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Mathematical Foundation of Data Science and Machine Learning
Course Objective: An introduction to mathematical foundations of machine learning.
Prerequisites include calculus, linear algebra, and probability theory at the undergraduate level.
Instructor: Shuyang LING (sl3635@nyu.edu)
Lecture Time/Location: 1:15PM - 2:30PM on Mondays and Wednesdays.
Discussion/Recitation: 1:15PM - 2:30PM on Fridays. This part will be used to discuss course projects.
Office: Room 1162-3
Textbook: I will provide lecture notes and reading materials throughout out the course. Here are several references we will use:
Grading policy:
Homework 40%
Final project 60%
Course schedule:
The lecture note will be updated after each lecture.
| Date | Topics |
| Feb 07 (M) | Singular value decomposition |
| Feb 09 (W) | Singular value decomposition |
| Feb 14 (M) | Principal component analysis |
| Feb 16 (W) | Random projection |
| Feb 21 (M) | Statistical learning theory |
| Feb 23 (W) | Statistical learning theory |
| Feb 28 (M) | Model selection and regularization |
| Mar 02 (W) | Ridge regression and Lasso |
| Mar 07 (M) | Rademacher complexity |
| Mar 09 (W) | Uniform law of large numbers |
| Mar 14 (M) | VC-dimension and excess risk |
| Mar 16 (W) | Generalization for ridge regression and Lasso |
| Mar 21 (M) | Support vector machine |
| Mar 23 (W) | Support vector machine |
| Mar 28 (M) | Generalization for SVM |
| Mar 30 (W) | Kernel methods: feature, Hilbert space, kernel |
| Apr 04 (M) | Kernel methods: PSD kernel and Mercer theorem |
| Apr 06 (W) | Kernel methods: Bochner's theorem and random features |
| Apr 11 (M) | Reproducing kernel Hilbert space |
| Apr 13 (W) | Representer theorem |
| Apr 18 (M) | Convex function |
| Apr 20 (W) | Gradient descent |
| Apr 24 (U) | Subgradient descent |
| Apr 25 (M) | Stochastic gradient method |
| Apr 27 (W) | Projected gradient method |
| May 04 (W) | Neural network, approximation and generalization |
| May 09 (M) | Interpolation, random feature model, NTK |
| May 11 (W) | Optimization in shallow networks |
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