data sets. 

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:  
- In case of the graph with max_depth=1 and max_depth=3 - Both the training and testing curves have (approx.) converged to a value and futher adding data will not change the convergence score for training and testing curve. The max_depth=1 curve seems to have converged at a low score. The model probably biased (underfitting data). This points to the low 'capacity' of the model and the hence we see score  value improving with max_depth increased to 3 ( higher capacity of model). 
- For max_depth=6 and 10, the training and testing curves seems to be asymtoting to different values (quite far apart from each other). This points to the possibility of viarnce in the model (overfitting data). Thus these cases may benefit from more data. 
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.tree import DecisionTreeRegressor
from sklearn.metrics import make_scorer
from sklearn.grid_search 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(random_state=0)

    # TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10
    params = {'max_depth':[x for x in 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_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:  The model with depth=1 seems to be suffering from high bias as the althogh the training and validation score are quite comaparable, the score is quite low.
In case of depth=10, the training and validation scores are far apart and hence the model is suffering from high variance. 
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:  4 seems to be most appropriate depth for the model for generalization. At this point the data the validation score is highest. Validation score is the best representative of the performance of model on unseen data and high validation score points to better generalization of model. 

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 technique is used to methodically searching the parameter space for an ML algorithm. We construct a grid of parameter values at which we want to evaluate the algorithm for a given data and objective. The model is created and trained for all the permutations of the parameter ranges provided and evaluated for each perm. The model with best performing parameter values is then selected.   
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 divides the dataset into k equal parts and then runs the training-testing routine k times each time taking one of the equal part as test data and rest as training data. K-fold cross validation helps to decrease the variance in the validation-score. 
It is necessary for the validation score to be accurate to allow grid search to report best parameter configuration.
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.
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)

"""
Explanation: Answer:  Optimal depth = 4. It indeed did match. Super cool. 
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 price predicted seem to resonably following trends in client_data
- Total number of rooms should be positively correlated with the prices - and so it does for predicted prices
- Neighbourhood poverty should negatively correlate with the prices - it holds true for predicted prices
- Student-teacher ratio hould negatively correlate with the prices - it holds true for predicted prices
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
"""


