Course Syllabus
Instructor:
Professor Chandrajit Bajaj
- Lecture Hours -- Mon, Wed- 9:30 -11:00 am; PAR 101
- Office hours – Tue, Thu 2:00 p.m. - 3:00 p.m. POB 2.324A or by appointment
- Contact: bajaj@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
Bo Sun
- Office hours – Fri. 3pm-4pm, TA Station 3
- Contact: bosun@cs.utexas.edu
Note: Please attempt to make reservations a day before for the office hours to avoid conflicts.
Course Motivation and Synopsis
This course is on fundamental algorithmic, computational aspects of data sciences, machine (deep) 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 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 mathematics and statistics at the level of first year graduate, plus linear algebra, geometry, plus introductory functional analysis and numeric optimization (e.g., for CS and ECE students) and combinatorial optimization (e.g.,for CSEM 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
- [CVX] Stephen Boyd, Lieven Vandenberghe. Convex Optimization .
- [ZLLS] Aston Zhang, Zachary C. Lipton, Mu Li, and Alexander J. Smola Dive into Deep Learning, v0.7.1
- [JK] Prateek Jain, Purshottam Kar Non-Convex Optimization for Machine Learning .
- [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
- [GBC] Ian Goodfellow, Yoshua Bengio, Aaron Courville Deep Learning, 2016
- [HF] Hermann Flaschka Principles of Analysis
- [KW19] Diederik P. Kingsma and Max Welling An Introduction to Variational Auto Encoders
- Extra reference materials .
TENTATIVE COURSE OUTLINE (in Flux).
Date | Topic | Reading | Assignments |
Wed 01-22-2020 |
1. Introduction to Data Science, Geometry of Data, High Dimensional Spaces [notes] Perceptrons and Deep Learning, Models, Applications [notes] [DL-models] |
[BHK] Ch 1, 12-Appendix [B1] Ch 1,2 [CVX] [MRT] Appendix [ZLLS] Introduction |
|
Mon 01-27-2020 |
2. Learning LInear Regression Models, Applications [notes] Geometry of Vector, Matrix, Functional Norms and Approximations [notes] |
[HF] Sec 1,2,3 [BHK] Ch 12-Appendix [ZLLS] Preliminaries Chap 2, LNN Chap 3 |
[A1] out today due before 02-12-2020, 11:59pm |
Wed 01-29-2020 |
3. Probability Theory, Noisy Regression, Bayes Thm , Maximum Likelihood[notes] Softmax and Cross Entropy Loss Functions. Linear Neural Networks [notes] |
[MU] Ch 1 -4 [B1] Appendix [ZLLS] LNN Chap 3 |
|
Mon 02-03-2020 |
4. Markov, Chebyshev, Chernoff Bounds [notes] Naive Bayes Classifier [ZLLS Appendix ] |
[MRT] Chap 1, 2 [MU] . Chap 1 |
|
Wed 02-05-2020 |
5. Multi-Layer (non-linear) Perceptron Learning [ZLLS Chap4] Convex and Non-Convex Optimization [notes] |
CVX [Chap1-5] |
|
Mon 02-10-2020 |
6. MonteCarlo Sampling [notes] Low Discrepancy Quasi-Monte Carlo Sampling, [slides], Integration Error H-K Inequality [notes] |
See Refs in Notes in Slides |
|
Wed 02-12-2020 |
7. Sampling Multivariate Gaussians in High Dimensions, Separating Mixture of Gaussians I [notes] |
[BHK Chap 2, Appendix] See References in Notes |
|
Mon 02-17-2020 |
8. Statistical Machine Learning I : Separating Mixture of Gaussians II, Expectation Maximization [notes] |
[BHK Chap2,3] See Refs in Notes |
|
Wed 02-19-2020 |
9. Random Projections and Johnson-Lindenstrauss [notes] Expectation Maximization II (Latent Variable Models, Soft Clustering, Mixed Regression) [notes] |
[BHK Chap 3] [CVX] Chap 1, 2, 3 See Refs in Notes |
|
Mon 02-24-2020 |
10. Low Rank Matrix Approximation with Applications [notes] Convex and Non-Convex Optimization [notes] |
