🎲 Bayesian Network Inference

Probabilistic graphical models, exact inference, and d-separation

Overview

A complete Bayesian network inference engine supporting directed acyclic graphs of random variables with conditional probability tables. Includes exact inference via enumeration and variable elimination, d-separation testing, and three classic example networks.

Concepts Demonstrated

Conditional probability tables (CPTs) — P(X | parents) specification
Enumeration inference — exact marginal/posterior computation via summation
Variable elimination — efficient inference by factor multiplication and marginalization
D-separation — conditional independence testing in DAGs
Record types — structured representation of nodes, CPTs, and networks
Classic networks — alarm, sprinkler, and Asia diagnostic models

Key Functions

Function	Description
`find_node`	Retrieve a node by variable name
`lookup_cpt`	Look up P(X=true \| parent values) from a CPT
`enumerate_ask`	Exact posterior P(X \| evidence) by enumeration
`variable_elimination`	Factor-based inference with marginalization
`d_separated`	Test conditional independence between variables
`children_of`	Find child nodes in the DAG

Network Structure

type node = {
  name: variable;
  parents: variable list;
  cpt: cpt_entry list;  (* P(true | each parent config) *)
}

(* Classic sprinkler network:
   Cloudy → Sprinkler → WetGrass
   Cloudy → Rain → WetGrass *)

(* Query: P(Rain | WetGrass=true) *)
let p = enumerate_ask sprinkler_net "Rain"
  [("WetGrass", true)]

Inference Methods

Method	Complexity	Approach
Enumeration	O(2ⁿ)	Sum over all hidden variable assignments
Variable Elimination	O(2ʷ)	Factor operations with optimal ordering (w = treewidth)