1. Introduce the Empirical Risk Minimization principle
  2. Define PAC Learning 
  3. Introduce the basic ideas of Probabilistic Inference
  4. Introduce Bayesian Networks and their factorization
  5. Conditional Independence in Bayesian Networks
  6. Introduce Random Markov Fields 
  7. Define Factor Graphs and How to convert Bayesian Networks  and Markov Random Fields to Factor Graphs
  8. Describe the Sum Product algorithm
  9. Describe the Max Plus algorithm
  10. Define HMM and different Inference problems in HMM
  11. Discuss closure properties of the Gaussian Distribution
  12. How to transform a generic Gaussian Distribution to a Standard Gaussian via Principal components
  13. Introduce the Bayesian Estimation Principles
  14. Introduce Bayesian Linear Regression 
  15. Prior and posterior over parameters in Bayesian Linear Regression
  16. Predictive distribution in Bayesian Linear Regression
  17. Discuss Model Evidence and hyper parameter optimization in Bayesian Linear Regression
  18. Discuss Bayesian Model Comparison
  19. Describe Laplace Approximation
  20. Discuss Bayesian Information Content for Model Comparison
  21. Introduce Bayesian Logistic Regression
  22. Introduce the kernel trick and the dual formulation of linear regression
  23. Introduce random functions and Gaussian Processes 
  24. Present Gaussian Process regression
  25. Rejection sampling
  26. Importance sampling
  27. Introduce Markov chain and the  Detailed Balance condition
  28. Introduce Markov Chain Monte Carlo and the  Metropolis Hastings criterion
  29. Discuss issues of vanilla MCMC
  30. Gibbs Sampling
  31. Discuss  Convergence Diagnostics and the Rhat index
  32. Introduce the ideas of effective sample size
  33. Hamiltonian Monte Carlo
  34. Introduce the problem that can be solved by EM and derive the  Evidence lower bound
  35. Discuss the Expectation Maximization algorithm (both E-step and M-step)
  36. Discuss convergence of the EM algorithm
  37. Discuss EM algorithm for Gaussian Mixtures
  38. Introduce  the problem formulation for Variational Inference
  39. Introduce Mean Field Variational Inference
  40. Example of Mean Field Variational Inference on Gaussian distribution
  41. Variational Inference with direct and inverse KL
  42. Variational Linear Regression 
  43. Introduce Black box Variational Inference 
  44. Discuss how to compute the gradient of the ELBO for a non-reparameterizable variational distribution
  45. Discuss Rao-Blackwellization for variance reduction
  46. Discuss Control variates for variance reduction
  47. Discuss Bayesian Neural Networks
  48. Introduce the generative modelling problem and present different models for generative AI
  49. Introduce Autoencoding Variational Bayes
  50. Introduce Denoising Diffusion Models



Last modified: Tuesday, 20 May 2025, 3:42 PM