Course Syllabus
Instructor:
Professor Chandrajit Bajaj
- Lecture Hours -- Mon, Wed- 3:30 - 5:00 pm. GDC 6.202 or Zoom
- Office hours – Mon, Wed 5:00 p.m. - 6:00 p.m. or by appointment ( Zoom or POB 2.324)
- Contact: bajaj@oden.utexas.edu
NOTE: . All questions related to class should be posted through Piazza. Here is the link to register for Piazza: You can also join via the Piazza Tab on the canvas course page
Teaching Assistant
Trung Nguyen
- Office hours – Mon/Wed 2:00 p.m. - 3:00 p.m. GDC 1.302 - TA station Desk 2 or Zoom
- Contact: trungnguyen@utexas.edu
Note: Please attempt to make reservations a day before for office hours to avoid conflicts.
Course Motivation and Synopsis
This fall course is on foundational mathematical, statistical and computational learning theory and application of data learned predictive models. Students shall be exposed to modern machine learning approaches in optimized decision making and multi-player games, involving stochastic dynamical systems, and optimal control. These latter topics are foundational to the training of multiple neural networks (agents) both cooperatively and in adversarial scenarios helping optimize the learning of all the agents.
An initial listing of lecture topics is given in the syllabus below. This is subject to modification, given the background and speed at which we cover ground. Homework exercises shall be given almost bi-weekly. Assignment solutions that are turned in late shall suffer a 10% per day reduction in credit, and a 100% reduction once solutions are posted. There will be a mid-term exam in class. The content will be similar to the homework exercises. A list of topics will also be assigned as take home final projects, to train the best of machine learned decision making (agents). The projects will involve ML programming, oral presentation, and a written report submitted at the end of the semester.
This project shall be graded, and be in lieu of a final exam.
The course is aimed at senior undergraduates and junior graduate students. Those in the 5-year master's program students, especially in the CS, CSEM, ECE, STAT and MATH. are welcome. You’ll need algorithms, data structures, numerical methods and programming experience (e.g. Python ) as a CS senior, mathematics and statistics at the level of CS, Math, Stat, ECE, plus linear algebra, computational geometry, plus introductory functional analysis and combinatorial and numerical optimization (CS, ECE, CSEM , Stat and Math. students).
Course Material.
- [B1] Chandrajit Bajaj (frequently updated) A Mathematical Primer for Computational Data Sciences
- [BHK] Avrim Blum, John Hopcroft and Ravindran Kannan. Foundations of Data Science
- [BV] Stephen Boyd and Lieven Vandenberghe Convex Optimization
- [M] Kevin Murphy Machine Learning: A Probabilistic Perspective
- [MU] Michael Mitzenmacher, Eli Upfal Probability and Computing (Randomized Algorithms and Probabilistic Analysis)
- [SD] Shai Shalev-Shwartz, Shai Ben-David Understanding Machine Learning, From Theory to Algorithms
- [SB] Richard Sutton, Andrew Barto Reinforcement Learning
- [Basar] Tamer Basar Lecture Notes on Non-Cooperative Game Theory.
- Extra reference materials .
TENTATIVE COURSE OUTLINE (in Flux).