[B2] Ch 5 [CVX] Ch 5, Ch 8 |
|
Wed 02-26-2020 |
11. Matrix Sampling, Matrix Sketching Algorithms, [notes] |
[B2] Ch 5 |
[A3] out today |
Mon 03-02-2020 |
12. Deep Autoencoders I : Learning Latent Variable Space [notes] Modern Convolutional Neural Networks I [notes] |
[ZLLS Chap 6]
|
|
Wed 03-04-2020 |
13. Variational Inference: Deep Variational Autoencoders II [notes] |
See References in notes |
|
Mon 03-09-2020 |
14: Spectral Methods for Learning: PCA, Kernel PCA, [notes] Multi-Hidden Layer Perceptron Networks [notes] |
See References in notes |
|
Wed 03-11-2020 |
MIDTERM in Class |
|
due before 03-30-2020, 11:59pm |
Mon-Fri 03-16-2020- 03-29-2020
|
Spring Break- March 16-29, 2020 |
|
|
Mon 03-30-2020 |
15.Convex and Non-Convex Optimization [notes] Lagrange Multipliers, Lagrangian Dual [notes]
|
[CVX] [ZLLS] |
|
Wed 04-01-2020 |
16. Spectral Methods for Learning : Fischer LDA, KDA [notes] Connectiions to Variational AutoEncoders [notes] |
See References in Notes |
|
Mon 04-06-2020 |
17. Non-Convex Optimization - Convex Relaxations [notes] Compressive Sensing and Tensor Sketching [notes]
|
|
Part 1: First Report due before 04-20-2020, 9:59pm
|
Wed 04-08-2020 |
18.Robust Sparse Recovery; Alternating Minimization [notes2] |
[JK] Ch 3,4 |
|
Mon 04-13-2020 |
19. Energy Based Optimization Loss Functions [notes] VC-Dimension and PAC learning revisited [notes]
|
|
|
Wed 04-15-2020 |
20. Energy Based Optimization Loss Functions II [notes] Stochastic Gradient Descent-- Simulated Annealing, Fockker-Planck [notes]
|
||
Mon 04-20-2020 |
21. Modern Convolutional Neural Networks II : Back Propagation [notes] Modern CNN - Residual Networks : Adjoint Method [notes]
Connections to Deep Encoder-Decoder Networks [notes] |
[CVX] Ch 7 |
Part 1 of Project Due Final Project Report Due May 09, 2020 |
Wed 04-22-2020 |
22. Stochastic Optimization [notes] Supervised. 'Soft ' Classification: SVM,KSVM [notes] Geometry of Unsupervised Soft Clustering I: Spectral and Normalized Cut [notes] |
[JK] Ch 5 |
|
Mon 04-27-2020 |
23. Geometry of Unsupervised Clustering II: Variational Inference [notes] Connections to Deep Variational Auto-Encoders |
[JK] Ch 5 | |
Wed 04-29-2020 |
24. Geometry of Deep Learning : Recurrent Neural Networks, Transformers, Attention [notes] |
|
|
Mon 05-04-2020 |
25. Geometry of Deep Learning: Generative Adversarial Networks [notes] |
[BHK] Ch 5 See Refs in Notes |
|
Wed 05-06-2020 |
26. Geometry of Deep Learning : Reinforcement Learning RL 1 [notes] |
[BHK] Ch 5 [GBC] Chap 6,9 |
|
|
27. Geometry of Deep Learning RL & Value Iterations II [notes] |
[GBC] Chap 7-8 See also Ref |
|
|
28. Geometry of Deep Learning IV: RL & Policy Gradients III [notes] | [GBC] Chap 10-12 | |
FRI 05-08-2020 |
Presentations TBD |
|
Final Project Report Due on May 15 |
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.
Tests
There will be one in-class midterm exam and one final project. The important deadline dates are:
- Midterm: Wednesday, March 11, 9:30am - 11:00am , PAR 101
- Final Project Written Report, Due: May 15, 11:59pm
Assignments
There will be four 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 (5%)
- HW assignments (44% 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 (16%)
- First Presentation & Report (10%)
- 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 | Due |
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