Probabilistic Machine learning For mechanics

1. Introduction to the course [lecture notes][lecture video]

2. Review of Bayesian Statistics - Part 1 [Lecture Notes][lecture video] 

3. Review of Bayesian Statistics (conclusion) and Bayesian inference [Lecture Notes][lecture video]

4. Bayesian inference, MLE, MAP, Posterior Predictive [Lecture Notes][lecture video]

5. Prior modeling, Conjugate Prior, Exponential Family [Lecture Notes][lecture video]

6. Non-information Prior, Hierarchical Bayes, Empirical Bayes [Lecture Notes][lecture video]

7. EB (Example) and Bayesian linear regression - Part 1 [Lecture Notes][lecture video] 

8. Bayesian linear regression - Part 2 [Lecture Notes][Lecture video]

9. Bayesian linear regression - Part 3 [Lecture Notes][lecture video]

10. Bayesian inference using sampling methods - Part 1 [Lecture Notes][lecture video]

11. Bayesian inference using sampling methods - Part 2 [Lecture Notes][lecture video]

12. Bayesian inference using sampling methods - Part 3 [Lecture Notes][lecture video]

13. Bayesian inference using sampling methods - Part 4 [Lecture Notes][lecture video]

14. Bayesian inference using sampling methods - Part 5 [Lecture Notes][lecture video]

15. Bayesian inference using sampling methods - Part 6 [Lecture Notes][lecture video]

16. Bayesian inference using sampling methods - Part 7 [Lecture Notes][lecture video]

17. Approximate methods for Bayesian inference - Part 1 [Lecture Notes][lecture video]

18. Approximate methods for Bayesian inference - Part 2 [Lecture Notes][lecture video]

19. Gaussian process - Part 1 [Lecture Notes][lecture video]

20. Gaussian process - Part 2 [Lecture Notes][lecture video]

21. Sparse Gaussian Process - Part 1 [Lecture Notes][lecture video]

22. Sparse Gaussian Process - Part 2 [Lecture Notes][lecture video]

23. Factor analysis, Probabilistic PCA, Duel Probabilistic PCA, and GP-LVM [Lecture Notes][lecture video]

24. Normalizing Flow - Part 1 [Lecture Notes][lecture video]

25. Normalizing Flow (Part 2) and Diffusion Model [Lecture Notes][lecture video]

26. Diffusion Model - Part 1

27. Diffusion Model - Part 2

28. Review of the course and way Ahead

• Introduction to Statistical Computing and Probability and Statistics

• Likelihood, Prior, Posterior, Posterior predictive distribution, Plug-in Approximation

• Bayesian linear regression

• Introduction to Monte Carlo Methods, Sampling from Discrete and Continuum Distributions, Reverse Sampling

• Importance sampling, Gibbs sampling, MCMC, Metropolis Hasting algorithm 

• Variational approach and approximate inference

• Sparse linear regression

• Gaussian process

• Latent variable model, probabilistic PCA, GP-LVM

• Some advanced topics in probabilistic ML: Flow-based model, Diffusion model

Lecture notes and references will be provided on the course web site. The following books are recommended:

• Bishop, C.M. Pattern recognition and Machine learning, Springer, 2007.

• Murphy, K.P. “Machine learning: A Probabilistic Perspective”, MIT press, 2022.

• Rasmussen, Carl Edward. Gaussian processes in machine learning, In Summer school on machine learning, pp. 63-71. Springer, Berlin, Heidelberg, 2003

• Homework-1: Bayesian linear regression, Sampling method [homework]

• Homework-2: Markov Chain, MCMC, Rejection Sampling, Gibbs Sampling, HMC, SMC [homework]

• Homework-3: Approximate inferenace and Gaussian Process [homework]

• Homework 4: Unsupervised learning and generative modeling [homework]

• Practical-0: Introduction to statistical computing [QP][solution template][solution]

• Practical-1: Priors, Bayesian linear regression [QP][solution template][solution]

• Practical-2: Sampling Method 1: Rejection Sampling, Importance Sampling, Metropolis Hasting Sampling [QP][solution]

• Practical-3: Sampling Method -2: Gibbs Sampling, Metropolis Hasting, Hamiltonian Monte Carlo, and Sequential Monte Carlo Sampling [QP]

• Practical-4: GP and Variational Bayes [QP]

• Each student will have to complete a term project as part of this course

Credit: 4 Units (3-0-2)

Timing: Lecture - Monday and Thursday (9:30 am - 11:00 am), Practical - Wednesday (3:00 pm - 5:00 pm)

Venue: LH613 (lecture), IV-LT2 (Practical)

Instructor: Dr. Souvik Chakraborty 

Teaching Assistants: Tapas Tripura, Sawan Kumar, Subhankar Sarkar

Course Objective: In this course, the students will be introduced to the fundamentals of probabilistic machine learning and its application in computational mechanics. Students are expected to learn different probabilistic machine learning algorithms and applications in solving mechanics problems The course will emphasize on the mathematical learning of these concepts along with applications. The course is particularly designed for PG, Ph.D., and senior UG students.

Intended audience: Senior UG, PG, and Ph.D. students