Exploring data with pandas, numpy and pyplot, make predictions with a simple custom algorithm, and calculate and compare accuracy with a simple custom algorithm.
Titanic Survival Data Exploration

Project 0: Titanic Survival Exploration¶

Machine Learning Engineer Nanodegree¶

In 1912, the ship RMS Titanic struck an iceberg on its maiden voyage and sank, resulting in the deaths of most of its passengers and crew. In this introductory project, we will explore a subset of the RMS Titanic passenger manifest to determine which features best predict whether someone survived or did not survive. To complete this project, you will need to implement several conditional predictions and answer the questions below. Your project submission will be evaluated based on the completion of the code and your responses to the questions.

Getting Started¶

To begin working with the RMS Titanic passenger data, we'll first need to import the functionality we need, and load our data into a pandas DataFrame.
Run the code cell below to load our data and display the first few entries (passengers) for examination using the .head() function.

Tip: You can run a code cell by clicking on the cell and using the keyboard shortcut Shift + Enter or Shift + Return. Alternatively, a code cell can be executed using the Play button in the hotbar after selecting it. Markdown cells (text cells like this one) can be edited by double-clicking, and saved using these same shortcuts. Markdown allows you to write easy-to-read plain text that can be converted to HTML.

In [1]:
import numpy as np
import pandas as pd

# RMS Titanic data visualization code
from titanic_visualizations import survival_stats
%matplotlib inline

in_file = 'titanic_data.csv'

# Print the first few entries of the RMS Titanic data

Out[1]:
PassengerId Survived Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
0 1 0 3 Braund, Mr. Owen Harris male 22 1 0 A/5 21171 7.2500 NaN S
1 2 1 1 Cumings, Mrs. John Bradley (Florence Briggs Th... female 38 1 0 PC 17599 71.2833 C85 C
2 3 1 3 Heikkinen, Miss. Laina female 26 0 0 STON/O2. 3101282 7.9250 NaN S
3 4 1 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1000 C123 S
4 5 0 3 Allen, Mr. William Henry male 35 0 0 373450 8.0500 NaN S

From a sample of the RMS Titanic data, we can see the various features present for each passenger on the ship:

• Survived: Outcome of survival (0 = No; 1 = Yes)
• Pclass: Socio-economic class (1 = Upper class; 2 = Middle class; 3 = Lower class)
• Name: Name of passenger
• Sex: Sex of the passenger
• Age: Age of the passenger (Some entries contain NaN)
• SibSp: Number of siblings and spouses of the passenger aboard
• Parch: Number of parents and children of the passenger aboard
• Ticket: Ticket number of the passenger
• Fare: Fare paid by the passenger
• Cabin Cabin number of the passenger (Some entries contain NaN)
• Embarked: Port of embarkation of the passenger (C = Cherbourg; Q = Queenstown; S = Southampton)

Since we're interested in the outcome of survival for each passenger or crew member, we can remove the Survived feature from this dataset and store it as its own separate variable outcomes. We will use these outcomes as our prediction targets.
Run the code cell below to remove Survived as a feature of the dataset and store it in outcomes.

In [2]:
type(full_data)

Out[2]:
pandas.core.frame.DataFrame
In [3]:
# Store the 'Survived' feature in a new variable and remove it from the dataset

# This stores the column 'Survived' in the variable outcomes
# This is also the response series (vector), y
outcomes = full_data['Survived']

# df.drop() drops categories or rows
# In this case as axis=1, it's droppping the category 'Survived'
# This are the features DataFrame (matrix) X
data = full_data.drop('Survived', axis = 1)

# Show the new dataset with 'Survived' removed

Out[3]:
PassengerId Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
0 1 3 Braund, Mr. Owen Harris male 22 1 0 A/5 21171 7.2500 NaN S
1 2 1 Cumings, Mrs. John Bradley (Florence Briggs Th... female 38 1 0 PC 17599 71.2833 C85 C
2 3 3 Heikkinen, Miss. Laina female 26 0 0 STON/O2. 3101282 7.9250 NaN S
3 4 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1000 C123 S
4 5 3 Allen, Mr. William Henry male 35 0 0 373450 8.0500 NaN S

The very same sample of the RMS Titanic data now shows the Survived feature removed from the DataFrame. Note that data (the passenger data) and outcomes (the outcomes of survival) are now paired. That means for any passenger data.loc[i], they have the survival outcome outcome[i].