Date | Topic | Reading | Assignments |
Mon 08-22-2022 |
1. Introduction to Geometry of Data, High Dimensional Spaces, Belief and Decision Making Spaces, [Lec1] Dynamical Systems and Deep Learning [notes] Modern Statistical Machine Learning [notes] |
[M] Ch 1.1, 1.2, 1.3
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Wed 08-24-2022 |
2. Learning High-Dimensional Regression and Dynamic Models [Lec2] Geometry of Norms and Approximations [notes]; |
[SD] Ch 9, Ch 14 [BHK] Chap 12.2,12.3 |
[A1] with [latex template] out today due by 09-07-2022, 11:59pm |
Mon 08-29-2022 |
3. Learning Theory and Model Selection [Lec3] PAC learning, Complexities [notes] Probability, Information and Probabilistic Inequalities [notes]
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[M] Ch 1.4.7, 1.4.8 [MU] Ch 1-3 |
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Wed 08-31-2022 |
4. Sampling in High Dimensional Space-Time 1 : MonteCarlo vs Quasi Monte-Carlo, Relationship to Integration Error H-K Inequality [Lec4-part1][Lec4-part2] High-Dimensional Sampling, Concentration of Measure [[notes] |
[MU] Chap 4, 24.2 [BHK] Chap 12.4,12.6 |
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Wed 09-07-2022 |
5. Sampling in High Dimensional Space-Time 2: [Lec-part1] Intro to Optimal Control of Dynamic System [notes] Learning Dynamics, Lyapunov Stability and connections to Training Deep Networks [notes] |
[SD] Chap 12 |
[A1] due by tomorrow midnight . |
Mon 09-12-2022 |
6. Statistical Machine Learning 1: Introduction to Markov Chains, Page Rank, MCMC [Lec-notes, notes2] Learning by Random Walks on Graphs [notes-BHK]
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Wed 09-14-2022 |
7. Statistical Machine Learning 2: Sampling and Learning with MCMC Variations [Lec7] (More MCMC & Implementation Notes) Bayesian Inference with MCMC and Variational Inference [notes] |
[BHK] Chap 4 [MU] Ch 7, 10
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[A1 solution] out so you can train / learn from this. [A2] out due by 09-28-2022, 11:59pm |
Mon 09-19-2022 |
8. Statistical Machine Learning 3: Bayesian Inference and Generative Models (VAEs and GANs) [notes1] |
[SD] Chap 24 [BV] Chap 1-5 |
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Wed 09-21-2022 |
9. Statistical Machine Learning 4: Transform Sampling, Sampling Non-Linear Probability Distributions [notes]. Generative Adversarial Networks [notes] |
[BHK] Chap 2.7 [SD] Chap 23,24 |
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Mon 09-26-2022 |
10. Statistical Machine Learning 5: Gaussian Processes I [notes] [notes2] Learning with Normalizing Flows [notes] |
[M] Chap 11 |
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Wed 09-28-2022 |
11. Statistical Machine Learning 6: Gaussian Processes II [notes] |
[M] Ch 2, 5 |
[A2] due today by 11:59pm. |
Mon 10-03-2022 |
12. Robust Sample based Bayesian Dynamic Learning using Sparse Gaussian Processes [notes] Connections to Variational AutoEncoders (VAEs) [notes] |
[M] Ch 4 |
[A2 solution] out [A3] out tomorrow due by 10-19-2022, 11:59pm |
Wed 10-05-2022 |
13. Learning Models with Latent Variables / Expectation Maximization [notes] MCE-VAE-Invariance based Equivariant Clustering [paper]
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[M] Ch 15 |
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Mon 10-10-2022 |
14: Learning SVM via Continuous Stochastic Gradient Descent Optimization [notes] Continuous Stochastic Gradient Descent (SGD) -- Simulated Annealing, Fockker-Planck [notes] |
[M] Ch 15 |
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Wed 10-12-2022 |
15. Learning with SGD variations, Adagrad, RMSProp, Adam, ...] [notes] |
[BHK] Chap 5 |
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Mon 10-17-2022 |
16. Learning Dynamics with Neural ODEs (NODEs) : Adjoint Method for BackProp [notes] |
[M] Chap 14 |
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Wed 10-19-2022 |
17. Learning Dynamics with Stochastic Processes [notes] Learning Dynamics with Stochastic Neural ODEs (SNODEs) : Stochastic Adjoint Methods I [notes]
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[A3] due Fri 10/21 by 5:00pm [A3] Solution shall post Fri night |
Mon 10-24-2022 |
[MIDTERM] (Hybrid) |
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Wed 10-26-2022 |
18. Robust Continuous learning of PDE's using Sparse Gaussian Processes [arxiv] Diffusion Models with Stochastic Langevin Dynamics [notes]
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Mon 10-31-2022 |
19 RL1: Learning Dynamics : Kalman Filtering, Machine Learning [notes]
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Non-convex Projected Gradient Descent [notes-references] |
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Wed 11-02-2022 |
20. RL2: Learning Dynamics with Optimal Control: Dynamics LQR, iLQR [notes] |
See references cited in notes
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Final PROJECT topics posted [here] Part 1: First PROJECT Report due before Nov 21-2022, 11:59pm
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Mon 11-07-2022 |
21. RL 3: Bandit Algorithms , Thompson Sampling[notes] |
See references cited in notes |
[A4] Out Nov 7 Due By Nov 20, 11:59pm |
Wed 11-09-2022 |
22. RL 4: Markov (Reward, Decision) Processes: MPs, MRPs, MDPs and POMDPs [notes] |
See references cited in notes and paper |
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Mon 11-14-2022 |
23. Game Theoretic Learning 1: MARL -Markov Games [notes]. Markov Decision Process (MDPs) and Markov Games -- [notes] |
See references cited in [notes] | |
Wed 11-16-2022 |
24. Games & MARL II [notes] Game Theoretic Learning 2: Stackelberg Equilibrium [notes] |
See references cited in [notes] |
Part 1 of Project Due before Nov 21, 11:59pm |
Mon 11-28-2022 |
25. Energy Based Learning: Hopfield Networks, Boltzmann Machines, Restricted Boltzmann Machines. [notes] Actionable Learning [notes]
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[SB] See Chap 3 Due by 11:59pm Dec 5.
