Machine Learning Engineer Nanodegree

Supervised Learning

Project: Finding Donors for CharityML

Welcome to the second project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and it will be your job to implement the additional functionality necessary to successfully complete this project. 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 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.

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.

In [33]:
# 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
import visuals as vs

# Pretty display for notebooks
%matplotlib inline

# Load the Census dataset
data = pd.read_csv("census.csv")

# 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
1 50 Self-emp-not-inc Bachelors 13.0 Married-civ-spouse Exec-managerial Husband White Male 0.0 0.0 13.0 United-States <=50K
2 38 Private HS-grad 9.0 Divorced Handlers-cleaners Not-in-family White Male 0.0 0.0 40.0 United-States <=50K
3 53 Private 11th 7.0 Married-civ-spouse Handlers-cleaners Husband Black Male 0.0 0.0 40.0 United-States <=50K
4 28 Private Bachelors 13.0 Married-civ-spouse Prof-specialty Wife Black Female 0.0 0.0 40.0 Cuba <=50K
5 37 Private Masters 14.0 Married-civ-spouse Exec-managerial Wife White Female 0.0 0.0 40.0 United-States <=50K
6 49 Private 9th 5.0 Married-spouse-absent Other-service Not-in-family Black Female 0.0 0.0 16.0 Jamaica <=50K
7 52 Self-emp-not-inc HS-grad 9.0 Married-civ-spouse Exec-managerial Husband White Male 0.0 0.0 45.0 United-States >50K
8 31 Private Masters 14.0 Never-married Prof-specialty Not-in-family White Female 14084.0 0.0 50.0 United-States >50K
9 42 Private Bachelors 13.0 Married-civ-spouse Exec-managerial Husband White Male 5178.0 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.

In [34]:
# 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*1.0)/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.

In [35]:
# 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

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.

In [36]:
# 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.

In [37]:
# 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 = 10))

age workclass education_level education-num marital-status occupation relationship race sex capital-gain capital-loss hours-per-week native-country
0 0.301370 State-gov Bachelors 0.800000 Never-married Adm-clerical Not-in-family White Male 0.021740 0.0 0.397959 United-States
1 0.452055 Self-emp-not-inc Bachelors 0.800000 Married-civ-spouse Exec-managerial Husband White Male 0.000000 0.0 0.122449 United-States
2 0.287671 Private HS-grad 0.533333 Divorced Handlers-cleaners Not-in-family White Male 0.000000 0.0 0.397959 United-States
3 0.493151 Private 11th 0.400000 Married-civ-spouse Handlers-cleaners Husband Black Male 0.000000 0.0 0.397959 United-States
4 0.150685 Private Bachelors 0.800000 Married-civ-spouse Prof-specialty Wife Black Female 0.000000 0.0 0.397959 Cuba
5 0.273973 Private Masters 0.866667 Married-civ-spouse Exec-managerial Wife White Female 0.000000 0.0 0.397959 United-States
6 0.438356 Private 9th 0.266667 Married-spouse-absent Other-service Not-in-family Black Female 0.000000 0.0 0.153061 Jamaica
7 0.479452 Self-emp-not-inc HS-grad 0.533333 Married-civ-spouse Exec-managerial Husband White Male 0.000000 0.0 0.448980 United-States
8 0.191781 Private Masters 0.866667 Never-married Prof-specialty Not-in-family White Female 0.140841 0.0 0.500000 United-States
9 0.342466 Private Bachelors 0.800000 Married-civ-spouse Exec-managerial Husband White Male 0.051781 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.

In [38]:
# TODO: One-hot encode the 'features_raw' data using pandas.get_dummies()
catagorical = ['workclass', 'education_level', 'marital-status', 'occupation', 'relationship', 'race', 'sex', 'native-country']
features= pd.concat([pd.get_dummies(features_raw[catagorical], prefix_sep='_'), features_raw[numerical]], axis=1)
#features = features_raw

