Professor Chandrajit Bajaj

  • Office hours – Mon, Tue,  Wed. 1:15 p.m. - 2:30 p.m. POB 2.324A
  • Contact: bajaj at cs.utexas.edu

NOTE: Most questions should be submitted to Canvas rather than by sending emails to the instructor. Please attempt to make reservation a day before for the office hour  to avoid conflicts. 


Teaching Assistant

Yi Wang

  • Office hours – Tues, Thur. 3:00 p.m.- 4:30 p.m. POB 2.102
  • Contact: panzer.wy@utexas.edu

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

Lecture Time and Location: M W 9:30 – 10:45 a.m. in GDC 4.302


Course Motivation and Synopsis

 As businesses and academic enterprises gather ever increasing amount of data/ information, new challenges arise for data analysts. There is also a growing demand for reliable software that can parse these big data sets, and make robust inferences from the information it contains. 

This course dwells on the geometric foundations as well as the computational aspects of data sciences, machine learning and statistical inference analysis. The topics spans scalable data analysis and geometric optimization, while  weaving  together discrete and continuous mathematics, computer science and statistics. Students shall delve with breadth-and-depth into dimensionality, sparsity, resolution, resolvability, recovery, prediction, for a variety of   data (sequence, stream, graph-based,  time-series, images, video, hyper-spectral), emanating from multiple sensors (big and small, slow and fast), and accumulated via the interactive WWW.  Issues of measurement errors, noise and outliers shall be central to bounding the precision, bias and accuracy of the data analysis. The geometric insight and characterization gained provides the basis  for  designing and improving existing approximation algorithms for NP - hard problems with better accuracy / speed tradeoffs.

 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 individual (or pair - group ) data science projects with a written/oral presentation, at the end of the semester. This project shall  be graded, and be in lieu of a final.

The course is aimed at senior undergraduate and those in the 5-year master's program students, especially in the CS, CSEM,  and MATH., but others are welcome. You’ll need math at the level of senior undergraduate, plus linear algebra, plus introductory functional analysis,  probability and statistics  (e.g., for  CS and ECE students) or more discrete math (e.g.,for  CSEM students).  

Course Material.

  1. [B1] Chandrajit Bajaj (frequently updated)  A Mathematical Primer for Computational Data Sciences 
  2. [BHK] Avrim Blum, John Hopcroft and Ravindran Kannan. Foundations of Data Science 
  3. [CVX] Stephen Boyd, Lieven Vandenberghe. Convex Optimization .
  4. [GBC] Ian Goodfellow, Yoshua Bengio, Aaron Courville Deep Learning .
  5. [JK] Prateek Jain, Purshottam Kar Non-Convex Optimization for Machine Learning .
  6. [MU] Michael Mitzenmacher, Eli Upfal Probability and Computing (Randomized Algorithms and Probabilistic Analysis)
  7. [SD] Shai Shalev-Shwartz, Shai Ben-David Understanding Machine Learning, From Theory to Algorithms
  8. Extra reference materials .



Date Topic Reading Assignments

1. Introduction to Data Science, Geometry of Data, High Dimensional Spaces,    [notes]

Learning Models, Applications I [notes]

 [BHK] Ch 1

 [B2]  Ch 1

 [A1] out today

due before 09-12-2018, 11:59pm


2. Geometry of Vector, Matrix, Functional Norms  and Approximations [notes] 

Supplementary Notes [notes]

Learning Models, Applications II [notes]

[B2]  Ch 2

 [BHK] Ch 12-Appendix



3. Probability Primer [notes]


[BHK] Ch 12

[B1] Appendix


4. Sampling, High Dimensional Probability and Geometry [notes

Low Discrepancy Sampling [slides]

[B2]  Ch 5

[BHK] Ch 2

[A1] due 

 [A2] out today

due before 09-26-2018, 11:59pm


5. Spectral Decomposition, SVD,  Applications [notes]

[BHK]  Ch 3

See Refs in Notes

09-19-2018 6.  Applications of Low Rank Matrix Approximation [notes]