To measure the performance of our predictions, we need a metric to score our predictions against the true outcomes of survival. Since we are interested in how accurate our predictions are, we will calculate the proportion of passengers where our prediction of their survival is correct. Run the code cell below to create our accuracy_score function and test a prediction on the first five passengers.

Think: Out of the first five passengers, if we predict that all of them survived, what would you expect the accuracy of our predictions to be?

In [4]:
def accuracy_score(truth, pred):
""" Returns accuracy score for input truth and predictions. """

# Ensure that the number of predictions matches number of outcomes
if len(truth) == len(pred):

# Calculate and return the accuracy as a percent

# {:2f}.format((truth == pred).mean()*100)
# ":" represents format specification
# "2f" represents 2 decimal places

# (truth == pred).mean()*100
return "Predictions have an accuracy of {:.2f}.".format((truth == pred).mean()*100)

else:
return "Number of predictions does not match number of outcomes!"

# Test the 'accuracy_score' function

# pd.Series() creates a series
# np.ones(5, dtype=int) creates a 5 x 1 array of ones
predictions = pd.Series(np.ones(5, dtype = int))

# Call accuracy_score function and passing the arguments outcomes[:5] and predictions
# Since we predictions is only a 5 x 1 array, we can only compare with the first 5 rows
print accuracy_score(outcomes[:5], predictions)

Predictions have an accuracy of 60.00.


Tip: If you save an iPython Notebook, the output from running code blocks will also be saved. However, the state of your workspace will be reset once a new session is started. Make sure that you run all of the code blocks from your previous session to reestablish variables and functions before picking up where you last left off.

Making Predictions¶

If we were asked to make a prediction about any passenger aboard the RMS Titanic whom we knew nothing about, then the best prediction we could make would be that they did not survive. This is because we can assume that a majority of the passengers (more than 50%) did not survive the ship sinking.
The predictions_0 function below will always predict that a passenger did not survive.

In [5]:
# We can calculate the null accuracy from this

def predictions_0(data):
""" Model with no features. Always predicts a passenger did not survive. """

predictions = []

# for index, row in data.iterrows()
for index, passenger in data.iterrows():

# Predict the survival of 'passenger'
predictions.append(0)

# Return our predictions
return pd.Series(predictions)

# Make the predictions
predictions = predictions_0(data)

# As you can see, everything is 0 here because we predicted that no one survived

Out[5]:
0    0
1    0
2    0
3    0
4    0
dtype: int64

Question 1¶

Using the RMS Titanic data, how accurate would a prediction be that none of the passengers survived?
Hint: Run the code cell below to see the accuracy of this prediction.

In [6]:
# the null accuracy is 61.62%
print accuracy_score(outcomes, predictions)

Predictions have an accuracy of 61.62.


Let's take a look at whether the feature Sex has any indication of survival rates among passengers using the survival_stats function. This function is defined in the titanic_visualizations.py Python script included with this project. The first two parameters passed to the function are the RMS Titanic data and passenger survival outcomes, respectively. The third parameter indicates which feature we want to plot survival statistics across.
Run the code cell below to plot the survival outcomes of passengers based on their sex.

In [7]:
survival_stats(data, outcomes, 'Sex')


Examining the survival statistics, a large majority of males did not survive the ship sinking. However, a majority of females did survive the ship sinking. Let's build on our previous prediction: If a passenger was female, then we will predict that they survived. Otherwise, we will predict the passenger did not survive.
Fill in the missing code below so that the function will make this prediction.
Hint: You can access the values of each feature for a passenger like a dictionary. For example, passenger['Sex'] is the sex of the passenger.

In [8]:
def predictions_1(data):
""" Model with one feature:
- Predict a passenger survived if they are female. """

# create a list of predictions
predictions = []
for index, passenger in data.iterrows():

# Remove the 'pass' statement below
# and write your prediction conditions here
if passenger['Sex'] == 'female':
predictions.append(1)
else:
predictions.append(0)

# Return our predictions
return pd.Series(predictions)

# Make the predictions
predictions = predictions_1(data)

Out[8]:
0    0
1    1
2    1
3    1
4    0
dtype: int64
In [9]:
# Here we can see how my code seems to be running well based on the first 5 rows
# rows 1 through 3 are ones, matching the Sex 'female'

