In this project, you will employ several supervised algorithms of your choice to accurately model individuals’ income using data collected from the 1994 U.S. Census. You will then choose the best candidate algorithm from preliminary results and further optimize this algorithm to best model the data. Your goal with this implementation is to construct a model that accurately predicts whether an individual makes more than $50,000. This sort of task can arise in a non-profit setting, where organizations survive on donations. Understanding an individual’s income can help a non-profit better understand how large of a donation to request, or whether or not they should reach out to begin with. While it can be difficult to determine an individual’s general income bracket directly from public sources, we can (as we will see) infer this value from other publically available features. The dataset for this project originates from the UCI Machine Learning Repository. The datset was donated by Ron Kohavi and Barry Becker, after being published in the article “Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid”. You can find the article by Ron Kohavi online. The data we investigate here consists of small changes to the original dataset, such as removing the 'fnlwgt' feature and records with missing or ill-formatted entries. Here is the code for this project which was a part of Udacity’s Machine Learning Engineer Nanodegree. ## Exploring the Data Run the code cell below to load necessary Python libraries and load the census data. Note that the last column from this dataset, 'income', will be our target label (whether an individual makes more than, or at most,$50,000 annually). All other columns are features about each individual in the census database.

# Import libraries necessary for this project
import numpy as np
import pandas as pd
from time import time
from IPython.display import display # Allows the use of display() for DataFrames

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

# Pretty display for notebooks
%matplotlib inline

# Load the Census dataset

# Success - Display the first record

age workclass education_level education-num marital-status occupation relationship race sex capital-gain capital-loss hours-per-week native-country income
0 39 State-gov Bachelors 13.0 Never-married Adm-clerical Not-in-family White Male 2174.0 0.0 40.0 United-States <=50K

### Implementation: Data Exploration

A cursory investigation of the dataset will determine how many individuals fit into either group, and will tell us about the percentage of these individuals making more than $50,000. In the code cell below, you will need to compute the following: • The total number of records, 'n_records' • The number of individuals making more than$50,000 annually, 'n_greater_50k'.
• The number of individuals making at most $50,000 annually, 'n_at_most_50k'. • The percentage of individuals making more than$50,000 annually, 'greater_percent'.

Hint: You may need to look at the table above to understand how the 'income' entries are formatted.

# TODO: Total number of records
n_records = len(data)

# TODO: Number of records where individual's income is more than $50,000 n_greater_50k = len(data[data.income == '>50K']) # TODO: Number of records where individual's income is at most$50,000
n_at_most_50k = len(data[data.income == '<=50K'])

# TODO: Percentage of individuals whose income is more than $50,000 greater_percent = (n_greater_50k / float(n_records)) * 100 # Print the results print "Total number of records: {}".format(n_records) print "Individuals making more than$50,000: {}".format(n_greater_50k)
print "Individuals making at most $50,000: {}".format(n_at_most_50k) print "Percentage of individuals making more than$50,000: {:.2f}%".format(greater_percent)

