Mathematics of Generative Models

Course Outcomes

• Learn extensive mathematical foundations required for generative models
• Learn to build mathematical models for a generative task.
• Analyze and solve complex optimization models and solvers.
• Analyze the obtained results with various benchmarks and scores.
• Learn to program basic generative model applications.

This course teaches mathematics required for understanding recent generative modeling algorithms to UG and PG students of IIIT-H.

Video Lectures

• Lecture 1: Brief review of Probability and Random processes
• Lecture 2: Ordinary differential equations
• Lecture 3: Optimization methods
• Lecture 4: The Gaussian VAE
• Lecture 5: ConvNets and ResNets
• Lecture 6: Posterior collapse
• Lecture 7: Discrete VAEs
• Lecture 8: f-GANs
• Lecture 9: Wasserstein GANs
• Lecture 10: Solvers for min-max
• Lecture 11: Generative Sinkhorn Modeling: KR-duality
• Lecture 12: Optimal Transport
• Lecture 13: Sinkhorn algorithm
• Lecture 14: Autoregressive flows
• Lecture 15: Invertible networks
• Lecture 16: Neural Ordinary Differential Equations
• Lecture 17: Stein's method and score matching
• Lecture 18: Langevin dynamics
• Lecture 19: Stochastic calculus
• Lecture 20: Diffusion Process
• Lecture 21: Stochastic differential equations
• Lecture 22: Simulated Annealing
• Lecture 23: Denoising diffusion models

References

• Course notes will be given during class. There is no standard textbook that covers all topics.
• Generative Models, John Thickstun, Link: https://courses.cs.washington.edu/courses/cse599i/20au/
• Machine Learning: A Probabilistic Perspective by Kevin P. Murphy.
• Computational Optimal Transport, arXiv:1803.00567
• Tutorial on Deep Generative Models. Aditya Grover and Stefano Ermon. International Joint Conference on Artificial Intelligence, July 2018.

Weightages

• Assignments: 10%
• Quiz-1: 10%
• Quiz-2: 10%
• Mid Semester Examination:25%
• End Semester Examination:30%
• Assessment of projects:15%

Pre-Requisites

• Probability and Statistics (Multiple random variables, bounds, distributions)
• Linear Algebra
• Calculus