Professor Chandrajit Bajaj

• Lecture Hours – Mon, Wed - 3:30-4:45 pm, GDC 4.302 
• Office hours – Tuesday - 1:00-3:00 p.m. or by appointment ( Zoom  or POB 2.324)
• Contact: bajaj@cs.utexas.edu, bajaj@oden.utexas.edu 

NOTE: Please do not send messages (questions or concerns) through Canvas because I rarely don’t check email messages on Canvas. All questions related to class should be posted through Piazza or bring them to the office hour. Here is the link to register for Piazza: You can also join via the Piazza Tab on the Canvas course page

Teaching Assistant

Eshan Balachandar

• Office hours – Thursday 11:00 AM - 12:00 PM Zoom, GDC Basement,  TA Desk 3, 
• Contact: eshan@cs.utexas.edu

Note: Please attempt to make reservations a day before for office hours to avoid conflicts. 

Course Motivation and Synopsis

This course is on the geometric foundations of data sciences and classical, deep and modern machine learning. In particular we shall dive deep into the mathematical, statistical and computational optimization fundamentals that are the basis of computational deep learning frameworks (e.g. classification, clustering, recommendation, prediction, generation)  and Markov decision making processes (single and multi-player game-playing, sequential and repeated forecasting).   We shall thus learn how data driven and continual learning is harnessed to learn the Hamiltonian's (governing energetic equations) underlying  dynamical systems, and multi-player games. These latter topics are foundational AI as they lead to the training of multiple neural networks (agents) learning  cooperatively and in adversarial scenarios to help solve any computational problem better.

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, cross-validate and test 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 junior and senior undergraduates  students. Those in the 5-year master's program students, especially in the CS, CSEM, ECE, STAT and MATH. are welcome if they would like to bolster their foundational knowledge. 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). 

Late Policy

For submission 1 day later from deadline  - 25% deduction. For 2 days later - 50% deduction. We will be revealing assignment on the 3rd day. Therefore 100% deduction on 3rd day.

Course Material.

1. [B1] Chandrajit Bajaj (frequently updated)  A Mathematical Primer for Computational Data Sciences  
2. [PML1] Kevin Murphy Probabilistic Machine Learning: An Introduction
3. [PML2] Kevin Murphy Probabilistic Machine Learning: Advanced Topics
4. [BHK] Avrim Blum, John Hopcroft and Ravindran Kannan. Foundations of Data Science
5. [BV] Stephen Boyd and Lieven Vandenberghe Convex Optimization
6. [B] Christopher Bishop Pattern Recognition and Machine Learning
7. [M] Kevin Murphy Machine Learning: A Probabilistic Perspective
8. [SB] Richard Sutton, Andrew Barto Reinforcement Learning
9. [SD] Shai Shalev-Shwartz, Shai Ben-David Understanding Machine Learning, From Theory to Algorithms
10. Extra reference materials .

