Concept
Variables and their dependencies as a graph. Bayesian networks (directed) and Markov random fields (undirected) — the framework of AI uncertainty.
Understand it in one breath
"Compress a high-dimensional joint distribution as a graph." With 100 variables a joint distribution has 2¹⁰⁰ entries, but conditional independencies drawn as edges shrink that to a tractable number. Medical diagnosis (symptoms → disease), robotic SLAM, and HMMs for speech recognition all live here.
At a glance
Model | Structure | Application |
|---|---|---|
Naive Bayes | Class → all features | Spam filtering; text classification |
Bayesian Network | Directed acyclic graph | Medical diagnosis; causal inference |
HMM (Hidden Markov) | Chain: zₜ₋₁ → zₜ → xₜ | Speech, NLP, and DNA |
MRF (Markov Random Field) | Undirected graph | Image segmentation |
Conditional Random Field | Conditional MRF | NER; semantic segmentation |
Variational Autoencoder | Deep Bayesian model | Image generation |
Represent conditional independence with graph edges: a 2¹⁰⁰-state joint distribution over 100 variables can collapse to a few hundred terms.
Key formula
Modern applications
Medical AI diagnosis, SLAM for autonomous systems, hidden Markov models in speech recognition, and causal inference.
Beyond MathVoyage
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