Shedrackeze002/Mathematical-Foundation-of-machine-Learning

CMU-Africa: Mathematical Foundation of Machine Learning course assignments # Mathematical Foundations of Machine Learning Graduate coursework from **Carnegie Mellon University Africa** — MS in Engineering Artificial Intelligence. This repository covers the mathematical foundations essential for machine learning, including linear algebra, probability, optimization, and numerical methods. ## 📚 Assignments Overview ### Assignment 1: Linear Algebra Foundations - **Topics:** Vector spaces, matrix operations, linear transformations - **Skills:** NumPy, matrix manipulation, theoretical proofs ### Assignment 2: Matrix Decomposition & Applications - **Topics:** Eigenvalues, eigenvectors, SVD applications - **Key Tasks:** - Singular Value Decomposition (SVD) implementation - Principal Component Analysis (PCA) from scratch - Image compression using SVD - **Skills:** Matrix factorization, dimensionality reduction ### Assignment 3: Optimization & Gradient Methods - **Topics:** Gradient descent, convex optimization, convergence analysis - **Key Tasks:** - Implementing gradient descent variants - Convexity proofs and analysis - Learning rate selection strategies - **Skills:** Optimization theory, numerical analysis ### Assignment 4: Probability & Statistical Foundations - **Topics:** Probability distributions, Bayesian inference, statistical estimation - **Key Tasks:** - Maximum Likelihood Estimation (MLE) - Bayesian parameter estimation - Hypothesis testing fundamentals - **Skills:** Probabilistic reasoning, statistical inference ## 🧮 Mathematical Topics Covered - **Linear Algebra:** Vectors, matrices, eigendecomposition, SVD - **Calculus:** Gradients, Hessians, multivariable optimization - **Probability:** Distributions, Bayes' theorem, expectation, variance - **Optimization:** Convex functions, gradient descent, constrained optimization ## 🛠️ Tech Stack - **Languages:** Python 3.8+ - **Libraries:** NumPy, SciPy, Matplotlib - **Tools:** Jupyter Notebooks, LaTeX for mathematical notation ## 📁 Repository Structure ``` ├── Assignment1/ …