Gain a deep mathematical understanding of machine learning and develop theory-based implementation skills
Series Overview
This series is an advanced educational content consisting of 5 chapters that teaches the mathematical foundations of machine learning from both theoretical and implementation perspectives.
Features:
- ✅ Integration of Theory and Implementation: Progressive learning from mathematical definitions to implementation
- ✅ Over 30 Implementation Examples: Implementations using NumPy/SciPy/PyTorch
- ✅ Systematic Coverage: Probability and statistics, linear algebra, optimization, information theory, and learning theory
- ✅ Practical Applications: Concrete applications of each theory to machine learning
Chapter Details
Chapter 1: Fundamentals of Probability and Statistics
Difficulty: Advanced | Learning Time: 30-35 minutes | Code Examples: 6
Learning Content
- Probability Foundations - Bayes' theorem, conditional probability
- Probability Distributions - Normal distribution, multivariate normal distribution
- Expected Value and Variance - Covariance, correlation coefficient
- Maximum Likelihood Estimation and Bayesian Estimation - MAP estimation
- Practical Applications: Naive Bayes, GMM, Bayesian linear regression
Chapter 2: Fundamentals of Linear Algebra
Difficulty: Advanced | Learning Time: 30-35 minutes | Code Examples: 6
Learning Content
- Vectors and Matrices - Inner product, norm, matrix operations
- Matrix Decomposition - Eigenvalue decomposition, SVD, QR decomposition
- Principal Component Analysis (PCA) - Mathematics of dimensionality reduction
- Linear Transformations and Projections - Geometry of least squares
- Practical Applications: Linear regression, Ridge regression, image PCA
Chapter 3: Optimization Theory
Difficulty: Advanced | Learning Time: 30-40 minutes | Code Examples: 6
Learning Content
- Optimization Foundations - Convex functions, gradients, Hessian
- Gradient Descent - Momentum, Adam, convergence
- Constrained Optimization - Lagrange multipliers, KKT conditions
- Convex Optimization - Linear programming, quadratic programming
- Practical Applications: Logistic regression, NN training, regularization
Chapter 4: Information Theory
Difficulty: Advanced | Learning Time: 25-30 minutes | Code Examples: 6
Learning Content
- Entropy - Information content, conditional entropy
- KL Divergence and Cross Entropy
- Mutual Information - Applications to feature selection
- Information Theory and Machine Learning - VAE, information bottleneck
- Practical Applications: Cross entropy loss, KL loss, ELBO
Chapter 5: Learning Theory in Machine Learning
Difficulty: Advanced | Learning Time: 35-40 minutes | Code Examples: 6
Learning Content
- PAC Learning - Learnability, sample complexity
- VC Dimension - Shattering, generalization error
- Bias-Variance Decomposition - Trade-offs
- Regularization Theory - L1/L2 regularization, Elastic Net
- Practical Applications: Early stopping, dropout, data augmentation
Prerequisites
Required (Must Have)
- ✅ Calculus Basics - Partial derivatives, multivariable functions
- ✅ Linear Algebra Introduction - Matrix operations, vector spaces
- ✅ Probability Theory Introduction - Random variables, expected value
- ✅ Intermediate Python - NumPy, basic numerical computing
Technologies Used
- NumPy 1.24+ - Numerical computing
- SciPy 1.10+ - Scientific computing
- PyTorch 2.0+ - Deep learning
- Matplotlib 3.7+ - Visualization
- scikit-learn 1.3+ - Machine learning
Update History
- 2025-10-23: v1.0 Initial release
Disclaimer
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