Professor Chandrajit Bajaj

• Lecture Hours – Mon, Wed - 3:30-5:00 pm, JGB 2.202 
• 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

Shubham Bhardwaj

• Office hours – Thur 3:00 p.m. - 5:00 p.m. ( Zoom or POB 2.102)
• Contact: shubham.bhardwaj@utexas.edu 

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

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

Course Motivation and Synopsis

This Fall course is on the geometric foundations of modern deep and reinforcement learning. In particular we shall dive deep into the mathematical, statistical and computational optimization fundamentals that are the basis of computational, data driven machine learning models (e.g. classification, clustering, generation, recommendation, prediction, forecasting)  and Markov decision making processes (single and multi-player game-playing, sequential and repeated forecasting).   We shall thus learn how data efficient and continuous action spaces are harnessed to learn the free energy Hamiltonian underlying  dynamical systems, and multi-player games. These latter topics 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 (We should remove this)
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
	Module 1: Data, Geometry & Foundations
Mon 08-25-2025	1. Introduction to Data Science, Geometry of Data, High Dimensional Spaces,  Belief Spaces  [Lec1] [colab]	[BHK] Ch 1,2 [PML1] Ch 1 Supplementary Notes  [Note1]
Wed 08-27-2025	2. Learning High-Dimensional Linear Regression Models [Lec2]	[SD] Ch 9, Appendix C [BHK] Chap 12.2,12.3 2.1  Geometry of Vector, Matrix, Functional Norms  and Approximations  [notes]	[A1] with [latex solution template] out today;
Wed 09-03-2025	3. Learning with Non-Determinism, Statistical Bayesian [Lec3]	[MU] Ch 1-3 [B] Chap 1 [PML1] Chap 2, 3, 4 3.1 Probability, Information and Probabilistic Inequalities  [notes]
	Module 2: Core Models of Learning
Mon 09-08-2025	4.Bayesian Regression  [lec]	[PML1] Chap 1 [BHK] Chap 7.1-7.4 4.1 [notes] 4. 2 [SuppNotes]
Wed 09-10-2025	5. Gaussian Processes [lec]	[M] Chap 3, 4 [Notes]
Friday 09-12-2025
	Module 3: Stochastic & Probabilistic Modeling
Mon 09-15-2025	6. Bayesian Classification with different priors [colab notebook][lec]		[A2] Released [A2 template] [A2 pdf]
Wed 09-17-2025	7. Gaussian Process vs BR - hands-on lecture with applications. [lec] [Real-time GP Trading application] [Kernel matrix visualization] [Surrogates textbook]
Mon 09-22-2025	8. Physics-Informed GP Regression [lec] [colab notebook]
	Module 4: Learning Dynamics & Inference
Wed 09-24-2025	9. Gaussian Process Mixtures [lec]
Mon 09-29-2025	10. Introduction to Sparse Gaussian Processes [lec]	[M] Chap 23, 24 [PML2] Chap 11 6.1  [notes]	[A2 Due Sep 28 midnight]
Wed 10-01-2025	7. Probabilistic Distribution Sampling in High Dimensional  Spaces [Lec5] 7.1 Concentration of Measure	[M] Chap 24 [PML2] Chapter 12  7.1 [notes]	[A3] will be out;
Mon 10-06-2025	8. Transforming and Sampling Probability Distributions [lec notes]. 8.1 Normalizing Flow Slides	[BHK] Chap 4 [MU] Chap 7, 10 8.1 [supp notes]
	9. Learning Dynamics I  - Markov Chain Monte Carlo Sampling [Lec7] 9.1 MCMC and Bayesian Inference  9.2 Learning Dynamics II - Random Walk	[SD] Chap 24 [BV] Chap 1-5 9.1 [Notes] 9.2 [notes] MCMC Demo
	10. Optimization for Machine Learning I  10.1 SVM via Stochastic Gradient Optimization  10.2 Spectral Methods for Learning : KSVM	[BHK] Chap 2.7 [SD] Chap 23,24 10  [notes] 10.1 [notes] 10.2 [Supp Notes]
	11. Variations of Gradient Descent in Machine Learning: ADA Grad, RMS Prop, Adam	[M] Chap 11 11. [notes]
	12.  Optimization for Machine Learning II: Constrained Optimization , KKT  12.1 Non-Convex optimization 2: Projected Gradient Descent and Variations	[M] Chap 14 12  [notes] 12.1 [notes]
	Module 5: Mixture Models & Variational Inference
Wed 10-08-2025	13. Statistical Machine Learning I : Mixtures & EM  - Separating Gaussian Mixtures	[M] Chap 2, 5 13 - [notes]
