Randomness & Simulation

Why Randomness?

Machine learning relies heavily on randomness: initializing weights, splitting data into train/test sets, and dropout regularization.

Setting the Seed

Computers generate pseudo-random numbers. Setting a seed ensures reproducibility:

np.random.seed(42) # Always generates the same "random" numbers

Essential Random Functions

• np.random.rand(d1, d2): Uniform distribution [0, 1)
• np.random.randn(d1, d2): Standard Normal (Gaussian) distribution (mean=0, std=1)
• np.random.randint(low, high): Random integers
• np.random.choice(array): Random sample from an array

Simulating the Central Limit Theorem (CLT)

The CLT states that if you take enough random samples from any distribution, the means of those samples will form a normal distribution. We can prove this easily with NumPy!