# TODO: Encode the 'income_raw' data to numerical values
income = income_raw.apply(lambda x: 0 if x == "<=50K" else 1)

# 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 encoded
display(features.head(n = 1))

103 total features after one-hot encoding.
['workclass_ Federal-gov', 'workclass_ Local-gov', 'workclass_ Private', 'workclass_ Self-emp-inc', 'workclass_ Self-emp-not-inc', 'workclass_ State-gov', 'workclass_ Without-pay', 'education_level_ 10th', 'education_level_ 11th', 'education_level_ 12th', 'education_level_ 1st-4th', 'education_level_ 5th-6th', 'education_level_ 7th-8th', 'education_level_ 9th', 'education_level_ Assoc-acdm', 'education_level_ Assoc-voc', 'education_level_ Bachelors', 'education_level_ Doctorate', 'education_level_ HS-grad', 'education_level_ Masters', 'education_level_ Preschool', 'education_level_ Prof-school', 'education_level_ Some-college', 'marital-status_ Divorced', 'marital-status_ Married-AF-spouse', 'marital-status_ Married-civ-spouse', 'marital-status_ Married-spouse-absent', 'marital-status_ Never-married', 'marital-status_ Separated', 'marital-status_ Widowed', 'occupation_ Adm-clerical', 'occupation_ Armed-Forces', 'occupation_ Craft-repair', 'occupation_ Exec-managerial', 'occupation_ Farming-fishing', 'occupation_ Handlers-cleaners', 'occupation_ Machine-op-inspct', 'occupation_ Other-service', 'occupation_ Priv-house-serv', 'occupation_ Prof-specialty', 'occupation_ Protective-serv', 'occupation_ Sales', 'occupation_ Tech-support', 'occupation_ Transport-moving', 'relationship_ Husband', 'relationship_ Not-in-family', 'relationship_ Other-relative', 'relationship_ Own-child', 'relationship_ Unmarried', 'relationship_ Wife', 'race_ Amer-Indian-Eskimo', 'race_ Asian-Pac-Islander', 'race_ Black', 'race_ Other', 'race_ White', 'sex_ Female', 'sex_ Male', 'native-country_ Cambodia', 'native-country_ Canada', 'native-country_ China', 'native-country_ Columbia', 'native-country_ Cuba', 'native-country_ Dominican-Republic', 'native-country_ Ecuador', 'native-country_ El-Salvador', 'native-country_ England', 'native-country_ France', 'native-country_ Germany', 'native-country_ Greece', 'native-country_ Guatemala', 'native-country_ Haiti', 'native-country_ Holand-Netherlands', 'native-country_ Honduras', 'native-country_ Hong', 'native-country_ Hungary', 'native-country_ India', 'native-country_ Iran', 'native-country_ Ireland', 'native-country_ Italy', 'native-country_ Jamaica', 'native-country_ Japan', 'native-country_ Laos', 'native-country_ Mexico', 'native-country_ Nicaragua', 'native-country_ Outlying-US(Guam-USVI-etc)', 'native-country_ Peru', 'native-country_ Philippines', 'native-country_ Poland', 'native-country_ Portugal', 'native-country_ Puerto-Rico', 'native-country_ Scotland', 'native-country_ South', 'native-country_ Taiwan', 'native-country_ Thailand', 'native-country_ Trinadad&Tobago', 'native-country_ United-States', 'native-country_ Vietnam', 'native-country_ Yugoslavia', 'age', 'education-num', 'capital-gain', 'capital-loss', 'hours-per-week']
workclass_ Federal-gov workclass_ Local-gov workclass_ Private workclass_ Self-emp-inc workclass_ Self-emp-not-inc workclass_ State-gov workclass_ Without-pay education_level_ 10th education_level_ 11th education_level_ 12th ... native-country_ Thailand native-country_ Trinadad&Tobago native-country_ United-States native-country_ Vietnam native-country_ Yugoslavia age education-num capital-gain capital-loss hours-per-week
0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 1.0 0.0 0.0 0.30137 0.8 0.02174 0.0 0.397959

1 rows × 103 columns

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.