Mon 10-13-2025	14. Statistical Machine Learning I : Mixtures & Variational Inference   14.1 Connections to MCMC and Variational Inference (VAE)	[M]  Chap 4 14  [notes]  14.1 [notes]
	Module 6: Compressive Sensing and Sampling
Wed 10-15-2025	15. Posterior Sampling – Posterior distributions, uncertainty quantification – Gibbs vs. Hamiltonian dynamics
Mon 10-20-2025	16. Importance Sampling – Role in high-dimensional inference – Contrast with MCMC & VI – Why IS is the differentiator
Wed 10-22-2025	17.   Johnson Lindenstrauss and Compressive Sensing  17.1 Compressive Sensing and Optimization  17.2 Robust Sparse Recovery; Alternating Minimization	[M]  Chap 15, [BHK] Chap 5 17 - [notes] 17.1 - [notes] 17.2 - AMRR
	Module 7: Unifying Perspectives
Mon 10-27-2025	18.  Statistical Foundations of Generative  Architecture (VAE, Flows, GANs, Diffusion, Stochastic Interpolants) Models from Data	[M] Chap 15   [PML2] Chapter 20. Go through the introductions of each of the subsequent chapters (21-26).  18 - [Review]
Wed 10-29-2025	Midterm in Class
Mon 11-03-2025	19. Optimal Transport & the Geometry of Learning – Wasserstein distance, probability geometry – Regression under OT loss, classification via barycenters – Clustering in ambient vs. latent space – OT for VI, flows, generative models (WGAN, diffusion)	Supplementary Reading [PML2] 6.8
Wed 11-05-2025	20. The Core Problem of ML is Posterior Inference – Regression, classification, clustering as posterior inference – VI vs. MCMC vs. IS vs. OT – Modern unification: Bayesian Deep Learning & generative models		[A4] will be out;
	Module 8: Data-efficient Online Learning
Mon 11-10-2025	21.    Multi-Armed Bayesian Bandit	[PML2] Chapter 34 [notes]	Project details released. Video and Final Report is due May 3
Wed 11-12-2025	22.   Matrix Sampling and Sketching	[M] Chap 14 [notes]
Mon 11-17-2025	23.  Data Clustering with Hamiltonians	See references cited in notes.  [PML2] 12.5.1 has a primer on Hamiltonian Mechanics.  [notes]
Wed 11-19-2025	24.   Learning (Gradient Descent) Dynamics with Optimal Control	Non-convex Projected Gradient Descent [notes-references]   [PML2] Chapter 35 [notes]
Mon 11-24-2025	25.  Gaussian Process Regression	See references cited in notes [PML1] Section 17.2 [notes]
Wed 11-26-2025	26.  The role of Sensors and Optimal Sensor Fusion: Illustrated Kalman Filters	See references cited in notes [PML2] Chapter 8, primarily 8.1 and 8.2  [notes]	Video and Final Report is due May 3
Mon  12-01-2025	27. Reinforcement Learning:  From Inference to Decision — Control and Reinforcement Learning  “We learned how to model & infer. The next frontier is how to act.”
Addtl. Material	Non-convex Optimization , Projected Gradient Descent [Notes] Statistical Machine Learning II: Bayesian Modeling [notes] Statistical Machine Learning III: Bayesian Inference,  Multivariate Gaussians [notes1] [notes] Spectral Methods in Dimension Reduction -KPCA [notes] Spectral Methods for Learning : Fischer LDA, KDA [notes]
Addtl. Material	Connections to Variational AutoEncoders [notes] Statistical Machine Learning IV: Gaussian Processes  [notes]  Stochastic Gradient Descent-- Simulated Annealing, Fockker-Planck [notes] Other Gradient Descent Methods [Adagrad, RMSProp, Adam, ...] [notes] Statistical Machine Learning V: Non-Gaussian Processes, Conjugate Priors [notes] Principled Reinforcement Learning with Hamiltonian-Dynamics-PMP-OCF  [notes].  Reward Reshaping with Optimal Control [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 26th, 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.

 

Extra Credit: All extra credit points accumulated from assignments will be used for later point deductions in future assignments. 

Course Requirements and Grading

Grades will be based on these factors:

• In-class 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