Total number of records: 45222
Individuals making more than $50,000: 11208 Individuals making at most$50,000: 34014
Percentage of individuals making more than $50,000: 24.78%  ## Preparing the Data Before data can be used as input for machine learning algorithms, it often must be cleaned, formatted, and restructured — this is typically known as preprocessing. Fortunately, for this dataset, there are no invalid or missing entries we must deal with, however, there are some qualities about certain features that must be adjusted. This preprocessing can help tremendously with the outcome and predictive power of nearly all learning algorithms. ### Transforming Skewed Continuous Features A dataset may sometimes contain at least one feature whose values tend to lie near a single number, but will also have a non-trivial number of vastly larger or smaller values than that single number. Algorithms can be sensitive to such distributions of values and can underperform if the range is not properly normalized. With the census dataset two features fit this description: ‘capital-gain' and 'capital-loss'. Run the code cell below to plot a histogram of these two features. Note the range of the values present and how they are distributed. # Split the data into features and target label income_raw = data['income'] features_raw = data.drop('income', axis = 1) # Visualize skewed continuous features of original data vs.distribution(data)  For highly-skewed feature distributions such as 'capital-gain' and 'capital-loss', it is common practice to apply a logarithmic transformation on the data so that the very large and very small values do not negatively affect the performance of a learning algorithm. Using a logarithmic transformation significantly reduces the range of values caused by outliers. Care must be taken when applying this transformation however: The logarithm of 0 is undefined, so we must translate the values by a small amount above 0 to apply the the logarithm successfully. Run the code cell below to perform a transformation on the data and visualize the results. Again, note the range of values and how they are distributed. # Log-transform the skewed features skewed = ['capital-gain', 'capital-loss'] features_raw[skewed] = data[skewed].apply(lambda x: np.log(x + 1)) # Visualize the new log distributions vs.distribution(features_raw, transformed = True)  ### Normalizing Numerical Features In addition to performing transformations on features that are highly skewed, it is often good practice to perform some type of scaling on numerical features. Applying a scaling to the data does not change the shape of each feature’s distribution (such as 'capital-gain' or 'capital-loss' above); however, normalization ensures that each feature is treated equally when applying supervised learners. Note that once scaling is applied, observing the data in its raw form will no longer have the same original meaning, as exampled below. Run the code cell below to normalize each numerical feature. We will use sklearn.preprocessing.MinMaxScaler for this. # Import sklearn.preprocessing.StandardScaler from sklearn.preprocessing import MinMaxScaler # Initialize a scaler, then apply it to the features scaler = MinMaxScaler() numerical = ['age', 'education-num', 'capital-gain', 'capital-loss', 'hours-per-week'] features_raw[numerical] = scaler.fit_transform(data[numerical]) # Show an example of a record with scaling applied display(features_raw.head(n = 1))  age workclass education_level education-num marital-status occupation relationship race sex capital-gain capital-loss hours-per-week native-country 0 0.30137 State-gov Bachelors 0.8 Never-married Adm-clerical Not-in-family White Male 0.02174 0.0 0.397959 United-States ### Implementation: Data Preprocessing From the table in Exploring the Data above, we can see there are several features for each record that are non-numeric. Typically, learning algorithms expect input to be numeric, which requires that non-numeric features (called categorical variables) be converted. One popular way to convert categorical variables is by using the one-hot encoding scheme. One-hot encoding creates a “dummy” variable for each possible category of each non-numeric feature. For example, assume someFeature has three possible entries: A, B, or C. We then encode this feature into someFeature_A, someFeature_B and someFeature_C. someFeature someFeature_A someFeature_B someFeature_C 0 B 0 1 0 1 C —-> one-hot encode —-> 0 0 1 2 A 1 0 0 Additionally, as with the non-numeric features, we need to convert the non-numeric target label, 'income' to numerical values for the learning algorithm to work. Since there are only two possible categories for this label (“<=50K” and “>50K”), we can avoid using one-hot encoding and simply encode these two categories as 0 and 1, respectively. In code cell below, you will need to implement the following: • Use pandas.get_dummies() to perform one-hot encoding on the 'features_raw' data. • Convert the target label 'income_raw' to numerical entries. • Set records with “<=50K” to 0 and records with “>50K” to 1. # TODO: One-hot encode the 'features_raw' data using pandas.get_dummies() features = pd.get_dummies(features_raw) # TODO: Encode the 'income_raw' data to numerical values income = income_raw.replace(["<=50K", ">50K"],[0, 1]) # print income_raw # print income # Print the number of features after one-hot encoding encoded = list(features.columns) print "{} total features after one-hot encoding.".format(len(encoded)) # Uncomment the following line to see the encoded feature names # print list(features_raw) # print list(features.columns)  103 total features after one-hot encoding.  ### Shuffle and Split Data Now all categorical variables have been converted into numerical features, and all numerical features have been normalized. As always, we will now split the data (both features and their labels) into training and test sets. 80% of the data will be used for training and 20% for testing. Run the code cell below to perform this split. # Import train_test_split from sklearn.cross_validation import train_test_split # Split the 'features' and 'income' data into training and testing sets X_train, X_test, y_train, y_test = train_test_split(features, income, test_size = 0.2, random_state = 0) # Show the results of the split print "Training set has {} samples.".format(X_train.shape[0]) print "Testing set has {} samples.".format(X_test.shape[0])  Training set has 36177 samples. Testing set has 9045 samples.  ## Evaluating Model Performance In this section, we will investigate four different algorithms, and determine which is best at modeling the data. Three of these algorithms will be supervised learners of your choice, and the fourth algorithm is known as a naive predictor. ### Metrics and the Naive Predictor CharityML, equipped with their research, knows individuals that make more than$50,000 are most likely to donate to their charity. Because of this, CharityML is particularly interested in predicting who makes more than $50,000 accurately. It would seem that using accuracy as a metric for evaluating a particular model’s performace would be appropriate. Additionally, identifying someone that does not make more than$50,000 as someone who does would be detrimental to CharityML, since they are looking to find individuals willing to donate. Therefore, a model’s ability to precisely predict those that make more than $50,000 is more important than the model’s ability to recall those individuals. We can use F-beta score as a metric that considers both precision and recall: In particular, when$\beta = 0.5$, more emphasis is placed on precision. This is called the F$_{0.5}$score (or F-score for simplicity). Looking at the distribution of classes (those who make at most$50,000, and those who make more), it’s clear most individuals do not make more than $50,000. This can greatly affect accuracy, since we could simply say “this person does not make more than$50,000” and generally be right, without ever looking at the data! Making such a statement would be called naive, since we have not considered any information to substantiate the claim. It is always important to consider the naive prediction for your data, to help establish a benchmark for whether a model is performing well. That been said, using that prediction would be pointless: If we predicted all people made less than $50,000, CharityML would identify no one as donors. ### Question 1 - Naive Predictor Performace If we chose a model that always predicted an individual made more than$50,000, what would that model’s accuracy and F-score be on this dataset?
Note: You must use the code cell below and assign your results to 'accuracy' and 'fscore' to be used later.

