# 6.435 Bayesian Modeling and Inference

Note: this course previously ran using the (temporary) number 6.882 in past years.
Spring 2019

Room 24-121 (MOVED FROM 36-153)

Tuesday, Thursday 2:30–4:00 PM

First class: Tuesday, February 5

**Instructor**:

Professor Tamara Broderick

Office Hours: Thursday, 4–5pm, 32-G498

Email:

(or )

**TA**:

Brian Trippe

Office Hours: Tuesday, 4–5pm, Location TBA

Email:

(or )

## Introduction

As both the number and size of data sets grow, practitioners are interested in learning increasingly complex information and interactions from data. Probabilistic modeling in general, and Bayesian approaches in particular, provide a unifying framework for flexible modeling that includes prediction, estimation, and coherent uncertainty quantification. In this course, we will cover the modern challenges of Bayesian inference, including (but not limited to) speed of approximate inference, making use of distributed architectures, streaming data, and complex data interactions. We will study Bayesian nonparametric models, wherein model complexity grows with the size of the data; this allows us to learn, e.g., a greater diversity of topics as we read more documents from Wikipedia, identify more friend groups as we process more of Facebook's network structure, etc.
## Piazza Site

Our course Piazza page is here: https://piazza.com/mit/spring2019/6435
## Description

This course will cover Bayesian modeling and inference at an advanced graduate level. A tentative list of topics (which may change depending on our interests) is as follows:
- Introduction to Bayesian inference; motivations from de Finetti, decision theory, etc.
- Hierarchical modeling, including popular models such as latent Dirichlet allocation
- Approximate posterior inference
- Variational inference, mean-field, stochastic variational inference, challenges/limitations of VI, etc.
- Monte Carlo, avoiding random-walk behavior, Hamiltonian Monte Carlo/NUTS/Stan, etc.
- Evaluation, sensitivity, robustness
- Bayesian nonparametrics: why and how
- Mixture models, admixtures, Dirichlet process, Chinese restaurant process
- Feature allocations, beta process, Indian buffet process
- Combinatorial stochastic processes
- Learning functions, Gaussian processes
- Probabilistic numerics
- Bayesian optimization

## Prerequisites

Requirements: A graduate-level familiarity with machine learning/statistics and probability is required. (E.g. at MIT, 6.437 or 6.438 or [6.867 and 6.436].)
We will assume familiarity with graphical models, exponential families, finite-dimensional Gaussian mixture models, expectation maximization, linear & logistic regression, hidden Markov models.

## Assessment

- Project
- A project proposal will be due in the first half of the semester.
- A project final report and presentation will be due at the end of the semester.
- Potential project ideas and more details on the project coming soon.

- Presentation and Participation
- There will be assigned reading (typically research papers) each week.
- Students will take turns presenting and leading the discussion in class.
- Students will submit a weekly reflection on the reading (<= 1 page) before class. There will be guiding questions for the reflection and discussion.

- Scribe
- Students will take turns scribing notes from lectures. A template will be provided.