An Insight Into Simpson'S Paradox In Machine Learning

Introduction

In the world of statistics and data analysis, paradoxes and anomalies can often stump scientists. One such intriguing phenomenon is Simpson's Paradox, an occurrence where a trend seen in several different groups of data disappears or reverses when these groups are combined.

In this blog post, we will delve into Simpson's Paradox, understand its relevance in Machine Learning, and illustrate a simple scenario using Python to understand this statistical conundrum better.

What is Simpson's Paradox?

Simpson's Paradox, named after the statistician Edward H. Simpson, occurs when a trend that is seen in multiple groups of data disappears or reverses when these groups are combined. In other words, aggregated data can reveal the opposite results of disaggregated data. Is it all sounding paradoxical yet?

But, how does it seep into Machine Learning?

Machine Learning models make predictions based on patterns observed from the data. If the data were to exhibit Simpson's Paradox, the learned models might be heavily influenced, yielding inaccurate and misleading results.

Simple Demonstration with Python

Let's see a working code snippet in Python to understand this paradox better.

# Importing necessary libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Create Data
group1 = pd.DataFrame({
    'x': [2, 3, 4, 5, 6],
    'y': [7, 10, 8, 7, 5],
    'group': 'Group1'
})

group2 = pd.DataFrame({
    'x': [6, 7, 8],
    'y': [2, 3, 5],
    'group': 'Group2'
})

# Concatenate data
data = pd.concat([group1, group2])

# Plot group1, group2 and combined data
for key, grp in data.groupby(['group']):
    plt.plot(grp['x'], grp['y'], label=key)

plt.plot(data['x'], data['y'], label='Combined')
plt.legend(loc='best')
plt.show()

This script generates two groups of randomly distributed data points, concatenates the data, and plots group-wise and the combined data. As you can see, a positive trend can be observed in each individual group when plotted separately. But, when combined, paradoxically, the trend appears to take a downward path, contradicting the individual groups' trends. This is Simpson's Paradox in a nutshell.

Conclusion

Simpson's Paradox is a reminder of the intricate aspects one needs to consider when working with statistics in machine learning. It showcases the importance of being aware of potential discrepancies between grouped and aggregated data and underscores the need for careful data analysis before any modeling stage.

Remember to be critical of your data. Always take that extra step to ensure clarity and accuracy because the devil is in the details, or in this case, the data!

Happy Machine Learning!