from sklearn.metrics import accuracy_score, fbeta_score

# Ah, looks like you want me to not use the built in functions yet

# TODO: Calculate accuracy
# accuracy = accuracy_score(income, [1 for each in income])
accuracy = n_greater_50k / float(n_records)

# TODO: Calculate F-score using the formula above for beta = 0.5
# fscore = fbeta_score(income, [1 for each in income], 0.5)

precision = accuracy # because everything is classified as positive
recall = 1 # all positive values were classified as positive
beta_squared = 0.5 ** 2

fscore = (1 + beta_squared) * (precision * recall) / ((beta_squared * precision) + recall)

# Print the results
print "Naive Predictor: [Accuracy score: {:.4f}, F-score: {:.4f}]".format(accuracy, fscore)

Naive Predictor: [Accuracy score: 0.2478, F-score: 0.2917]


### Supervised Learning Models

The following supervised learning models are currently available in scikit-learn that you may choose from:

• Gaussian Naive Bayes (GaussianNB)
• Decision Trees
• Ensemble Methods (Bagging, AdaBoost, Random Forest, Gradient Boosting)
• K-Nearest Neighbors (KNeighbors)
• Stochastic Gradient Descent Classifier (SGDC)
• Support Vector Machines (SVM)
• Logistic Regression

### Question 2 - Model Application

List three of the supervised learning models above that are appropriate for this problem that you will test on the census data. For each model chosen

• Describe one real-world application in industry where the model can be applied. (You may need to do research for this — give references!)
• What are the strengths of the model; when does it perform well?
• What are the weaknesses of the model; when does it perform poorly?
• What makes this model a good candidate for the problem, given what you know about the data?

#### Gaussian Naive Bayes (GaussianNB)

** Real world application **
As discussed in the course, spam filtering is a very good use-case.
** Strengths **
a. Trains fast b. Produces good results with smaller datasets too because it is not a complex algorithm.
** Weaknessess **
Assumes features are all independent.
** Why **
Dataset is small, so it is best to choose a simple algorithm that uses less features and trains fast.

#### Decision Tree Classifier

** Real world application **
It seems to be widely used- here’s a decision tree predicting risk of major depressive disorder
** Strengths **
a. Picks most important features b. Easy to interpret results c. Needs little data preparation
** Weaknessess **
a. Easily overfits b. Not as accurate as other algorithms c. Non-robust: small change in training data causes big change in the tree and thus the predictions.
** Why **
Will help pick out the most important features from the many features in the dataset.

#### Logistic Regression

** Real world application **
Risk modelling to find out likelihood to default on a bank loan
** Strengths **
a. Fast and simple
b. Performs very well for two class problems
** Weaknessess **
Gives a linear class boundary, which doesn’t work for all problems
** Why **
a. Performs very well for two class problems

### Implementation - Creating a Training and Predicting Pipeline

To properly evaluate the performance of each model you’ve chosen, it’s important that you create a training and predicting pipeline that allows you to quickly and effectively train models using various sizes of training data and perform predictions on the testing data. Your implementation here will be used in the following section. In the code block below, you will need to implement the following:

