Instructor: Professor Haiyan Wang
Section: 96893 (Fall 2022)
1.2. Elements of Linear Algebra
- Orthogonality
- Gram-Schmidt Process
- Eigenvalues and Eigenvectors
1.3. Linear Regression
- QR Decomposition
- Least Squares
- Linear Regression
- Gradient Descent
1.4. Principal Component Analysis
- Singular Value Decomposition
- Low-Rank Matrix Approximations
- Principal Component Analysis
- Image Compression
2.2. Probability Distribution
- Probability Axioms
- Conditional Probability
- Discrete Random Variables
- Continuous Random Variables
2.3. Independent Variables and Random Samples
- Joint Probability Distributions
- Random Samples
- Correlation and Covariance
- Central Limit Theorem
2.4. Maximum Likelihood Estimation
- MLE for Random Samples
- Linear Regression
3.2. Continuity and Differentiation
- Limits and Continuity
- Derivatives
- Partial Derivatives
- Jacobian
- Chain Rule
- Directional Derivatives
- Gradient
- Hessian
- Mean Value Theorem
- Taylor's Theorem
3.3 Unconstrained Optimization
- Local and Global Minimizers
- Convexity
- Gradient Descent
3.4 Logistic Regression
- Logit Function
- Sigmoid Function
- Cross-Entropy Loss
- Gradient Descent
3.5 K-Means
- Within-Cluster Sum of Squares (WCSS)
- K-Means Algorithm
3.6 Support Vector Machines
- Hyperplane
- Margin
- Support Vectors
- Loss Function
3.7 Neural Networks
- Mathematical Model
- Activation Functions
- Cost Functions
- Backpropagation
4.1 Introduction
- Graph Models
- Laplacian Matrix
4.2 Spectral Graph Bipartitioning
- Graph Partitioning
- Raleigh Quotient
- Balancing the Cut