Causality / Methods
verifiedCausal Discovery
Given only observational data, which way do the arrows point? Sometimes you can tell and often you cannot: several different graphs can produce exactly the same correlations, and no amount of that data separates them. What discovery algorithms return is usually a set of graphs rather than one, and the honest output says so.
Constraint-based methods test conditional independences and keep every graph consistent with them; score-based methods search graph space against a penalised likelihood. Both are limited by the Markov equivalence class — the arrows they cannot orient are not a failure of the search. Extra assumptions buy orientation: additive noise, non-Gaussianity, or observed interventions, each trading generality for a definite answer.
Two DAGs are Markov equivalent when they share a skeleton and the same v-structures, and no observational test distinguishes them. Continuous relaxations replace the combinatorial search over orderings with a smooth acyclicity constraint — tr(e super A∘A ) − d = 0 is zero exactly for a DAG — which turns structure learning into ordinary constrained optimisation.
10 queries against 10 keys; a brighter cell means more of that query's attention went to that key. Each query sees itself and everything before it, and nothing after — the upper triangle is masked.
Variables against variables under a topological order, the upper triangle empty because a cause cannot follow its effect. Drag the variable count up to watch the space of candidate graphs grow — it grows faster than the data available to choose among them.
Reviewed by opendroid · 2026-08-18
- arXiv:1803.01422 — DAGs with NO TEARS: Continuous Optimization for Structure Learning
- arXiv:1309.6779 — Causal Discovery with Continuous Additive Noise Models