[BHK]  Ch 3

See Refs in Notes




7. Geometry of Matrix Norms, Optimization, Under- and Over-constrained Linear Systems [notes]

[CVX] Ch 1,2, Appendix

See Refs in Notes



8. Geometry of Convex Optimization, Duality-I [notes] 

[CVX] Ch 3,4

See Refs in Notes

[A2]  due 

[A2] code sample

 [A3] out today

due before 10-10-2018, 11:59pm


9. Geometry of  Optimization, Primal-Dual  [notes]

[CVX] Ch 5

See Refs in Notes



 10. Geometry of Machine Learning, Perceptron, SVM, Kernel SVM [notes] 


[BHK] Ch 5

[B2]  Ch 5

[CVX] Ch 8




11. Geometry of Machine Learning, PCA, Primal-Dual [notes]

Applications [notes]

[BHK] Ch 10,12

[B2]  Ch 5



12. Spectral Methods for Learning: Sparse and Kernel PCA,   [notes]  

[BHK] Ch 12

[B2]  Ch 5

[A3]  due 

 [A4] out today

due before 10-24-2018, 11:59pm



 13. Geometry of  Spectral Methods for Learning: Fischer LDA, KDA, Applications [notes]

See References in notes



 14. Geometry of Spectral Methods for Learning: CCA ,QR, Applications [notes]




15. Matrix Sampling, Matrix Sketching  (PAC) Algorithms, [notes]  

[BHK] Ch 2, Appendix

[B2]  Ch 5



16. Random Projections, Johnson Lindenstrauss 

Compressive Sensing, Sparse Recovery  [notes]

[A4]  due on Oct 28th

[A5] out Oct 28

due before 11-11-2018, 11:59pm


 17.  Convex and Non-Convex Projected Gradient Descent [notes]

[JK]  Ch 3,4

[CVX] Ch 9



18.  Generalized Projected Gradient Descent: convergence criteria [notes]

[B2]  Ch 2

[JK]  Ch 2, 3




19. Sparse Robust Recovery; Alternating Minimization I [notes] 

[JK]  Ch 6

[BHK] Ch 10 



 20. Sparse Robust Recovery; Alternating Minimization II [notes] 

See Refs in Notes

[A5] Due Nov 11,11:59pm



21. Review (Lecture Topics 1-20, Assignments 1 - 5)

Notes, Solutions to Assignments.


21. Mid-Term Exam (in class)


Projects Assigned



22.  Bayes Rule [notes] , Expectation Maximization, Maximum Likelihood [notes]

[BHK] Ch 5,12

[CVX] Ch 6


Final Project 

Due Dec 10, 2018



 Thanksgiving Holiday



23. Alternating Maximization for Expectation Maximization, Gaussian Mixture Models [notes]


[JK]  Ch 5

See Refs in Notes

Additional Notes on Final Project (Background & Datasets) Digital Pathology


24. Geometry of Clustering I:   Kernel, Optimization [notes]

25. Geometry of Clustering II:  Spectral Analysis [notes]

[BHK] Ch 7

See Refs in Notes



26.  CNN,RNN, Geometry of Deep Learning, Applications, Next Steps   [notes]


[BHK] Ch 5

[GBC] Chap 6-9




28. CNN,RNN, Geometry of Deep Learning, Applications, Next Steps   [notes]

[GBC]  Chap 10-12

See also Refs in Notes


Final PROJECT PRESENTATION DAY (Project Doc) POB 2.402, ViZ Lab


Final Project Report Due Due by 9am


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 May 11 midnight. You will get feedback on your presentations,  that should also be incorporated in your final report.


There will be one in-class midterm exam and one final project. The important deadline dates are:

  • Midterm: Monday, October 29, 9:30am - 10:45am
  • Final Project Due: Dec 10, 11:59pm



There will be five written HW assignments and one 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 (10%)
  • HW assignments (45% 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 (20%) 
  • Final Presentation & Report (25%) 



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