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	Lecture 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	Lecture 02: Eigenvalues, Spectral Decomposition, and SVD [Lec2]	[SD] Ch 9, Appendix C [BHK] Chap 12.2,12.3	[A1] with [latex solution template] out today;
Wed 09-03-2025	Lecture 03: Probabilistic Linear Models [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	Lecture 4.Bayesian Regression in Practice [lec]	[PML1] Chap 1 [BHK] Chap 7.1-7.4
Wed 09-10-2025	Lecture 5a. Gaussian Processes [lec]	[M] Chap 3, 4
Friday 09-12-2025	Lecture 5b. Gaussian Processes Continued [lec]	[M] Chap 3, 4
	Module 3: Stochastic & Probabilistic Modeling
Mon 09-15-2025	Lecture 6. Bayesian Classification with different priors [colab notebook][lec]	For extra reading see references cited in the lecture	[A2] Released [A2 template] [A2 pdf]
Wed 09-17-2025	Lecture 07: Gaussian Process vs BR - hands-on lecture with applications. [lec] [Real-time GP Trading application] [Kernel matrix visualization] [Surrogates textbook]	For extra reading see references cited in the lecture
Mon 09-22-2025	Lecture 08: Physics-Informed GP Regression [lec] [colab notebook]
	Module 4: Learning Dynamics & Inference
Wed 09-24-2025	Lecture 9. Gaussian Process Mixtures [lec]	For extra reading see references cited in the lecture
Mon 09-29-2025	10. Introduction to Sparse Gaussian Processes  - Subset of Regressors Approximation (SoR) [lec]	[M] Chap 23, 24 [PML2] Chap 11 6.1  [notes]	[A2 Due Sep 28 midnight]
Wed 10-01-2025	10 (contd).  Introduction to Sparse Gaussian Processes  - Subset of Regressors Approximation (SoR) [lec]	[M] Chap 24 [PML2] Chapter 12  7.1 [notes]
Mon 10-06-2025	Lecture 11: Advanced Sparse GPs - From Overconfidence to Optimality - SoR < FITC < VFE [lec]	[BHK] Chap 4 [MU] Chap 7, 10 8.1 [supp notes]
Tue 10-07-2025	Assignment 3 - released		[A3 latex] [A3 pdf]
	Module 5: Mixture Models & Variational Inference
Wed 10-08-2025	Lecture 12: Sparse GPs are attention [lec]	For extra reading see references cited in the lecture
Mon 10-13-2025	Lecture 13: Transformers as Meta-Bayesian Learners [lec]	For extra reading see references cited in the lecture	[A1 solutions] [A2 solutions]
	Module 6: Compressive Sensing and Sampling
Wed 10-15-2025	Lecture 14: The Bayesian Loop - From Point Estimates to Automated Inference — A Unified Journey [lec]	For extra reading see references cited in the lecture
Mon 10-20-2025	Lecture 15: Distilling Symbolic Priors into Neural Networks Meta-Learning as the Bridge from Implicit to Explicit Structure [lec]	For extra reading see references cited in the lecture
10-24-2025	Mock Midterm [pdf]	[A3 solutions]
10-26-2025	Mock midterm solutions [pdf]
	Module 7: Unifying Perspectives
Mon 10-27-2025	Lecture 16: Low discrepancy (Importance Sampling) with applications [lec]	For extra reading see references cited in the lecture
Wed 10-29-2025	Midterm in Class
Mon 11-03-2025	Lect 17 - Physics-Informed Computer Vision - Markov Chain Monte Carlo [lec]	For extra reading see references cited in the lecture
Wed 11-05-2025	Lect 18 - Physics-Informed Computer Vision - Variational Inference & Deep Learning [lec]	For extra reading see references cited in the lecture	Project template [pdf][latex]
	Module 8: Online Learning, Reinforcement Learning, Game Theory
Mon 11-10-2025		For extra reading see references cited in the lecture
Wed 11-12-2025	Presentations:  1. Brian Jiang - ScatterNeRF: Seeing Through Fog with Physically-Based Inverse Neural Rendering 2. Ben Bouttavong - Tensor Logic: Toward Differentiable Reasoning	[M] Chap 14 [notes]
Mon 11-17-2025	Presentations:  1. Aaroh Gokhale: Physics-informed neural networks via stochastic Hamiltonian dynamics learning 2. Hailey Chau: Motion Simulator Pushing the Limit of World Models in Reinforcement Learning		Final Project Assignment Details [here]
Wed 11-19-2025	Presentations:  1. Dhanush Jain: Physical Inertial Poser (PIP) Physics-aware Real- time Human Motion Tracking from Sparse Inertial Sensors  2. Isabella: TimesNet: Temporal 2DVariation Modeling for General Time Series Analysis
Mon 11-24-2025	The following are not assigned (need to email me)	Akul Saxena Sebastian Tenorio Jay Chakraborti Heilal Mordahl Arya Majumdar	Final Project Phase I is due Nov 24
Wed 11-26-2025
Mon  12-01-2025	Presentations:  1. Ian Chen - DNBP - Differentiable Nonparametric Belief Propagation
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]		Final Project Phase II is due  Dec 12.
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 29th, 3:30pm - 5:00pm, In Class
  
• Final Project Presentation, Part 1,  November in class
• Final Project Written Report, Part 2, Due: Dec  7, 11:59pm

 

Assignments

There will be four written take-home HW assignments, an in-class presentation, and one take-home final project report. Please refer to the above schedule for assignments, in-class presentation  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