Bayesian Networks

Acyclic graph: a graph without any cycles (or loops).
BNs: Bayesian Networks
CDs: conditional dependencies
Probability distributions: everything depends on everything else
- Naive Bayes: everything is conditionally independent
  - The network is compact representation of joint probability distributions.

Sam

BNs: a general-purpose graphical framework for representing CDs and reasoning under uncertainty.

Sequence:

Learn parent facts
After accounting for these ^, learn how variables are dependent of independent on each other.

Term	Intuition	Example
Node	A measurable fact, an RV.	`IceCreamSales`
Edge (arrow)	Direct influence.	`Season → SharkAttacks`
Parents	Immediate influencers of a node.	`Parents(IceCreamSales) = {Season}`
Root	Node with no parents.	`Season`
Leaf	Node with no children.	`SharkAttacks`
Directed Acyclic Graph (DAG)	No feedback loops (1-direction only)	`Season → IceCreamSales`, `Season → SharkAttacks`

Compact: Instead of listing probabilities for every possible combination of variables, a BN stores only the pieces that really matter.
Intuitive & transparent: Arrows show “this causes that”, easy for stakeholders
Efficient inference: Once built, algorithms can answer “what‑if?” questions faster than brute‑force enumeration.

Strength	Weakness / Pitfall
Encodes why not just what.	Building a reliable structure can be hard without expert input.
Handles missing data gracefully.	Parameter explosion if many parents per node.
Supports causal reasoning (with caveats).	Assumes the graph is acyclic—loops need Dynamic BNs.

A BN encodes one master rule:

Given its parents, a node is conditionally independent of its non‑descendants.

That rule plus the graph’s geometry lets us test independence with d‑separation:

Chain (A → B → C): Knowing B “blocks” A from C.
Fork (A ← B → C): Knowing B blocks A from C.
Collider (A → B ← C): Not knowing B keeps A and C independent, but observing B unblocks the path—“explaining away.”