• Import fbeta_score and accuracy_score from sklearn.metrics.
• Fit the learner to the sampled training data and record the training time.
• Perform predictions on the test data X_test, and also on the first 300 training points X_train[:300].
• Record the total prediction time.
• Calculate the accuracy score for both the training subset and testing set.
• Calculate the F-score for both the training subset and testing set.
• Make sure that you set the beta parameter!
# TODO: Import two metrics from sklearn - fbeta_score and accuracy_score
from sklearn.metrics import fbeta_score, accuracy_score

def train_predict(learner, sample_size, X_train, y_train, X_test, y_test):
'''
inputs:
- learner: the learning algorithm to be trained and predicted on
- sample_size: the size of samples (number) to be drawn from training set
- X_train: features training set
- y_train: income training set
- X_test: features testing set
- y_test: income testing set
'''

results = {}

# TODO: Fit the learner to the training data using slicing with 'sample_size'
start = time() # Get start time
learner = learner.fit(X_train[:sample_size], y_train[:sample_size])
end = time() # Get end time

# TODO: Calculate the training time
results['train_time'] = end - start

# TODO: Get the predictions on the test set,
#       then get predictions on the first 300 training samples
start = time() # Get start time
predictions_test = learner.predict(X_test)
predictions_train = learner.predict(X_train[:300])
end = time() # Get end time

# TODO: Calculate the total prediction time
results['pred_time'] = end - start

# TODO: Compute accuracy on the first 300 training samples
results['acc_train'] = accuracy_score(y_train[:300], predictions_train)

# TODO: Compute accuracy on test set
results['acc_test'] = accuracy_score(y_test, predictions_test)

# TODO: Compute F-score on the the first 300 training samples
results['f_train'] = fbeta_score(y_train[:300], predictions_train, beta=0.5)

# TODO: Compute F-score on the test set
results['f_test'] = fbeta_score(y_test, predictions_test, beta=0.5)

# Success
print "{} trained on {} samples.".format(learner.__class__.__name__, sample_size)

# Return the results
return results


### Implementation: Initial Model Evaluation

In the code cell, you will need to implement the following:

• Import the three supervised learning models you’ve discussed in the previous section.
• Initialize the three models and store them in 'clf_A', 'clf_B', and 'clf_C'.
• Use a 'random_state' for each model you use, if provided.
• Note: Use the default settings for each model — you will tune one specific model in a later section.
• Calculate the number of records equal to 1%, 10%, and 100% of the training data.
• Store those values in 'samples_1', 'samples_10', and 'samples_100' respectively.

Note: Depending on which algorithms you chose, the following implementation may take some time to run!

# TODO: Import the three supervised learning models from sklearn
from sklearn.naive_bayes import GaussianNB
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression

# TODO: Initialize the three models
clf_A = GaussianNB()
clf_B = DecisionTreeClassifier(random_state=9)
clf_C = LogisticRegression(random_state=9)

# TODO: Calculate the number of samples for 1%, 10%, and 100% of the training data
samples_1 = len(X_train)/100
samples_10 = len(X_train)/10
samples_100 = len(X_train)

# Collect results on the learners
results = {}
for clf in [clf_A, clf_B, clf_C]:
clf_name = clf.__class__.__name__
results[clf_name] = {}
for i, samples in enumerate([samples_1, samples_10, samples_100]):
results[clf_name][i] = \
train_predict(clf, samples, X_train, y_train, X_test, y_test)

# Run metrics visualization for the three supervised learning models chosen
vs.evaluate(results, accuracy, fscore)

GaussianNB trained on 361 samples.
GaussianNB trained on 3617 samples.
GaussianNB trained on 36177 samples.
DecisionTreeClassifier trained on 361 samples.
DecisionTreeClassifier trained on 3617 samples.
DecisionTreeClassifier trained on 36177 samples.
LogisticRegression trained on 361 samples.
LogisticRegression trained on 3617 samples.
LogisticRegression trained on 36177 samples.


## Improving Results

In this final section, you will choose from the three supervised learning models the best model to use on the student data. You will then perform a grid search optimization for the model over the entire training set (X_train and y_train) by tuning at least one parameter to improve upon the untuned model’s F-score.

