# Bayesian networks

(2.1 hours to learn)

## Summary

Bayesian networks are a graphical formalism for representing the structure of a probabilistic model, i.e. the ways in which the random variables may depend on each other. Intuitively, they are good at representing domains with a causal structure, and the edges in the graph determine which variables directly influence which other variables. They can be equivalently viewed as representing a factorization structure of the joint probability distribution, or as encoding a set of conditional independence assumptions about the distribution.

## Context

This concept has the prerequisites:

- random variables (Bayes nets are a way of structuring information about random variables.)
- conditional independence (Bayes nets can be viewed as encoding a set of conditional independence assumptions.)
- Bayes' rule (Bayes nets are used for forms of reasoning based on Bayes' Rule.)

## Core resources (read/watch one of the following)

## -Free-

→ Coursera: Machine Learning

An online machine learning course aimed at advanced undergraduates.

Other notes:

- Click on "Preview" to see the videos.

→ Coursera: Probabilistic Graphical Models (2013)

An online course on probabilistic graphical models.

Other notes:

- Click on "Preview" to see the videos.

→ Artificial Intelligence II (IIT video lectures)

Other notes:

- Youtube comment from user "SiddharthBhaiVideos" provides a nice outline of the lecture

## -Paid-

→ Probabilistic Graphical Models: Principles and Techniques

A very comprehensive textbook for a graduate-level course on probabilistic AI.

Location:
Sections 3.1-3.2.2, pages 45-60

→ Artificial Intelligence: a Modern Approach

A textbook giving a broad overview of all of AI.

Location:
Sections 14.1-14.2, pages 492-499

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Sections 10.1-10.2.4, pages 307-318

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Sections 8-8.1.3, pages 359-369

Additional dependencies:

- linear regression

## See also

- Bayes nets are closely related to Markov random fields (MRFs) , a graphical model formalism which is good at representing soft constraints between variables.
- Neither Bayes nets nor MRFs are strictly more powerful than the other.
- Bayes nets can also be characterized in terms of their conditional independencies. The conditional independencies can be found using d-separation .
- Often we are interested in
- inferring the conditional probabilities of some variables given others
- learning the parameters of the network from data