1. Introduce the Empirical Risk Minimization principle
  2. Define PAC Learning 
  3. Define VC Dimension(Vapnik–Chervonenkis)
  4. Introduce the basic ideas of Probabilistic Inference
  5. Introduce Bayesian Networks and their factorization
  6. Conditional Independence in Bayesian Networks
  7. Introduce Random Markov Fields 
  8. Define Factor Graphs and How to convert Bayesian Networks  and Markov Random Fields to Factor Graphs
  9. Describe the Sum Product algorithm
  10. Describe the Max Plus algorithm
  11. Define HMM and different Inference problems in HMM
  12. Discuss closure properties of the Gaussian Distribution
  13. How to transform a generic Gaussian Distribution to a Standard Gaussian via Principal components
  14. Introduce the Bayesian Estimation Principles
  15. Introduce Bayesian Linear Regression 
  16. Prior and posterior over parameters in Bayesian Linear Regression
  17. Predictive distribution n Bayesian Linear Regression
  18. Discuss Model Evidence and hyper parameter optimization
  19. Introduce the idea of Effective number of parameters
  20. Discuss Bayesian Model Comparison
  21. Describe Laplace Approximation
  22. Discuss Bayesian Information Content for Model Comparison
  23. Introduce Bayesian Logistic Regression
  24. Rejection sampling
  25. Importance sampling
  26. Introduce Markov chain and the  Detailed Balance condition
  27. Introduce Markov Chain Monte Carlo and the  Metropolis Hastings criterion
  28. Discuss issues of vanilla MCMC
  29. Gibbs Sampling
  30. Discuss  Convergence Diagnostics and the That index
  31. Introduce the ideas of Effective sample size
  32. Hamiltonian Monte Carlo
  33. Introduce the problem that can be solved by EM
  34. Introduce 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
  49. Introduce Autoencoding Variational Bayes
  50. Introduce Denoising Diffusion Models


Ultime modifiche: sabato, 22 giugno 2024, 13:37