Based on the evaluation you performed earlier, in one to two paragraphs, explain to *CharityML which of the three models you believe to be most appropriate for the task of identifying individuals that make more than $50,000.* Hint: Your answer should include discussion of the metrics, prediction/training time, and the algorithm’s suitability for the data. **Answer: ** Logistic Regression is the most appropriate because: • it produces the highest accuracy on the testing (unseen) dataset. • it takes the least amount of time for prediction and this seems to remain the same no matter the size of the testing/prediction dataset, which is great for scalability when the list of potential donors is huge. • f score is the hightest among the algorithms. • it generally performs very well when there are only two classes- which is the case here. ### Question 4 - Describing the Model in Layman’s Terms In one to two paragraphs, explain to *CharityML, in layman’s terms, how the final model chosen is supposed to work. Be sure that you are describing the major qualities of the model, such as how the model is trained and how the model makes a prediction. Avoid using advanced mathematical or technical jargon, such as describing equations or discussing the algorithm implementation.* **Answer: ** The model chosen is built using Logistic Regression. In this case, after the initial training using the training data, it finds a linear boundary based on features such as age, education level, occupation etc. to seperate people who make more than$50k and those who don’t. This is done by assigning a weight to each input feature depending on how important/influential the algorithm learns that feature is.

For any new person, given the person’s age, eductation level etc., it can then predict whether or not that person makes more than $50k based on multiplying each feature value with its corresponding weight. The sum of these values falls on one side of the linear boundary which is the prediction for that person. When the logistic function is applied to this sum, it outputs the probability that the person falls in that category. Althought it takes longer to build the model as the training dataset increases, it is very fast while generating predictions for large datasets. This is helpful when there are a lot of potential donors. ### Implementation: Model Tuning Fine tune the chosen model. Use grid search (GridSearchCV) with at least one important parameter tuned with at least 3 different values. You will need to use the entire training set for this. In the code cell below, you will need to implement the following: • Import sklearn.grid_search.GridSearchCV and sklearn.metrics.make_scorer. • Initialize the classifier you’ve chosen and store it in clf. • Set a random_state if one is available to the same state you set before. • Create a dictionary of parameters you wish to tune for the chosen model. • Example: parameters = {'parameter' : [list of values]}. • Note: Avoid tuning the max_features parameter of your learner if that parameter is available! • Use make_scorer to create an fbeta_score scoring object (with$\beta = 0.5$). • Perform grid search on the classifier clf using the 'scorer', and store it in grid_obj. • Fit the grid search object to the training data (X_train, y_train), and store it in grid_fit. Note: Depending on the algorithm chosen and the parameter list, the following implementation may take some time to run! # TODO: Import 'GridSearchCV', 'make_scorer', and any other necessary libraries from sklearn.grid_search import GridSearchCV from sklearn.metrics import make_scorer # from sklearn.cross_validation import # TODO: Initialize the classifier clf = LogisticRegression(random_state=9) # TODO: Create the parameters list you wish to tune parameters = {'C': [10**i for i in xrange(-3, 4)]} # TODO: Make an fbeta_score scoring object scorer = make_scorer(fbeta_score, beta=0.5) # TODO: Perform grid search on the classifier using 'scorer' as the scoring method grid_obj = GridSearchCV(clf, parameters, scoring=scorer) # TODO: Fit the grid search object to the training data and find the optimal parameters grid_fit = grid_obj.fit(X_train, y_train) # Get the estimator best_clf = grid_fit.best_estimator_ # Make predictions using the unoptimized and model predictions = (clf.fit(X_train, y_train)).predict(X_test) best_predictions = best_clf.predict(X_test) # Report the before-and-afterscores print "Unoptimized model\n------" print "Accuracy score on testing data: {:.4f}".format(accuracy_score(y_test, predictions)) print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, predictions, beta = 0.5)) print "\nOptimized Model\n------" print "Final accuracy score on the testing data: {:.4f}".format(accuracy_score(y_test, best_predictions)) print "Final F-score on the testing data: {:.4f}".format(fbeta_score(y_test, best_predictions, beta = 0.5))  Unoptimized model ------ Accuracy score on testing data: 0.8483 F-score on testing data: 0.6993 Optimized Model ------ Final accuracy score on the testing data: 0.8494 Final F-score on the testing data: 0.7008  ### Question 5 - Final Model Evaluation What is your optimized model’s accuracy and F-score on the testing data? Are these scores better or worse than the unoptimized model? How do the results from your optimized model compare to the naive predictor benchmarks you found earlier in Question 1? Note: Fill in the table below with your results, and then provide discussion in the Answer box. #### Results: Metric Benchmark Predictor Unoptimized Model Optimized Model Accuracy Score 0.2478 0.8483 0.8494 F-score 0.2917 0.6993 0.7008 **Answer: ** The accuracy and F-score of the Optimized Model are only slightly better than the unoptimized model. Perhaps doing a gird search on more parameters and ranges can bump these scores even more. The optimized model perfoms so much better than naive predictor as can be seen in the above table. ## Feature Importance An important task when performing supervised learning on a dataset like the census data we study here is determining which features provide the most predictive power. By focusing on the relationship between only a few crucial features and the target label we simplify our understanding of the phenomenon, which is most always a useful thing to do. In the case of this project, that means we wish to identify a small number of features that most strongly predict whether an individual makes at most or more than$50,000.