In [39]:
# 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])
display(X_test.head(n = 1))
display(y_test.head(n = 1))

Training set has 36177 samples.
Testing set has 9045 samples.
workclass_ Federal-gov workclass_ Local-gov workclass_ Private workclass_ Self-emp-inc workclass_ Self-emp-not-inc workclass_ State-gov workclass_ Without-pay education_level_ 10th education_level_ 11th education_level_ 12th ... native-country_ Thailand native-country_ Trinadad&Tobago native-country_ United-States native-country_ Vietnam native-country_ Yugoslavia age education-num capital-gain capital-loss hours-per-week
41387 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0 0.082192 0.733333 0.0 0.0 0.44898

1 rows × 103 columns

41387    0
Name: income, dtype: int64

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:

$$ F_{\beta} = (1 + \beta^2) \cdot \frac{precision \cdot recall}{\left( \beta^2 \cdot precision \right) + recall} $$

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.

In [47]:
# TODO: Calculate accuracy
from sklearn.metrics import accuracy_score
from sklearn.metrics import precision_score
from sklearn.metrics import recall_score
from sklearn.metrics import fbeta_score

#The naive model always predict that an individual make more than 50,000 
naive_prediction = [1 for i in range(len(income))]

TP=sum(map(lambda x,y: 1 if x==1 and y==1 else 0, income,naive_prediction)) #True Pos
TN=sum(map(lambda x,y: 1 if x==0 and y==0 else 0, income,naive_prediction)) #True Neg
FP=sum(map(lambda x,y: 1 if x==0 and y==1 else 0, income,naive_prediction)) #False Pos
FN=sum(map(lambda x,y: 1 if x==1 and y==0 else 0, income,naive_prediction)) #False Neg

# accuracy = Σ TP + Σ TN / Σ total population
accuracy = float(TP+TN)/n_records

# precision = Σ TP/Σ prediction positive
precision = float(TP)/(TP+FP)

# recall = Σ TP/Σ condition positive

# TODO: Calculate F-score using the formula above for beta = 0.5
fscore = (1+beta**2)*(precision*recall)/(beta**2*precision+recall)

# Accuracy, F-score using sklearn
accuracy_sk = accuracy_score(income, naive_prediction)
fscore_sk = fbeta_score(income, naive_prediction, beta = 0.5, pos_label=1)

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

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

Answer: Logisitic Regression, Gaussiam Naive Baywa (GaussianNB) and Decision Trees are the three Supervised learning models that are appropriate for this problem and these will be used to test on the census data.

Logistic Regression :

Real-world application : Use logistic regression to predict parking difficulty.

Strengths of the model : Logistic regression is well understood, and it tends to be resilient to noise in the training data. When the decision boundries are linear Logisitic regression model performs well. Using logistic regression, we will be able to infer which predictor are important by generating table of co-efficients.

Weaknesses of the model : We cannot expect this model to perform well when decision boundry is highly non-linear. This model is not used that often for response variable that has more than 2 classes (not binary classification).

What makes model a good candidate : We know that this problem is binary classification. Logistic regression is one of the baseline model and it is easy to interpret and explain.

Gaussian Naive Bayes (GaussianNB) : Real-world application : The Gaussian Naive Bayes model has been widely used in the industry for text classification purposes. In particular for classifying and filtering spam emails based on the likelihood of certain words appearing on an spam email as compared to a non-spam email (ref:

Strengths of the model : The strenght of this model lies in its simplicity inherited from the assumption that all features needed correctly to classify the data are "independent" from each other. This allows for the algorithm to be trained quickly and using less data. Furthermore, even when the underlying independence assumption is broken (i.e. when features have relationships between them), this algorithm still performs very well and is able to classify based on the maximum likelihood of a label given the set of features rather than on the actual probabilities of each feature.

Weaknesses of the model : Naive Bayes performs badly for problems where probabilities are sometimes greater than zero for a particular classification. Simplistic nature can yield bad generalizations or suboptimal solutions. This model doesn't account for interactions between features i.e. Naive Bayes assumes features are completely independent. In real life, it is almost impossible that we get a set of predictors which are completely independent. There is possibility of high bias when there is a small amount of data.

What makes model a good candidate : After one-hot encoding, our data has a lot of features - 103 in total - which could influence the the type of donor. Naive Bayes could be a good candidate on this basis. Assuming a typical charity environment where high-end hardware is not available for generating the model, this will be a good candidate for lightweight learning.

Decision Trees : Real-world application : Decesion Trees learning algorithm is used in detection of Fraudulent Financial Statements (FFS).

