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Graphical models overview

**Probabilistic graphical models** make dependence structure explicit—Bayes nets, Markov random fields, and related factorizations. **Causal** graphs are a related but stricter commitment: arrows mean assumed cause, not only allowed stat...

What it is

Probabilistic graphical models make dependence structure explicit—Bayes nets, Markov random fields, and related factorizations. Causal graphs are a related but stricter commitment: arrows mean assumed cause, not only allowed statistical dependence. Pearl’s *Causality* unifies probabilistic, manipulative, counterfactual, and structural views; Stanford STATS 361 lists graphical models and structure learning among causal-inference topics.

MEDIUM PRIORITYDIAGRAM
◷ IN PRODUCTION

Visual Spec & Architecture Diagram

Tiny Bayesian network: Rain → Sprinkler, Rain → Wet grass ← Sprinkler. Conditional probability tables as small matrices. Label 'graph + local distributions'.

Educational Focus: Introduces graphical models before causal DAGs.

Why it matters

Graphs force teams to say what they believe depends on what. That bridges Course 06 Bayes nets to causal identification—and stops “everything correlates with everything” modeling without thought.

How it works (plain)

Choose variables → draw allowed dependencies → factor the joint (probabilistic PGMs) or state causal assumptions (DAGs) → do inference, learning, or identification. Structure is a modeling choice you must justify.

Everyday example

A medical checklist where some symptoms share causes—the drawing changes which tests and adjustments make sense.

Try it

For five variables in a toy domain, compare a fully connected guess vs a sparse graph. Which edges can you defend?

Myths

⚠️ Myth: More edges mean a better model.
✓ Reality: Extra edges need data and can overfit dependence; causal graphs also risk wrong interventions if arrows are wrong.
⚠️ Myth: Any Bayes net is automatically a causal model.
✓ Reality: You need causal semantics (and usually acyclicity + intervention rules) before \(do\)-calculus applies.

Sources