Bayes Nets A Bayes net is an efficient

Bayes’ Nets A Bayes’ net is an efficient encoding of a probabilistic model of a domain Questions we can ask: Inference: given a fixed BN, what is P(X | e)? Representation: given a BN graph, what kinds of distributions can it encode? Modeling: what BN is most appropriate for a given domain? 1

Bayes’ Net Semantics Let’s formalize the semantics of a Bayes’ net A 1 An A set of nodes, one per variable X A directed, acyclic graph A conditional distribution for each node X A collection of distributions over X, one for each combination of parents’ values CPT: conditional probability table Description of a noisy “causal” process A Bayes net = Topology (graph) + Local Conditional Probabilities 2

Example: Alarm Network Burglary Earthqk Alarm John calls Mary calls

Reasoning over Time Often, we want to reason about a sequence of observations Speech recognition Robot localization User attention Medical monitoring Need to introduce time into our models Basic approach: hidden Markov models (HMMs) More general: dynamic Bayes’ nets This slide deck courtesy of Dan Klein at UC Berkeley 4

Dynamic Bayes Nets (DBNs) We want to track multiple variables over time, using multiple sources of evidence Idea: Repeat a fixed Bayes net structure at each time Variables from time t can condition on those from t-1 Discrete valued dynamic Bayes nets are also HMMs