Bayesian Networks 4  Probabilistic Inference  Stanford CS221: AI (Autumn 2021)  Summary and Q&A
TL;DR
This video explains how to convert Bayesian networks into Markov networks for probabilistic inference using optimization techniques.
Questions & Answers
Q: What is a Bayesian network and how is it defined?
A Bayesian network is a graphical model that represents a set of random variables and their dependencies. It consists of a directed acyclic graph and local conditional distributions for each variable given its parents.
Q: How can a factor graph be derived from a Bayesian network?
The joint distribution of the variables in a Bayesian network can be factorized using the local conditional distributions. Each local conditional distribution becomes a factor, and the factors are connected in a factor graph.
Q: How can conditioning on evidence be incorporated into the inference process?
To condition on evidence, the values of the evidence variables are substituted into the factors. The resulting factor graph only includes the variables that are not part of the evidence.
Q: What can be done to optimize the inference process in Bayesian networks?
Unobserved leaves, such as variables that are not part of the evidence, can be removed from the factor graph. Additionally, disconnected components in the factor graph can be discarded.
Summary & Key Takeaways

Bayesian networks consist of random variables and define a qualitative and quantitative relationship between them.

The joint distribution of the variables in a Bayesian network can be represented as a factor graph, which can be converted into a Markov network.

Conditioning on evidence and removing unobserved leaves and disconnected components can optimize the inference process.

Markov networks allow various inference algorithms, such as Gibbs sampling, to be applied.