202502012215
tags: #machine-learning #optimization #computation

Vectorization replaces explicit loops with matrix operations, dramatically speeding up machine learning computations by leveraging optimized linear algebra libraries.

Why vectorization matters:

• 10-100x faster than explicit loops
• Takes advantage of parallel processing (CPU/GPU)
• More concise and readable code
• Reduces bugs from manual indexing

Example comparison:

# Non-vectorized (slow)
z = 0
for i in range(n):
    z += w[i] * x[i]

# Vectorized (fast)
z = np.dot(w, x)

In machine learning:

• Gradient Descent updates: θ := θ - α∇J(θ)
• Forward propagation in neural networks
• Computing predictions for entire datasets at once

Key libraries:

• NumPy (Python), built on BLAS/LAPACK
• TensorFlow/PyTorch for deep learning
• MATLAB's built-in matrix operations

Vectorization is essential for implementing Gradient Descent efficiently with multiple variables and large datasets.

Reference

Machine Learning Yearning by Andrew Ng