Strengths of the model :

  1. Easy to Understand: Decision tree output is very easy to understand even for people from non-analytical background. It does not require any statistical knowledge to read and interpret them. Its graphical representation is very intuitive and users can easily relate their hypothesis.
  2. Useful in Data exploration: Decision tree is one of the fastest way to identify most significant variables and relation between two or more variables. With the help of decision trees, we can create new variables / features that has better power to predict target variable.
  3. Data type is not a constraint: It can handle both numerical and categorical variables.
  4. Non Parametric Method: Decision tree is considered to be a non-parametric method. This means that decision trees have no assumptions about the space distribution and the classifier structure.

Weaknesses of the model :

  1. Over fitting: Over fitting is one of the most practical difficulty for decision tree models. This problem gets solved by setting constraints on model parameters and pruning.
  2. Not fit for continuous variables: While working with continuous numerical variables, decision tree looses information when it categorizes variables in different categories.

What makes model a good candidate : Considering we have a one-hot encoding of features in our dataset, this is well suited to a decision tree. It should also be able to handle lots of data easily, and it is also easy to visualize which would be great for intepretation by Charity ML.

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!

In [41]:
# 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): 
       - 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[: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!

In [42]:
# TODO: Import the three supervised learning models from sklearn
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB
# TODO: Initialize the three models
clf_A = LogisticRegression(random_state=10)
clf_B = DecisionTreeClassifier(criterion="entropy",random_state=10)
clf_C = GaussianNB()

# TODO: Calculate the number of samples for 1%, 10%, and 100% of the training data
samples_1 = (X_train.shape[0]*1/100)
samples_10 = (X_train.shape[0]*10/100)
samples_100 = (X_train.shape[0]*100/100)

# 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)

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

Question 3 - Choosing the Best Model

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 model for CharityML.

Logistic Regression has little overfitting problem as there's no large gap between training scores and testing scores. GaussianNB model has the fastest training speed and least variance of scores between training and testing, however, it may have undefitting problem and need more training samples or iterations. Decision Tree model has the most training data accuracy & f-score and on-par to Logistic Regression model for testing data accuracy & f-score, clearly depicting the overfitting.

Logistic Regression training times are better than Decision Tree model, and poorer than GaussianNB model. In terms of Prediction times, Logistic Regression model is the best compared to GaussianNB & Decision Tree models.

Logistic Regression has the most promising results on the testing set, has higher accuracy and f-score compared to other models. Hence, it is reccomended to choose the Logistic Regression as a model for CharityML. It has the most consistent performance regardless of training set size, and consistently delivers high F1 scores around 0.7. Decision Trees offer very similar performance to Logistic regression on the test set, and score highly on the training set - but this is most likely due to overfitting. On the other hand, GaussianNB delivers a very un-robust and poor accuracy score of 0.3-0.6 on the test and training sets. I would advise the selection of Logistic Regression due to performance on the testing set based upon providing the highest accuracy and F-score.

Whilst Logistic Regression appear to be influenced heavily by the size of the number of records, even with a large training and prediction time, it is likely that the model would be trained and used on occasion during funding rounds rather than persistently. This is because such donors are typically targetted for more prestigious events such as Charity Dinners. Considering this, performance and time are unlikely to be mission-critical even if order of magnitudes higher (i.e. seconds). This means it is fine to stick with Logistic Regression despite any performance concerns.

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: CharityML uses Logistic Regression to accurately predict and classify whether an individual makes more than \$50,000. Logistic regression is a linear approach to solve finding donors a binary classification problem. This means our model will predict, based on independent variables (individuals census data), whether the data belongs to one class (i.e income of indiviudal is >\$50k) or another.

Let's consider an example of a classification problem is will a person go swimming today or will he not? There are only two options. He goes swimming or he doesn’t go swimming. So how does logistic regression work? Logistic regression outputs a probability between zero and one. This probability informs us of which class we will predict our data belongs to. I will further simplify the example by saying there is only one independent variable, the temperature. Thus the problem becomes, given a certain temperature, will the person choose to swim or not to swim. Lets take a look at the image below to visualize how logistic regression works.