Out[9]:
PassengerId Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
0 1 3 Braund, Mr. Owen Harris male 22 1 0 A/5 21171 7.2500 NaN S
1 2 1 Cumings, Mrs. John Bradley (Florence Briggs Th... female 38 1 0 PC 17599 71.2833 C85 C
2 3 3 Heikkinen, Miss. Laina female 26 0 0 STON/O2. 3101282 7.9250 NaN S
3 4 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1000 C123 S
4 5 3 Allen, Mr. William Henry male 35 0 0 373450 8.0500 NaN S

Question 2¶

How accurate would a prediction be that all female passengers survived and the remaining passengers did not survive?
Hint: Run the code cell below to see the accuracy of this prediction.

In [10]:
print accuracy_score(outcomes, predictions)

Predictions have an accuracy of 78.68.


Using just the Sex feature for each passenger, we are able to increase the accuracy of our predictions by a significant margin. Now, let's consider using an additional feature to see if we can further improve our predictions. For example, consider all of the male passengers aboard the RMS Titanic: Can we find a subset of those passengers that had a higher rate of survival? Let's start by looking at the Age of each male, by again using the survival_stats function. This time, we'll use a fourth parameter to filter out the data so that only passengers with the Sex 'male' will be included.
Run the code cell below to plot the survival outcomes of male passengers based on their age.

In [11]:
survival_stats(data, outcomes, 'Age', ["Sex == 'male'"])


Examining the survival statistics, the majority of males younger than 10 survived the ship sinking, whereas most males age 10 or older did not survive the ship sinking. Let's continue to build on our previous prediction: If a passenger was female, then we will predict they survive. If a passenger was male and younger than 10, then we will also predict they survive. Otherwise, we will predict they do not survive.
Fill in the missing code below so that the function will make this prediction.
Hint: You can start your implementation of this function using the prediction code you wrote earlier from predictions_1.

In [12]:
def predictions_2(data):
""" Model with two features:
- Predict a passenger survived if they are female.
- Predict a passenger survived if they are male and younger than 10. """

predictions = []
for index, passenger in data.iterrows():

# Remove the 'pass' statement below
# and write your prediction conditions here
if passenger['Sex'] == 'female':
predictions.append(1)
elif (passenger['Sex'] == 'male') & (passenger['Age'] < 10):
predictions.append(1)
else:
predictions.append(0)

# Return our predictions
return pd.Series(predictions)

# Make the predictions
predictions = predictions_2(data)

Out[12]:
0     0
1     1
2     1
3     1
4     0
5     0
6     0
7     1
8     1
9     1
10    1
11    1
12    0
13    0
14    1
15    1
16    1
17    0
18    1
19    1
dtype: int64
In [13]:
# I checked the data and row 7 and 16 should be 1 on the table above
# Hence, as you can see from the table above, rows 7 and 16 are indeed ones
data.loc[(data.Age < 10) & (data.Sex == 'male'), 'Age'].head(2)

Out[13]:
7     2
16    2
Name: Age, dtype: float64

Question 3¶

How accurate would a prediction be that all female passengers and all male passengers younger than 10 survived?
Hint: Run the code cell below to see the accuracy of this prediction.

In [14]:
print accuracy_score(outcomes, predictions)

Predictions have an accuracy of 79.35.


Adding the feature Age as a condition in conjunction with Sex improves the accuracy by a small margin more than with simply using the feature Sex alone. Now it's your turn: Find a series of features and conditions to split the data on to obtain an outcome prediction accuracy of at least 80%. This may require multiple features and multiple levels of conditional statements to succeed. You can use the same feature multiple times with different conditions.
Pclass, Sex, Age, SibSp, and Parch are some suggested features to try.

Use the survival_stats function below to to examine various survival statistics.
Hint: To use mulitple filter conditions, put each condition in the list passed as the last argument. Example: ["Sex == 'male'", "Age < 18"]

In [15]:
# EXAMINING MALE

# Playing with Pclass (Passenger Class)
survival_stats(data, outcomes, 'Pclass', ["Sex == 'male'"])
survival_stats(data, outcomes, 'Age', ["Sex == 'male'", "Pclass == 3"])
survival_stats(data, outcomes, 'Age', ["Sex == 'male'", "Pclass == 2"])
survival_stats(data, outcomes, 'Age', ["Sex == 'male'", "Pclass == 1"])