COURSE OUTLINE 

Date	Topic	Reading	Assignments
Mon 01-13-2025	1. Introduction to Data Science, Geometry of Data, High Dimensional Spaces,  Belief Spaces  [Lec1]	[BHK] Ch 1,2 [PML1] Ch 1 Supplementary Notes  [Note1]
Wed 01-15-2025	2. Learning High-Dimensional Linear Regression Models [Lec2]   Geometry of Vector, Matrix, Functional Norms  and Approximations (Introductory functional analysis) [notes];	[SD] Ch 9, Appendix C [BHK] Chap 12.2,12.3	[A1] with [latex solution template] out today;
Fri 01-17-2025	3. Learning Theory and Model Selection [Lec3] Probability, Information and Probabilistic Inequalities [notes]	[MU] Ch 1-3 [B] Chap 1 [PML1] Chap 2, 3, 4
Mon 01-27-2025	4. Stochastic Machine Learning |:  Cross, Conditional and Relative Entropy,  [Lec 4] Log-Sum-Exponential-Stability [notes]	[MU] Chap 4, 24.2 [BHK] Chap 12.4,12.6
Wed 01-29-2025	5. Probabilistic Distribution Sampling in High Dimensional  Spaces [Lec5] Concentration of Measure  [notes]	[M] Chap 23	[A2] will be out;
Mon 02-03-2025	6. Statistical Machine Learning using MonteCarlo and Quasi-MonteCarlo[Lec6]	[M] Chap 24
Wed 02-05-2025	7. Quasi-Monte-Carlo Methods, Integration Error H-K Inequality  [notes]	[M] Chap 24
Mon 02-10-2025	8.  Learning Dynamics I  - Markov Chain Monte Carlo Sampling [Lec7] MCMC and Bayesian Inference [Notes]	[BHK] Chap 4 [MU] Chap 7, 10
Wed 02-12-2025	9. Learning Dynamics II - Random Walk  [notes]	[SD] Chap 24 [BV] Chap 1-5
Mon 02-17-2025	10. Convex Optimization for Machine Learning [notes]	[BHK] Chap 2.7 [SD] Chap 23,24
Wed 02-19-2025	11.  SVM via Stochastic Optimization [notes]	[M] Chap 11	[A3] will be out;
Mon 02-24-2025	12. Spectral Methods in Dimension Reduction -KPCA [notes Spectral Methods for Learning : KSVM [Notes], Fischer LDA, KDA [notes]	[M} Chap 14
Wed 02-26-2025	13. Statistical Machine Learning I : Separating Mixture of Gaussians  - Expectation Maximization   [notes]	[M] Chap 2, 5
Mon 03-03-2025	14.  Statistical Machine Learning II: Bayesian Modeling [notes]	[M]  Chap 4
Wed 03-05-2025	15: Statistical Machine Learning III: Bayesian Inference,  Multivariate Gaussians [notes1] [notes]	[M]  Chap 15, [BHK] Chap 5
Mon 03-10-2025	16.  Statistical Machine Learning IV: Gaussian Processes  [notes]	[M] Chap 15
Wed 03-12-2025	MIDTERM in Class
Mon 03-24-2025	17. Statistical Machine Learning V: Non-Gaussian Processes, Conjugate Priors [notes]	[M] Chap 14	[A4} will be out;
Wed 03-26-2025	18.  Learning Dynamics,  Lyapunov Stability  and connections to Training Deep Networks [notes]	See references cited in [notes]
Mon 03-31-2025	19. Stochastic Gradient Descent-- Simulated Annealing, Fockker-Planck [notes]	See references cited in [notes]
Wed 04-02-2025	20.   Other Gradient Descent Methods [Adagrad, RMSProp, Adam, ...] [notes]	Non-convex Projected Gradient Descent [notes-references]
Mon 04-07-2025	21. Learning Stochastic Dynamics and Optimal Control:  Dynamics with Stability, LQR [notes] [another notes]	See references cited in notes	Project details will be out;
Wed 04-09-2025	22. The role of Sensors and Optimal Sensor Fusion: Basics of Kalman Filters [notes] Illustrated Kalman Filters [notes]	See references cited in notes
Mon 04-14-2025	23. Reinforcement Learning I:  Optimal Control, Hamilton-Jacobi-Bellman Optimality Principle [notes]	See references cited in notes
Wed 04-16-2025	24. Reinforcement Learning II:  Learning with Trajectory (Stochastic) Optimization:  iLQR, ilQG [notes]	See references cited in [notes]
Mon 04-21-2025	25.  Reinforcement Learning III:  MDP, POMDP, Optimal Control  [notes]	[SB]  See Chap 3
Wed 04-23-2025	26.Reward Reshaping with Optimal Control [notes]
Mon 04-28-2025	27.   Principled Reinforcement Learning with Hamiltonian-Dynamics-PMP-OCF  [notes].
Addtl. Material	Non-convex Optimization , Projected Gradient Descent [Notes]
Addtl. Material	Robust Sparse Recovery; Alternating Minimization  [notes2] Connections to Variational AutoEncoders [notes]
Addtl. Material	Geometry of Game Theoretic Learning I :  Actionable Learning [[notes] Nash Equilibrium  [notes] Geometry of Game Theoretic Learning II: Stackelberg Equilibrium [notes]  Games & MARL  II [notes]

 

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. You will get feedback on your presentations,  that should also be incorporated in your final report.

Assignments, Exam, Final Project

There will be four 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: March 12th, 3:30pm - 5:00pm, In Class
  
• Final Project Written Report, Part 1, Due: April 20th, 11:59pm
• Final Project Written Report, Part 2, Due: May 1st, 11:59pm

 

Assignments

There will be four 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.

Course Requirements and Grading

Grades will be based on these factors:

• In-class attendance and participation (5%)
• HW assignments (50% and with potential to get extra credit) 

4 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 Report (10%)
• Final Presentation Video & Report (20%)  

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/