Dynamic Bayesian Network

A Bayesian Network $\mathcal{D}$ is called dynamic iff its Random Variables are indexed by a time structure.

$\mathcal{D}$ is

• time sliced, which means time slices are isomorphic

• a stationary Markov Chain

• Every HMM is a single-variable DBN

• Every discrete DBN is an HMM

• DBNs have sparse dependencies

Exact Inference

Unrolling the network and running an exact algorithm on the unrolled network.

![[CleanShot 2023-10-02 at 15.15.41@2x.png]]

• Rollup filtering