Bayesian Network
A Bayesian network represents a joint probability distribution with a directed acyclic graph and a conditional distribution for each variable given its parents. Observing evidence lets probabilistic inference update beliefs about other variables.
Also known as: belief network, Bayes network
Consider variables for burglary, earthquake and whether an alarm sounds. A simple network gives burglary and earthquake arrows into alarm, and specifies the probability of the alarm for each combination of its parents. The graph plus those probabilities defines a joint model; arrows alone are not enough.
Hearing an alarm can increase the estimated probability of burglary. Learning that there was an earthquake can reduce that estimate because the model includes another explanation for the alarm. How much the probabilities change depends on the values supplied to the model. This is an illustrative reasoning example, not a measured security system.
The graph encodes conditional-independence assumptions and must have no directed cycles. It differs from a knowledge graph that stores entities and relationships for traversal. This matters when making causal claims: a Bayesian network fitted to observations need not be a causal model. Causal interpretation requires additional assumptions about what interventions mean.
Sources
- Stanford CS228: Bayesian networks — Explains directed acyclic graphs, conditional factorization, independence and explaining away.
Go deeper
- Stanford CS228: Variable elimination course
Work through exact inference by combining factors and summing out variables.