The X axis represents the temperature and the Y axis represents the probability the given person will go swimming. If the probability is below 0.5 we predict the person won’t swim. If the probability is above 0.5 we predict he will swim. 0.5 probability corresponds to about 30 degrees celsius on the model. Thus, if it is above 30 degrees celsius we predict the person will go swimming, otherwise we predict he won’t. The dots themselves represent the true decisions of all our samples.

To recap, logistic regression is a binary classification model. This means the prediction can only belong to one of two classes. Logistic regression works by computing a probability based on independent variables. The predicted class is based on which class has the greatest predicted probability. While logistic regression is a very simple model, it is still highly effective for many problems and should not be overlooked due to its simplicity.

Logistic Regression is the go-to method for classification problems. Because of the way that the model is learned, the predictions made by logistic regression can be used as the probability of a given data instance belonging to class 0 (Income <\$50K) or class 1 (Income > \$50K). Logistic regression measures the relationship between the categorical dependent variable Income (target class: yes (>\$50k)/no…) and one or more independent variables (among 103 features) by estimating probabilities.

During CharityML's Logistic Regression model training, model is fit to training data to estimate coefficients of input features (like age, capital gail,.. et al). CharityML's prediction for the output is transformed using a non-linear function called the logistic function (some variations this name are: sigmoid function and logit function). Using the coefficients of input features, CharityML's Logistic Regression model will predict test data and classify wheather income is greater than $50k or not.

Logistic Regression does work better when you remove attributes that are unrelated to the output variable as well as attributes that are very similar (correlated) to each other.

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!

In [43]:
# TODO: Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import make_scorer

# TODO: Initialize the classifier
clf = LogisticRegression(random_state=10)

# TODO: Create the parameters list you wish to tune
parameters = {'solver': ['newton-cg', 'lbfgs', 'sag'],\
              'C': [0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]}

# 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 =, y_train)

# Get the estimator
best_clf = grid_fit.best_estimator_

# Make predictions using the unoptimized and model
predictions = (, 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))

# show best parameters
print "\nBest Classifier\n------"
print best_clf

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

Best Classifier
LogisticRegression(C=100.0, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
          penalty='l2', random_state=10, solver='lbfgs', tol=0.0001,
          verbose=0, warm_start=False)

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.


Metric Benchmark Predictor Unoptimized Model Optimized Model
Accuracy Score 0.2478 0.8483 0.8494
F-score 0.2917 0.6993 0.7008


  • In terms of accuracy, F-score Optimized Model is marginally better. Improvement of Optimized Model is small compared to Unoptimized Model as the grid serach of paramteres is coarse
  • The Optimized Model has larger accuracy and F-score compared to Benchmark Predictor Given that the F-Score in particular has been able to reveal the advantage of optimizing the model, I would suggest the Charity ML continue to perform gridsearches and tuning.

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?

In [44]:
print data.columns.values

['age' 'workclass' 'education_level' 'education-num' 'marital-status'
 'occupation' 'relationship' 'race' 'sex' 'capital-gain' 'capital-loss'
 'hours-per-week' 'native-country' 'income']


Given that we're trying to estimate amount of income >\$50k, I would use the following 5 features:

  • Education-num: Assuming people who are better educated can attain better jobs, this should have a strong impact on income levels
  • marital-status: Those who earn more probably plan for stable life style, and are likely to be married.
  • age: Age typically directly correlates with level of income, experianced professional earn more and choose better career.
  • capitals-gain: Paying high amounts of capital gains tax suggests that more investments and more net-worth.
  • hours-per-week: Those who work a high number of hours per week most likely earn more, as this typically directly correlates with earnings.

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_'.

In [45]:
# TODO: Import a supervised learning model that has 'feature_importances_'
from sklearn.ensemble import RandomForestClassifier
# TODO: Train the supervised model on the training set 
model = RandomForestClassifier(random_state=10), y_train)
# TODO: Extract the feature importances
importances = model.feature_importances_

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

# show most importance features
a = np.array(importances)
factors = pd.DataFrame(data = np.array([importances.astype(float), features.columns]).T,
                       columns = ['importances', 'features'])
factors = factors.sort_values('importances', ascending=False)

print "\n top 5 important features"

 top 5 important features
importances features
98 0.237128 age
102 0.112679 hours-per-week
100 0.106252 capital-gain
99 0.0833611 education-num
25 0.0643363 marital-status_ Married-civ-spouse

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?


