Markov equivalence class

As explained in Causal AI

A Markov equivalence class is a set of causal directed acyclic graphs that encode the same conditional independence relationships through d-separation.

When conditional-independence evidence is used to recover a causal graph, it may identify several DAGs rather than one. A Markov equivalence class groups DAGs with the same d-separation relationships. The true causal DAG is one candidate among them, so observational data alone generally cannot determine every edge direction. section 4.6.3 section 6.2.2

A partially directed acyclic graph (PDAG) can represent the class compactly: directed edges record shared orientations, while undirected edges mark directions on which class members disagree. Dependence and independence usually reveal adjacency but not direction; colliders provide an important exception. section 4.6.3

Collider-based orientation

For a structure T → E ← L, observing T and L as independent but dependent after conditioning on E supports a collider at E. By contrast, evidence of dependence for an A–T edge alone does not establish its direction. This distinction limits what a discovery algorithm can claim from observational data. section 4.6.3

Figure 4.24 Supposing the DAG on the left is the ground truth DAG, the (wrong) DAG on the right is in the same Markov equivalence class. The PDAG in the middle represents the equivalence class, where undirected edges represent edges where members disagree on direction.

Compare a ground-truth DAG, an alternative DAG in the same equivalence class, and the class-level PDAG with undirected uncertain edges. section 4.6.3

How Causal AI covers it

How deep it goes

Explains d-separation equivalence, PDAG encoding, collider exceptions, and limits of data alone; defers full causal identifiability.

Examples

Uses alternative DAGs, Figure 4.24’s PDAG, and the collider T → E ← L to demonstrate ambiguity and orientation.

What it assumes

Assumes conditional independence, d-separation, and causal faithfulness, while distinguishing graph recovery from causal identifiability.

What you can do after

Evaluate causal-discovery outputs as constrained DAG candidates rather than treating one observationally compatible graph as uniquely established.

How it connects

Connects Markov equivalence classes to d-separation, causal faithfulness, PDAGs, colliders, causal discovery, and structural causal models.

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Related concepts

• causal graphical modelhas part · A causal graphical model is a probabilistic or structural model whose graph represents causal relationships and whose mechanisms support reasoning about interventions.
• directed acyclic graphhas part · A directed acyclic graph is a graph with directed edges and no directed cycles.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.