ML Data Distribution

ML Data Distributions: Uniform, Normal, & Random Generation

Statistical distributions describe how feature values are distributed. In Machine Learning, synthetic distribution generation is vital for data augmentation and initial algorithm validation.

Distribution Types

• Uniform Distribution: All intervals of equal length have equal probability (np.random.uniform).
• Normal / Gaussian Distribution: Bell-shaped symmetric curve governed by mean $\mu$ and standard deviation $\sigma$ (np.random.normal).

Practical Code Example

import numpy as np
from typing import Tuple

def generate_synthetic_distributions(size: int = 1000) -> Tuple[np.ndarray, np.ndarray]:
    # Reproducible seed
    np.random.seed(42)

    # Uniform distribution between 0.0 and 10.0
    uniform_data = np.random.uniform(low=0.0, high=10.0, size=size)

    # Normal distribution with mean=50.0 and std_dev=5.0
    normal_data = np.random.normal(loc=50.0, scale=5.0, size=size)

    return uniform_data, normal_data

if __name__ == "__main__":
    u_data, n_data = generate_synthetic_distributions()
    
    print("--- Uniform Distribution ---")
    print(f" Min: {np.min(u_data):.2f}, Max: {np.max(u_data):.2f}, Mean: {np.mean(u_data):.2f}")

    print("
--- Normal Distribution ---")
    print(f" Mean: {np.mean(n_data):.2f} (Target ~50.0), Std: {np.std(n_data):.2f} (Target ~5.0)")

Best Practices & Gotchas

• Set Seeds for Reproducibility: Always use np.random.seed() or np.random.default_rng(seed) when generating synthetic datasets.
• Normal Distribution Assumption: Linear models assume continuous numeric features follow a Gaussian normal distribution.
• Use Modern Generator API: Use rng = np.random.default_rng() in modern NumPy code instead of legacy np.random.

Self-Check Challenge

Generate a 1D NumPy array of 100 values sampled from a normal distribution with mean 0 and standard deviation 1 using np.random.normal().