## Topics in Probabilistic Modeling and Inference |

Instructor: Piyush Rai: (office: RM-502, email: piyush AT cse DOT iitk DOT ac DOT in)

Office Hours: Wednesday 11:00am-12:00pm (or by appointment)

Class Venue: KD-101

Class Timings: T/Th 5:10-6:30pm

TAs: Shivam Bansal, Smrithi Prabhu, Vinay Verma

TA Office Hours: TBD

Date |
Topics |
Readings/References |
Slides/Notes |

Jan 4 | Logistics and Introduction to the course | Nature article on probabilistic modeling, Probability Refresher slides | slides, (print version) |

Jan 9 | Basics of Probabilistic Modeling and Inference, Single-Parameter Models | Parameter Estimation (only up to section 3), BDA Section 1.1-1.3, 1.8, BDA 2.1-2.6 | slides, (print version) |

Jan 11 | Single-Parameter Models (Contd.), Intro to Bayesian Linear Regression | BDA 2.1-2.6, MLAPP 7.1-7.3, 7.6 (7.6.1-7.6.2) | slides, (print version) |

Jan 16 | Bayesian Linear Regression (Contd) | PRML 3.3, MLAPP 7.1-7.3, 7.6 (7.6.1-7.6.2) | slides, (print version) |

Jan 18 | Learning Hyperparameters via MLE-II, and Introduction to Multiparameter Models | PRML 3.5, Optional: BDA (Chapter 3), Recommended: Bayesian Inference tutorial paper | slides, (print version) |

Jan 23 | Multiparameter Models (Contd.) | Optional: BDA (Chapter 3), Recommended: Conjugate Bayesian analysis for Gaussians | slides, (print version) |

Jan 25 | Classification: (Bayesian) Logistic Regression (and our first tryst with non-conjugacy!) | MLAPP Sec 8.4, PRML Sec 4.4-4.5 | slides, (print version) |

Jan 30 | Generative Classification, Exponential Family Distributions | CS772 Lec-4 and Lec-5, MLAPP 8.6, MLAPP Sections 9.1-9.3 (exp. family) | slides, (print version) |

Feb 1 | Gaussian Process for Learning Nonlinear Functions | PRML Sec. 6.4, MLAPP Sections 15.1-15.2.5, (Optional: 15.3-15.5) | slides, (print version) |

Feb 6 | Gaussian Process (Contd.) and Intro to Latent Variable Models | Recommended: Chapter 2 and 3 of the GP book | slides, (print version) |

Feb 8 | Inference in Latent Variable Models: The EM Algorithm | PRML 9.3, 9.4 | slides, (print version) |

Feb 13 | The EM Algorithm (Contd.) and Some Examples | PRML 9.3, 9.4, 12.2 (EM for PPCA in 12.2.2). Also recommended: MLAPP Chapter 11, MLE step of GMM | slides, (print version) |

Feb 15 | Conditional Mixture Models and Mixture of Experts | PRML 14.5, MLAPP 11.2.4, 11.4.3, Recommended: Twenty Years of Mixture of Experts | slides, (print version) |

March 13 | Probabilistic Models for Sparse Regression and Classification | MLAPP 13.1, 13.2, 13.4.4, 13.7 | slides, (print version) |

March 15 | Introduction to Variational Inference | PRML 10.1, 10.2, 10.4 | slides, (print version) |

March 20 | Variational Inference (Contd.) | PRML 10.1, 10.2, 10.3, 10.4, Recommended: Variational Inference Review, Life after EM | slides, (print version) |

March 22 | Stochastic Variational Inference | Recommended: Variational Inference Review (Section 4), SVI paper | slides, (print version) |

March 24 | Expectation Propagation and Intro to Sampling Methods | PRML 10.7, 11.1 | slides, (print version) |

March 27 | Approx. Inference via Markov Chain Monte Carlo | PRML 11.2, 11.3, Recommended: Detailed Intro to MCMC | slides, (print version) |

April 3 | Sampling (Contd.) and Gradient-based Monte Carlo | Recommended: Section 3.4 of this monograph, SGLD paper, A Brief article on Hamiltonian Monte Carlo | slides, (print version) |

April 5 | Probabilistic Models for Text and Graphs | Recommended: Topic Models, MMSB paper | slides, (print version) |

April 7 | Probabilistic Models for Sequential Data | Recommended: PRML Chapter 13 (sections relevant to LDS), MLAPP Chapter 18 | slides, (print version) |

April 10 | Nonparametric Bayesian Modeling | Recommended: Overview of Nonparametric Bayesian Models | slides, (print version) |

April 12 | Probabilistic/Bayesian Models for Deep Learning | Recommended: Chapter 1 and 6 of this tutorial, Weight Uncertaintly in Neural Networks, VAE paper | slides, (print version) |

April 17 | Bayesian Optimization | Recommended: Survey on Bayesian Optimization | slides, (print version) |

April 19 | Probabilistic Numerics, Conclusion | Recommended: An Overview of Probabilistic Numerics, Other resources on probabilistic numerics | slides, (print version) |

- (PRML) Christopher Bishop, Pattern Recognition and Machine Learning, Springer, 2007.
- (MLAPP) Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press, 2012.
- (BDA) Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin. Bayesian Data Analysis, Chapman \& Hall/CRC, 2013
- (ITILA) David Mackay. Information Theory, Inference, and Learning Algorithms. Cambridge Univ. Press, 2003.
- Papers from conference/journals in machine learning and Bayesian statistics (e.g., ICML, NIPS, AISTATS, Journal of Machine Learning Research, Machine Learning Journal, Bayesian Analysis, Biometrika, Annals of Statistics, etc.)