## Topics in Probabilistic Modeling and Inference |

Instructor: Piyush Rai: (email: piyush AT cse DOT iitk DOT ac DOT in)

TAs and email: Soumya Banerjee (soumyab AT cse), Dhanajit Brahma (dhanajit AT cse), Amit Chandak (amitch AT cse), Pratik Mazumder (pratikm AT cse), Rahul Sharma (rsharma AT cse)

- Kevin Murphy, Machine Learning: A Probabilistic Perspective (MLAPP), MIT Press, 2012
- Christopher Bishop, Pattern Recognition and Machine Learning (PRML), Springer, 2007.

Lecture No. |
Topics |
Readings/References/Comments |
Videos/Slides/Notes |

1 | Course Logistics, Intro to Probabilistic Modeling and Inference | [Z15], [B14] (for now, up to sec 3), a brief prob-stats refresher, a basic tutorial on Bayesian inference | will be posted on mooKIT |

2 | Basics of Probabilistic/Bayesian Modeling and Parameter Estimation | Wikipedia entries (to be read in the same order) on Bayesian Inference, Prior, Likelihood, Posterior, Posterior Predictive, Credible Intervals (for now, these articles are meant for cursory reading; may safely skip the parts that seem too advanced to you), Additional Reading: MLAPP Section 3.1-3.3, Conjugate Priors | will be posted on mooKIT |

3 | Bayesian Inference for Some Basic Models | Lecture 2 suggested readings + MLAPP 3.3-3.5, Bayesian Inference for Gaussians, Wikipedia entry on Dirichlet distribution | will be posted on mooKIT |

4 | Bayesian Inference for Gaussians (Contd) and Exponential Family | MLAPP 4.3-4.6 (it is far more detailed than you probably need at the moment; you may skip very detailed proofs, can focus more on the examples and the standard results on Gaussian properties, inference, etc), PRML 2.3, Bayesian Inference for Gaussians, MLAPP 9.1-9.2, some notes on exp-family (if further interested, may skim through the Wikipedia article on exp-fam) | will be posted on mooKIT |

5 | Probabilistic Linear Regression | PRML 3.3, MLAPP 7.1-7.3, 7.6 (7.6.1-7.6.2), Recommended Readings: Bayesian Inference tutorial (with Bayesian linear regression as case study; as of now, may read up to section 3) | will be posted on mooKIT |

6 | Probabilistic Approaches for Sparse Modeling | Recommended Readings: Section 4 of Bayesian Inference tutorial, The Relevance Vector Machine paper (don't need to read all of it in detail; can just skim over to see the key ideas at a high level, and the experimental results), and the other references mentioned in the slides | will be posted on mooKIT |

7 | (1) Probabilistic Models for Classification: Logistic Regression, (2) Laplace Approximation | MLAPP 8.4 | will be posted on mooKIT |

8 | (1) Generalized Linear Models, (2) Generative Models for Supervised Learning | MLAPP 9.3 (for GLM), 3.5.1.2, 3.5.2, 3.5.5 (for some examples of generative classification, including the Bayesian way) | will be posted on mooKIT |

9,10,11 | Gaussian Processes | PRML Sec. 6.4, MLAPP Sections 15.1-15.2.5, (Optional: 15.3-15.4), Illustration of various kernels for GP, Some GP software packages: GPFlow (Tensorflow based), GPyTorch (PyTorch based), GPML (MATLAB based) | will be posted on mooKIT |

12 | Probabilistic Approaches to Active Learning | Bayesian Active Learning, BALD paper (sections 1-2, rest optional). An old but classic paper on this topic: Information-Based Objective Functions for Active Data Selection | will be posted on mooKIT |

13 | Bayesian Optimization | An introduction to Bayesian Optimization (with some code), Another Python Notebook on Bayesian Optimization | will be posted on mooKIT |

14 | Multi-parameter Models, Conditional Posteriors, Local Conjugacy | Highly recommended: Paper on Bayesian Matrix Factorization, and Gibbs Sampling for the Uninitiated (note: we will look at Gibb sampling again in more detail and formally when talking about MCMC but if you want to get a good and practical overview then this tuutorial is very nice and doesn't require you to understand MCMC in much detail beforehand) | will be posted on mooKIT |

15 | Latent Variable Models and EM | PRML Chapter 9 (has examples of EM for Gaussian Mixture Model and Bayesian Linear Regression), MLAPP 11.4, Optional readings: Original EM paper (technically very dense but lots of interesting insights), Another classic paper on EM (more accessible), Online EM (practically oriented), Online EM (theoretically oriented) | will be posted on mooKIT |

16 | Introduction to Variational Inference | Readings: PRML 10.1,10.2,10.3.10.4, Life after EM (shows the connection between EM, variational EM, and variational inference, through several examples), VI: A Review for Statisticians | will be posted on mooKIT |

17 | VI (Contd) and Recent Advances in VI | VI: A Review for Statisticians (Sec 4.3 on SVI), SVI paper (if you are interested in a more in-depth treatment of SVI), Advances in Variational Inference (a bit long but I would suggest skimming it over to get a sense of the various recent advances in VI) | will be posted on mooKIT |

18 | Approximate Inference via Sampling | Readings: PRML 11.1-11.3, MLAPP 24.1-24.3, Recommended: Intro to MCMC for Machine Learning, Monte Carlo for Absolute Beginners, Gibbs Sampling for the Uninitiated | will be posted on mooKIT |

19 | Gibbs Sampling Examples, Some Aspects about MCMC | Readings: PRML 11.1-11.3, MLAPP 24.1-24.4, Gibbs Sampling for the Uninitiated | will be posted on mooKIT |

20 | MCMC with Gradient Information, Recent Advances in MCMC | Recommended: SGLD paper and other papers referenced in the slides (not required to get into every technical detail but try skimming through some of these papers to get a high level idea), Survey paper on SGMCMC methods like SGLD and improvements, Patterns of Scalable Bayes (See sec 4.2 for parallel MCMC, though other parts are also useful for a general introduction to approximate inference methods, including scalable methods), No U-Turn Sampler (section 2 describes the basics of HMC), | will be posted on mooKIT |

21 | Introduction to Nonparametric Bayesian Modeling | Suggested Readings: For NPBayes modeling general intro - this tutorial survey paper, For NPBayes Clustering, this paper on Dirichlet Process | will be posted on mooKIT |

22 | Probabilistic Models for Deep Learning | Suggested Readings: Weight Uncertainty in Neural Networks (Blundell et al, 2015), and other papers references in the slides; this tutorial paper on Bayesian Deep Learning | will be posted on mooKIT |

23 | Deep Generative Models | Suggested Readings (also look at the references in the slides): For PPCA, FA, etc (classical models), see MLAPP Chap 12; for gamma-Poisson latent factor model and Dirichlet-multinomial PCA, see this paper and this paper; for LDA, see this tutorial paper; for VAE, see the VAE paper, and see this tutorial paper and this survey; for GAN, see the GAN paper, and also see this survey; | will be posted on mooKIT |