Mathematics for Machine Learning

Machine learning is fundamentally built on mathematical concepts. This chapter covers the essential mathematical foundations needed to understand and implement machine learning algorithms.

Core Mathematical Areas in ML

1. Linear Algebra

  • Vectors and vector operations
  • Matrices and matrix operations
  • Eigenvalues and eigenvectors
  • Principal Component Analysis (PCA)

2. Calculus

  • Derivatives and gradients
  • Optimization and gradient descent
  • Backpropagation in neural networks
  • Automatic differentiation

3. Probability and Statistics

  • Probability distributions
  • Bayes’ theorem
  • Maximum likelihood estimation
  • Bayesian inference

4. Optimization Theory

  • Convex optimization
  • Gradient descent variants
  • Constrained optimization
  • Regularization techniques

Chapter Contents

  1. Linear Algebra for ML
  2. Calculus and Optimization
  3. Probability Theory in ML
  4. Statistical Learning Theory
  5. Information Theory
  6. Numerical Methods

Prerequisites

  • Basic calculus and linear algebra
  • Programming experience (Python recommended)
  • Understanding of basic statistics

Tools and Libraries

  • NumPy: Numerical computing
  • SciPy: Scientific computing
  • Scikit-learn: Machine learning algorithms
  • TensorFlow/PyTorch: Deep learning frameworks
  • Matplotlib/Seaborn: Data visualization