Bayesian Networks

A probabilistic graphical model that represents variables and their conditional dependencies using a directed acyclic graph (DAG).

1. Nodes: Random variables (e.g., Disease, Symptom). 2. Edges: Conditional dependencies (cause → effect). 3. Conditional Probability Tables (CPT): Probability distribution for each node given its parents.

Node 1: Rain, Node 2: Sprinkler, Node 3: Wet Grass.

Rain → Wet Grass and Sprinkler → Wet Grass.

P(X1, X2, …, Xn) = Π P(Xi | Parents(Xi)).

The probability of the whole network, which is the product of each node’s probability given its parents.

Rain | Sprinkler | P(WetGrass=Yes): Yes | Yes | 0.99, Yes | No | 0.90, No | Yes | 0.80, No | No | 0.00.

1. Medical Diagnosis → Disease → Symptoms. 2. Spam Filtering → Words → Spam probability. 3. Decision Support Systems → Risks and outcomes. 4. Robotics → Sensor fusion under uncertainty.

1. Handles uncertainty effectively. 2. Provides a graphical view of dependencies. 3. Easy to update beliefs with new evidence. 4. Supports reasoning about cause–effect relationships.