https://www.bradyneal.com/causal-inference-course
Introduction to Causal Inference라는 강의를 듣고 정리했습니다.

11. Causal Discovery from Interventions

11-1. Structural Interventions

Single-Node Interventions

2 Variables

• Need more than one intervention to identify the graph
• Two interventions are sufficient and necessary to identify the graph.

Complete Graphs Are the Worst Case

• 같은 skeleton이고, 같은 immoralities이면 두 그래프는 markov equivalent하다.
• complete graph는 immoralities가 없다. → essential graph가 complete skeleton graph
• immorality는 아래 그림에서 A와 B에 edge가 없다.
  

n variables

• Single Variable Interventions: n – 1 are sufficient for n > 2
• empty set까지 포함하면 worst case에서 n개가 necessary
  
• Single Variable Interventions: n – 1 Are Necessary in the Worst Case
  

Multi-Node Interventions

$log_2(n)+1$ multi-node interventions가 sufficient
$log_2(n)+1$ multi-node interventions가 necessary in the worst case
$log_2(c)$ multi-node interventions이 sufficient, necessary in the worst case (c: largest clique)

11-2. Parametric Interventions

Structural vs. Parametric Interventions

• structural intervention은 구조를 다 break
  
  

Number of parametric single-node intervention

• n – 1 interventions are sufficient
• n – 1 interventions are necessary in the worst case (same as with structural interventions)

11-3. Interventional Markov Equivalence

Interventions Introduce Immoralities: Single-Node

• structure를 보존하기 때문에 immorality가 생긴다.
  
  
  
• 같은 skeletons과 immoralities를 가지면, single-node interventions을 한 두 augmented graph는 interventionally markov equivalent
• n – 1 interventions are sufficient
• n – 1 interventions are necessary in the worst case (same as with structural interventions)

Interventional Graph: Multi-Node Interventions

• 같은 skeletons과 immoralities를 가지면, multi-node interventions을 한 두 augmented graph는 interventionally markov equivalent
  

11-4. Miscellaneous Other Settings