Shedrackeze002/Mathematical-Foundation-of-machine-Learning
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project
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She
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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/ …
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