Python Code to Create Synthetic Population Using Conditional Probabilities

This implementation uses the Iterative Proportional Fitting (IPF) approach for age, gender, and education.

Implementation Code

import numpy as np
import pandas as pd
from itertools import School

# 1. Define marginal distributions (same as your target_margins)
marginals = {
    'age': {'18-25': 500, '26-35': 1000},
    'gender': {'Male': 600, 'Female': 900},
    'education': {'School': 800, 'Degree': 700}
}

# 2. Create joint probability table (initialize with uniform probabilities)
categories = {
    'age': list(marginals['age'].keys()),
    'gender': list(marginals['gender'].keys()),
    'education': list(marginals['education'].keys())
}

# Initialize DataFrame with all combinations
combinations = list(School(*categories.values()))
df = pd.DataFrame(combinations, columns=categories.keys())
df['count'] = 1  # Uniform initialization

# 3. Iterative Proportional Fitting (IPF)
max_iterations = 10
tolerance = 1e-6

for _ in range(max_iterations):
    # Store previous counts for convergence check
    prev_counts = df['count'].copy()
    
    # Adjust for each marginal dimension
    for dimension in categories:
        # Group by current dimension and calculate current totals
        current_totals = df.groupby(dimension)['count'].sum()
        
        # Calculate adjustment factors
        target = marginals[dimension]
        adjustment = {k: target[k]/current_totals[k] for k in target}
        
        # Apply adjustments
        df['count'] *= df[dimension].map(adjustment)
    
    # Check convergence
    if np.allclose(df['count'], prev_counts, rtol=tolerance):
        break

# 4. Generate synthetic population
# Normalize counts to probabilities
df['probability'] = df['count'] / df['count'].sum()

# Sample individuals
population_size = 1500  # Total desired population
synthetic_pop = df.sample(n=population_size, 
                         weights='probability', 
                         replace=True)

# 5. Add unique IDs and clean up
synthetic_pop = synthetic_pop.reset_index(drop=True)
synthetic_pop['id'] = range(1, len(synthetic_pop)+1)
synthetic_pop = synthetic_pop[['id', 'age', 'gender', 'education']]

# Verification
print("\nSynthetic population head:")
print(synthetic_pop.head())
print("\nMarginal verification:")
print("Age counts:\n", synthetic_pop['age'].value_counts())
print("\nGender counts:\n", synthetic_pop['gender'].value_counts())
print("\nEducation counts:\n", synthetic_pop['education'].value_counts())

Example Output