# EXAMINING FEMALE

# Playing with Pclass
# Majority of Pclass 1 and 2 survived
survival_stats(data, outcomes, 'Pclass', ["Sex == 'female'"])
survival_stats(data, outcomes, 'Age', ["Sex == 'female'", "Pclass == 3"])
survival_stats(data, outcomes, 'Age', ["Sex == 'female'", "Pclass == 2"])
survival_stats(data, outcomes, 'Age', ["Sex == 'female'", "Pclass == 1"])


After exploring the survival statistics visualization, fill in the missing code below so that the function will make your prediction.
Make sure to keep track of the various features and conditions you tried before arriving at your final prediction model.
Hint: You can start your implementation of this function using the prediction code you wrote earlier from predictions_2.

In [16]:
def predictions_3(data):
""" Model with multiple features. Makes a prediction with an accuracy of at least 80%. """

predictions = []
for index, passenger in data.iterrows():
if passenger['Sex'] == 'female':
if passenger['Pclass'] == 3 and passenger['Age'] > 40 and passenger['Age'] < 60:
predictions.append(0)
elif passenger['Pclass'] == 1 and passenger['Age'] < 10:
predictions.append(0)
else:
predictions.append(1)
if passenger['Sex'] == 'male':
if passenger['Pclass'] == 2 and passenger['Age'] < 10:
predictions.append(1)
elif passenger['Pclass'] == 1 and passenger['Age'] < 40:
predictions.append(1)
else:
predictions.append(0)

# Return our predictions
return pd.Series(predictions)

# Make the predictions
predictions = predictions_3(data)


Question 4¶

Describe the steps you took to implement the final prediction model so that it got an accuracy of at least 80%. What features did you look at? Were certain features more informative than others? Which conditions did you use to split the survival outcomes in the data? How accurate are your predictions?
Hint: Run the code cell below to see the accuracy of your predictions.

In [17]:
print accuracy_score(outcomes, predictions)

Predictions have an accuracy of 80.92.


• I looked at the following features
• Sex
• Age
• Pclass
• And I broke down PClass to 1, 2 and 3
• With these features, we arrive at 8 graphs
• 2 graphs
• Male and Age
• Female and Age
• Remaining 6 graphs
• Sex=Male, Age and Pclass=1
• Sex=Male, Age and Pclass=2
• Sex=Male, Age and Pclass=3
• Sex=Female, Age and Pclass=1
• Sex=Female, Age and Pclass=1
• Sex=Female, Age and Pclass=1
• We can now clearly observe where females survived and where males survived
• Females
• Sex=Female, 40 < Age < 60, and Pclass=3 mostly did not survive
• Sex=Female, Age < 10, and Pclass=1 mostly did not survive
• All else survived for Sex=Female
• Males
• Sex=Male, Age < 10, and Pclass=2 mostly survived
• Sex=Male, Age < 40, and Pclass=2 mostly survived
• All else did not survive for Sex=Male
• The reason why I labelled "all else female survived" with an else statement is because most of them. On the contrary, most males did not survive, hence I labelled "all else male did not survive" with an else statement.
• I ran many graphs with different features, and the most meaningful ones came up with segregating in detail using Pclass
• The accuracy exceeds the requirement of 80%

Conclusion¶

After several iterations of exploring and conditioning on the data, you have built a useful algorithm for predicting the survival of each passenger aboard the RMS Titanic. The technique applied in this project is a manual implementation of a simple machine learning model, the decision tree. A decision tree splits a set of data into smaller and smaller groups (called nodes), by one feature at a time. Each time a subset of the data is split, our predictions become more accurate if each of the resulting subgroups are more homogeneous (contain similar labels) than before. The advantage of having a computer do things for us is that it will be more exhaustive and more precise than our manual exploration above. This link provides another introduction into machine learning using a decision tree.

A decision tree is just one of many models that come from supervised learning. In supervised learning, we attempt to use features of the data to predict or model things with objective outcome labels. That is to say, each of our data points has a known outcome value, such as a categorical, discrete label like 'Survived', or a numerical, continuous value like predicting the price of a house.

Question 5¶

Think of a real-world scenario where supervised learning could be applied. What would be the outcome variable that you are trying to predict? Name two features about the data used in this scenario that might be helpful for making the predictions.

Answer: There is the typical spam detection scenario where we predict if an email is a spam or ham (not spam). Features that may be used include emails' headers, country of origin, and content.

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