The observations are largely consistent with the five features I discussed in the previous questions, order is different. I thought education to be the most critical factor compared to all other features, but it seems age is critical factor. Simillarly hours-per-week feature is a better indicators than the marital status.

Visualization vividly articulates the order that model revealed the importance factors.

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.

In [46]:
# Import functionality for cloning a model
from sklearn.base import clone

# Reduce the feature space
X_train_reduced_5 = X_train[X_train.columns.values[(np.argsort(importances)[::-1])[:5]]]
X_test_reduced_5 = X_test[X_test.columns.values[(np.argsort(importances)[::-1])[:5]]]

X_train_reduced_44 = X_train[X_train.columns.values[(np.argsort(importances)[::-1])[:44]]]
X_test_reduced_44 = X_test[X_test.columns.values[(np.argsort(importances)[::-1])[:44]]]

# Train on the "best" model found from grid search earlier
start = time()
full_clf = (clone(best_clf)).fit(X_train, y_train)
end = time()
train_time_full = end - start

start = time()
reduced_5_clf = (clone(best_clf)).fit(X_train_reduced_5, y_train)
end = time()
train_time_reduced_5 = end - start

start = time()
reduced_44_clf = (clone(best_clf)).fit(X_train_reduced_44, y_train)
end = time()
train_time_reduced_44 = end - start

# Make new predictions
full_predictions = full_clf.predict(X_test)
reduced_5_predictions = reduced_5_clf.predict(X_test_reduced_5)
reduced_44_predictions = reduced_44_clf.predict(X_test_reduced_44)

# Report scores from the final model using both versions of data
print "Final Model trained on full data\n------"
print "Final Model Train time {} s full data\n------".format(train_time_full)
print "Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, full_predictions))
print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, full_predictions, beta = 0.5))
print "\nFinal Model trained on reduced to 5 features data\n------"
print "Final Model Train time {} s full data\n------".format(train_time_reduced_5)
print "Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, reduced_5_predictions))
print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, reduced_5_predictions, beta = 0.5))
print "\nFinal Model trained on reduced to 44 features data\n------"
print "Final Model Train time {} s full data\n------".format(train_time_reduced_44)
print "Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, reduced_44_predictions))
print "F-score on testing data: {:.4f}".format(fbeta_score(y_test, reduced_44_predictions, beta = 0.5))

Final Model trained on full data
Final Model Train time 0.451095819473 s full data
Accuracy on testing data: 0.8494
F-score on testing data: 0.7008

Final Model trained on reduced to 5 features data
Final Model Train time 0.0743699073792 s full data
Accuracy on testing data: 0.8347
F-score on testing data: 0.6678

Final Model trained on reduced to 44 features data
Final Model Train time 0.288591861725 s full data
Accuracy on testing data: 0.8498
F-score on testing data: 0.7019

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?


Metric Benchmark Predictor Unoptimized Model Optimized Model Features 5 Features 44
Accuracy Score 0.2478 0.8483 0.8494 0.8347 0.8498
F-score 0.2917 0.6993 0.7008 0.6678 0.7019

As expected, reducing the number of features to 5 has a negative impact upon our model. The optimized model with reduced features 5 has dropped in accuracy F-Score. As training time is a factor and it is a large consideration, I would like to reduced the features set to around 44, I found at reduced feature set 44, Optmized Model with reduced features set 44 beats the accuracy score and F-score of Optimized Model with all the features. Increasing features set to 44 also reduces the bais that might result due to only 5 features, though we might have to sacrifice the perfomance gain in training time we achive with feature set 5. However by choosing reduced dataset 44 we still achive 40+% traning time gain compared to full feature set. While choosing optimized model as Logistic regression we ensured that there is less variance of the data based on training and test results. Achiving a right trade off of bais and variance is very important for any machine learning model. So by choosing reduced features set 44 and using tuned Logistic Regression model we achive good results and better prediction of CharityML.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to
File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.