Data Exploration

First look at our dataset

In this notebook, we will look at the necessary steps required before any machine learning takes place. It involves:

• loading the data;
• looking at the variables in the dataset, in particular, differentiate between numerical and categorical variables, which need different preprocessing in most machine learning workflows;
• visualizing the distribution of the variables to gain some insights into the dataset.

Loading the adult census dataset

We will use data from the 1994 US census that we downloaded from OpenML.

You can look at the OpenML webpage to learn more about this dataset: http://www.openml.org/d/1590

The dataset is available as a CSV (Comma-Separated Values) file and we will use pandas to read it.

import pandas as pd

adult_census = pd.read_csv("../data/adult-census.csv")

Note

The goal with this data is to predict whether a person earns over 50K a year based on heterogeneous data such as age, employment, education, family information, etc.

Response variable

The column named class is our target variable (i.e., the variable which we want to predict).

The two possible classes are <=50K (low-revenue) and >50K (high-revenue).

Consequently, this is called a binary classification problem.

target_column = 'class'
adult_census[target_column].value_counts()

 <=50K    37155
 >50K     11687
Name: class, dtype: int64

Note

Classes are slightly imbalanced, meaning there are more samples of one or more classes compared to others. Class imbalance happens often in practice and may need special techniques when building a predictive model.

Features

The other columns represent pieces of information (aka "features") that may be useful in predicting the response variable.

In the field of machine learning and descriptive statistics, commonly used equivalent terms are "variable", "attribute", or "covariate".

features = adult_census.drop(columns='class')
features.head()

	age	workclass	education	education-num	marital-status	occupation	relationship	race	sex	capital-gain	capital-loss	hours-per-week	native-country
0	25	Private	11th	7	Never-married	Machine-op-inspct	Own-child	Black	Male	0	0	40	United-States
1	38	Private	HS-grad	9	Married-civ-spouse	Farming-fishing	Husband	White	Male	0	0	50	United-States
2	28	Local-gov	Assoc-acdm	12	Married-civ-spouse	Protective-serv	Husband	White	Male	0	0	40	United-States
3	44	Private	Some-college	10	Married-civ-spouse	Machine-op-inspct	Husband	Black	Male	7688	0	40	United-States
4	18	?	Some-college	10	Never-married	?	Own-child	White	Female	0	0	30	United-States

import numpy as np

numeric_columns = (
    features.select_dtypes(include=np.number).columns.values
)
categorical_columns = (
    features.drop(columns=numeric_columns).columns.values
)

print(f'''
There are {features.shape[0]} observations and {features.shape[1]} features.

Numeric features: {', '.join(numeric_columns)}.

Categorical features: {', '.join(categorical_columns)}.
''')

There are 48842 observations and 13 features.

Numeric features: age, education-num, capital-gain, capital-loss, hours-per-week.

Categorical features: workclass, education, marital-status, occupation, relationship, race, sex, native-country.

Visual inspection of the data

Before building a predictive model, it is a good idea to look at the data:

• maybe the task you are trying to achieve can be solved without machine learning;
• you need to check that the information you need for your task is actually present in the dataset;
• inspecting the data is a good way to find peculiarities. These can arise during data collection (for example, malfunctioning sensor or missing values), or from the way the data is processed afterwards (for example capped values);
• we may identify feature engineering tasks that could improve modeling performance.

adult_census.hist(figsize=(20, 14));

Tip

In the previous cell, we used the following pattern: func(); where the semi-colon follows the plot function. We do this to avoid showing the ugly <matplotlib.axes object ...> output.

We can already make a few comments about some of the variables:

• age: there are not that many points for age > 70. The dataset description does indicate that retired people have been filtered out (hours-per-week > 0);
• education-num: peak at 10 and 13, hard to tell what it corresponds to without looking much further. We'll do that later in this notebook;
• hours-per-week peaks at 40, this was very likely the standard number of working hours at the time of the data collection;
• most values of capital-gain and capital-loss are close to zero.

