#
CS886 Fall 2010 - Syllabus: Bayesian Data Analysis

## Objectives

Information technologies have given rise to an abundance of data that
needs to be analyzed. While there are many ways to analyze data,
Bayesian methods distinguish themselves by their explicit use of
probabilities to quantify uncertainty. Taking into account
uncertainty is critical when making predictions, recognizing patterns
and drawing conclusions. The use of probability theory to
represent uncertainty leads to conceptually simple methods that are
principled, facilitate generalization, tend to avoid
overfitting, can be easily composed for information fusion and
facilitate model selection. However, these benefits come at a
price: inference is often computationally complex.

This course focuses on the theory of Bayesian learning, models for
Bayesian analysis and algorithms for Bayesian inference. The
theory, models and algorithms covered will be of general interest and
therefore applicable to a wide range of domains beyond machine learning
and computational statistics. This course should be of interest
to researchers in a variety of fields where there is a need to analyze
data, including natural language processing, information retrieval,
data mining, bioinformatics, computer vision, computational finance,
health informatics and robotics.

## References

We will make use of four textbooks with additional readings
from selected research papers. The first textbook is on reserve
at the library and the second textbook is
available
online.

- Gelman, Carlin, Stern and Rubin (2004), Bayesian Data Analysis,
2nd edition
- Rasmussen and Williams (2006), Gaussian Processes

- Gosh and Ramamoorthi (2003), Bayesian Nonparametrics
- Koller and Friedman (2009), Probabilistic Graphical Models

## Outline

Topics:

- Basics of probability theory, machine learning and statistics
- Models
- Single and multi-variate models
- Bayesian networks

- Second-order models (i.e., distributions over distribution
parameters)

- Infinite models
- Gaussian process
- Dirichlet process

- Hierarchical models
- Non-parameteric models

- Prior construction

- Conjugate priors
- Informative and non-informative priors
- Hierarchical priors

- Inference (for learning and predictions)

- Bayes' theorem
- Exact inference with conjugate distributions
- Approximate inference with Markov chain simulation

- Model checking

Applications domains:

- Natural language processing and Information retrieval
- Latent semantic analysis
- Topic modeling

- Machine Learning and Bioinformatics
- Model selection
- Kernel learning

- Computer vision
- Robotics
- Control
- Bayesian reinforcement learning

- Health informatics
- Computational finance
- Data mining