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Numerical Methods for Machine Learning: Course Notes
1. What is this?
2. Guidance
2.1. Getting a Job
2.2. Good Coding
2.3. Psuedo Code Exercise
3. Array Basics
3.1. Arrays in Numpy
3.2. Broadcasting Examples
3.3. Dot Product
3.4. Matrix Multiplication
3.5. Solving Systems of Equations
4. Mathematics
4.1. Single Variable Calculus
4.2. Multivariable Calculus
4.3. Automatic Differentiation with Jax
4.4. Derivatives, a Helpful Lesson
4.5. Complex Numbers
4.6. Representation of Numbers on the Computer
5. Matrices
5.1. Transpose, Inverse, and Norm
5.2. Linear Transformations
5.3. Matrix Determinant
5.4. Orthogonal Matrix (Unitary for Real Matrices)
5.5. Matrix Rank
5.6. Matrix Condition Number
5.7. EigenValues and Principle Component Analysis
5.8. Matrix Factorization Methods
5.9. SVD and PCA
6. Fourier Analysis
6.1. Introduction to Fourier Analysis
6.2. Convolution and Correlation
7. Interpolation
8. Numerical Optimization
8.1. Introduction to Optimization via Linear Regression
8.2. Convex Functions and Optimization
8.3. The Nelder-Mead Algorithm, Downhill Simplex, or the Amoeba
8.4. Measuring the Temperature of the Universe with SciPy’s fmin
8.5. Particle Swarm and the Eggholder Challenge
8.6. Newton’s method for Root Finding
8.7. Newton’s Method for Optimization
8.8. Problems with the Hessian Matrix
8.9. Introduction to Gradient Descent
8.10. Gradient Descent in 1-Dimension
8.11. Gradient Descent with Momentum
8.12. The Levenberg-Marquardt Method
9. Neural Networks
9.1. Feed Forward Neural Networks
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