For categorical variables, we can look at the distribution of values:

adult_census['sex'].value_counts()

 Male      32650
 Female    16192
Name: sex, dtype: int64

adult_census['education'].value_counts()

 HS-grad         15784
 Some-college    10878
 Bachelors        8025
 Masters          2657
 Assoc-voc        2061
 11th             1812
 Assoc-acdm       1601
 10th             1389
 7th-8th           955
 Prof-school       834
 9th               756
 12th              657
 Doctorate         594
 5th-6th           509
 1st-4th           247
 Preschool          83
Name: education, dtype: int64

Question

What do you think the difference is between education and education-num?

pd.crosstab(
    index=adult_census['education'],
    columns=adult_census['education-num']
)

education-num	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
education
10th	0	0	0	0	0	1389	0	0	0	0	0	0	0	0	0	0
11th	0	0	0	0	0	0	1812	0	0	0	0	0	0	0	0	0
12th	0	0	0	0	0	0	0	657	0	0	0	0	0	0	0	0
1st-4th	0	247	0	0	0	0	0	0	0	0	0	0	0	0	0	0
5th-6th	0	0	509	0	0	0	0	0	0	0	0	0	0	0	0	0
7th-8th	0	0	0	955	0	0	0	0	0	0	0	0	0	0	0	0
9th	0	0	0	0	756	0	0	0	0	0	0	0	0	0	0	0
Assoc-acdm	0	0	0	0	0	0	0	0	0	0	0	1601	0	0	0	0
Assoc-voc	0	0	0	0	0	0	0	0	0	0	2061	0	0	0	0	0
Bachelors	0	0	0	0	0	0	0	0	0	0	0	0	8025	0	0	0
Doctorate	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	594
HS-grad	0	0	0	0	0	0	0	0	15784	0	0	0	0	0	0	0
Masters	0	0	0	0	0	0	0	0	0	0	0	0	0	2657	0	0
Preschool	83	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Prof-school	0	0	0	0	0	0	0	0	0	0	0	0	0	0	834	0
Some-college	0	0	0	0	0	0	0	0	0	10878	0	0	0	0	0	0

Another way to inspect the data is to do a pairplot and show how each variable differs according to our target, i.e. class. Plots along the diagonal show the distribution of individual variables for each class. The plots on the off-diagonal can reveal interesting interactions between variables.

import seaborn as sns

# We will plot a subset of the data to keep the plot readable and make the
# plotting faster
n_samples_to_plot = 5000
columns = ['age', 'education-num', 'hours-per-week']
sns.pairplot(data=adult_census[:n_samples_to_plot], vars=columns,
             hue=target_column, plot_kws={'alpha': 0.2},
             height=3, diag_kind='hist', diag_kws={'bins': 30});

Creating decision rules by hand

By looking at the previous plots, we could create some hand-written rules that predicts whether someone has a high- or low-income.

Your Turn

Looking at the prior pairplot, what type of decision rules would you suggest?

For instance, we could focus on the combination of the hours-per-week and age features.

import matplotlib.pyplot as plt

ax = sns.scatterplot(
    x="age", y="hours-per-week", data=adult_census[:n_samples_to_plot],
    hue="class", alpha=0.5,
)

age_limit = 27
plt.axvline(x=age_limit, ymin=0, ymax=1, color="black", linestyle="--")

hours_per_week_limit = 40
plt.axhline(
    y=hours_per_week_limit, xmin=0.18, xmax=1, color="black", linestyle="--"
)

plt.annotate("<=50K", (17, 25), rotation=90, fontsize=35)
plt.annotate("<=50K", (35, 20), fontsize=35)
plt.annotate("???", (45, 60), fontsize=35);

Unbiased decision rules

Machine learning models will work similarly.

However, ML models chose the "best" decision rules based on the data without human intervention or inspection.

ML models are extremely helpful when creating rules by hand is not straightforward, for example because we are in high dimension (many features) or because there are no simple and obvious rules that separate the two classes as in the top-right region of the previous plot.

To sum up, the important thing to remember is that in a machine-learning setting, a model automatically creates the "rules" from the data in order to make predictions on new unseen data. And this is where we'll turn our attention to in future modules.

Wrapping up

In this module we have:

• loaded the data from a CSV file using pandas;
• looked at the different kind of variables to differentiate between categorical and numerical variables;
• inspected the data with pandas and seaborn. Data inspection can allow you to decide whether using machine learning is appropriate for your data and to highlight potential peculiarities in your data.