A5 Solution Template
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A5 (Optional Extra Credit) Released on Nov 28 and Due by 11:59pm Dec 5, 2022 |
Wed 11-30-2022 |
26. Active Learning 2 : Dynamic POMDPS , Longitudnal VAEs [notes] |
[SB] See Chap 9, 10, 11 |
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Mon 12-05-2022 |
27. NeuralPMP: Reinforcement Learning with Stochastic Hamiltonian Dynamics , Pontryagin Maximum Principle [arxiv] |
[Basar] See Lectures 1, 2, 3 |
Final Project Report (Part II) Due December 9 11:59pm |
Addtl. Material |
Robust Sparse Recovery; Alternating Minimization [notes2] Non-convex Optimization : Projected Stochastic Policy Gradient [Notes] [Notes] [Notes] Random Projections, Johnson-Lindenstrauss, Compressive Sensing, Sketching in Space-Time[notes] Spectral Methods for Learning Dimension Reduction -KPCA , Eigen- Fischer-Faces[notes] [notes] E. KSVM [Notes], Fischer LDA, KDA [notes] Statistical Machine Learning : (a) Separating Mixture of Gaussians [notes] (b) Expectation Maximization [notes] |
Some important Classical Machine Learning Background. | |
Addtl. Material |
Robustness Guarantees for Bayesian Inference and Gaussian Processes [paper] Risk Averse No Regret Learning for Convex Games [paper] |
Some Theoretical Bounds on Bayesian Optimization and Reinforcement Learning.
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Project FAQ
1. How long should the project report be?
Answer: See directions in the Class Project List. For full points, please address each of the evaluation questions as succinctly as possible. Note the deadline for the report is December 07 midnight. You will get feedback on your presentations, that should also be incorporated in your final report.
Assignments, Exam, Final Project
There will be five take-home bi-weekly assignments, one in-class midterm exam and one take home final project (in lieu of a final exam). The important deadline dates are:
- Midterm: Wednesday, October 10, 3:30pm - 5:00pm, BUR 2.220
- Final Project Written Report, Due: December 07, 11:59pm
Assignments
There will be five written take-home HW assignments and one take-home final project report. Please refer to the above schedule for assignments and final project report due time.
Assignment solutions that are turned in late shall suffer a 10% per day reduction in credit, and a 100% reduction once solutions are posted.
Course Requirements and Grading
Grades will be based on these factors:
- In-class attendance and participation (5%)
- HW assignments (60% and with potential to get extra credit)
5 assignments. Some assignments may have extra questions for extra points you can earn. (They will be specified in the assignment sheet each time.)
- In-class midterm exam (15%)
- First Presentation & Report (10%)
- Final Presentation & Report (15%)
Students with Disabilities. Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities, 471-6259, http://www.utexas.edu/diversity/ddce/ssd
Accommodations for Religious Holidays. By UT Austin policy, you must notify the instructor of your pending absence at least fourteen days prior to the date of observance of a religious holiday. If you must miss a class or an examination in order to observe a religious holiday, you will be given an opportunity to complete the missed work within a reasonable time before or after the absence, provided proper notification is given.
Statement on Scholastic Dishonesty. Anyone who violates the rules for the HW assignments or who cheats in in-class tests or the final exam is in danger of receiving an F for the course. Additional penalties may be levied by the Computer Science department, CSEM and the University. See http://www.cs.utexas.edu/academics/conduct/
Course Summary:
Date | Details | Due |
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