How to Randomly Select Groups in a Proportionate Way

In this article, we will explore how to randomly select groups of rows from a dataset in a proportionate way. We will use the pandas library in Python to achieve this.

Introduction

When dealing with large datasets, it’s common to need to randomly sample rows from specific groups or categories. In this case, we want to sample rows from different “Teams” based on their unique ID counts. The idea is to select rows proportionally to the number of unique IDs in each team.

For example, let’s say we have a dataset with three teams: A, B, and C. Team A has 3 unique IDs, team B has 2 unique IDs, and team C has 1 unique ID. If we want to sample 8 rows from this dataset, we should end up with approximately the same number of rows for each team.

Problem Statement

The provided code has a working method that basically does this but sometimes ends up with zero selected for a group. We want to modify this code so that all groups with less than 0.5% unique IDs round up to one and can be selected, without exceeding the total number of rows (n_total).

Solution Overview

We will break down the solution into several steps:

1. Compute proportions: Calculate the proportion of each team’s unique IDs relative to the total number of unique IDs.
2. Deal with low proportions: Round up the proportions for teams with less than 0.5% unique IDs and adjust the remaining proportions accordingly.
3. Get sample: Use the adjusted proportions to select rows from each team.

Step 1: Compute Proportions

import pandas as pd

# Setup
N_TOTAL = 8

if N_TOTAL < df["Team"].nunique():
    raise ValueError(
        f"Number of rows ({N_TOTAL}) can not be less than "
        + f"number of unique teams ({df['Team'].nunique()})."
    )

# Compute proportions 
proportions = (
    pd.DataFrame(
        N_TOTAL * df.groupby(["Team"]).nunique()["ID"]
        / df.groupby(["Team"]).nunique()["ID"].sum()
    )
    .round()
    .astype(int)
    .rename(columns={"ID": "Num"})
)

# Deal with low proportions to get at least one row
proportions["Num"] = proportions.apply(
    lambda x: 1 if x["Num"] == 0 else x["Num"], axis=1
)
proportions["Num"] = proportions.apply(
    lambda x: x["Num"]
    if x["Num"] == 1
    else x["Num"] - (proportions["Num"].sum() - N_TOTAL),
    axis=1,
)
proportions = proportions.reset_index()

Step 2: Get Sample

# Get sample
sample = (
    df.groupby("Team", group_keys=False)
    .apply(
        lambda x: x.sample(
            n=proportions.loc[proportions["Team"] == x.name, "Num"].values[0],
            replace=False,
        )
    )
    .sort_values(by=["Team", "ID"])
    .reset_index(drop=True)
)

print(sample)

Conclusion

In this article, we explored how to randomly select groups of rows from a dataset in a proportionate way. We used the pandas library in Python to compute proportions and adjust them for teams with less than 0.5% unique IDs. Finally, we selected rows from each team using the adjusted proportions.

The resulting sample is approximately proportional to the number of unique IDs in each team, ensuring that the selection process meets our requirements.

Example Use Case

Suppose you have a dataset of customers with different countries of origin. You want to randomly select 10% of the total customers from each country based on their country’s population density. You can use the code above to achieve this by computing proportions and adjusting them for countries with low population densities.

# Import necessary libraries
import pandas as pd

# Load dataset
df = pd.read_csv("customers.csv")

# Compute population density ratios
country_density = df.groupby(["Country"])["Population"].mean()

# Compute proportions 
proportions = (
    country_density
    / country_density.sum()
    * 0.1
)

In this example, we compute the average population of each country and divide it by the total population to get the proportion of customers from that country. We then multiply the result by 0.1 (10%) to get the desired proportion.

Last modified on 2024-08-17