Choose a scikit-learn classifier (e.g., adaboost, random forests) that has a feature_importance_ attribute, which is a function that ranks the importance of features according to the chosen classifier. In the next python cell fit this classifier to training set and use this attribute to determine the top 5 most important features for the census dataset.

### Question 6 - Feature Relevance Observation

When Exploring the Data, it was shown there are thirteen available features for each individual on record in the census data.
Of these thirteen records, which five features do you believe to be most important for prediction, and in what order would you rank them and why?

1. Country- On average, people in developed countries like US make more than developing countries.
2. Occupation- Executives/Managers make more than clerical workers
3. Education level: Higher degree likely means better pay.
4. Age- younger people are less experienced and likely make less money.
5. Relationship- people likely marry/have children after they start making a certain amount of money

Why this order:

• Same job in developing countries probably pays less than in the US.
• Person doing the same job with a higher degree likely makes more.
• Age and relationship are less direct factors than above

### Implementation - Extracting Feature Importance

Choose a scikit-learn supervised learning algorithm that has a feature_importance_ attribute availble for it. This attribute is a function that ranks the importance of each feature when making predictions based on the chosen algorithm.

In the code cell below, you will need to implement the following:

• Import a supervised learning model from sklearn if it is different from the three used earlier.
• Train the supervised model on the entire training set.
• Extract the feature importances using '.feature_importances_'.
# TODO: Import a supervised learning model that has 'feature_importances_'
from sklearn.ensemble import RandomForestClassifier as RFS

# TODO: Train the supervised model on the training set
model = RFS().fit(X_train, y_train)

# TODO: Extract the feature importances
importances = model.feature_importances_

# Plot
vs.feature_plot(importances, X_train, y_train)


### Question 7 - Extracting Feature Importance

Observe the visualization created above which displays the five most relevant features for predicting if an individual makes at most or above \$50,000.
How do these five features compare to the five features you discussed in Question 6? If you were close to the same answer, how does this visualization confirm your thoughts? If you were not close, why do you think these features are more relevant?

1. Age- Confirms my thoughts but much more significant that I thought.
2. Hours per week- looks like most people in the dataset are paid by the hour. I assumed there were a lot more full time employees who did not get paid extra for working more hours.
3. Capital Gain- makes sense, more savings because of more income
4. Education- guessed it but looks like age is more significant- I guess education level doesn’t matter after initial stage of career.
5. Husband- Confirms my thoughts- can’t marry without making enough money :)

### Feature Selection

How does a model perform if we only use a subset of all the available features in the data? With less features required to train, the expectation is that training and prediction time is much lower — at the cost of performance metrics. From the visualization above, we see that the top five most important features contribute more than half of the importance of all features present in the data. This hints that we can attempt to reduce the feature space and simplify the information required for the model to learn. The code cell below will use the same optimized model you found earlier, and train it on the same training set with only the top five important features.

# Import functionality for cloning a model
from sklearn.base import clone

# Reduce the feature space
X_train_reduced = X_train[X_train.columns.values[(np.argsort(importances)[::-1])[:5]]]
X_test_reduced = X_test[X_test.columns.values[(np.argsort(importances)[::-1])[:5]]]

# Train on the "best" model found from grid search earlier
clf = (clone(best_clf)).fit(X_train_reduced, y_train)

# Make new predictions
reduced_predictions = clf.predict(X_test_reduced)

# Report scores from the final model using both versions of data
print "Final Model trained on full data\n------"
print "Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, best_predictions))
print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, best_predictions, beta = 0.5))
print "\nFinal Model trained on reduced data\n------"
print "Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, reduced_predictions))
print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, reduced_predictions, beta = 0.5))

Final Model trained on full data
------
Accuracy on testing data: 0.8494
F-score on testing data: 0.7008

Final Model trained on reduced data
------
Accuracy on testing data: 0.8347
F-score on testing data: 0.6678


### Question 8 - Effects of Feature Selection

How does the final model’s F-score and accuracy score on the reduced data using only five features compare to those same scores when all features are used?
If training time was a factor, would you consider using the reduced data as your training set?