Bayesian Networks - Probabilistic

Introduction

Bayesian networks are graphical models that represent probabilistic relationships among variables using directed acyclic graphs (DAGs). They provide a compact, intuitive way to encode joint probability distributions over many variables, enabling efficient reasoning under uncertainty. In the real world, most decisions must be made with incomplete information. Bayesian networks give AI systems a principled framework for combining prior knowledge with observed evidence to compute the probability of unobserved events.

Structure of a Bayesian Network

Conditional Probability Tables

Inference: Computing Probabilities from Evidence

Exact Inference by Enumeration

Variable Elimination

Types of Reasoning in Bayesian Networks

D-Separation: Conditional Independence

Applications

Medical Diagnosis: Model relationships between diseases, symptoms, and test results. Observe symptoms → infer most likely disease. Used in clinical decision support systems.

Fault Diagnosis: In complex systems (aircraft, power grids), model causal chains from faults to observable symptoms. When alarm triggers, compute most probable root cause.

Spam Filtering: Model relationships between email features (words, sender, links) and spam/ham classification. Update beliefs as new features observed.

Risk Assessment: Insurance, credit scoring, and project management use Bayesian networks to assess risk given partially observed factors.

Summary

Bayesian networks provide an elegant framework for representing and reasoning about uncertain knowledge. By combining graph structure (encoding independence assumptions) with probability theory (quantifying relationships), they enable efficient computation of posterior probabilities given evidence. The ability to perform causal, diagnostic, and intercausal reasoning makes them invaluable for AI systems operating in uncertain real-world environments where decisions must be made with incomplete information.