1. 1Causal Inference and the KMSS

2. Predicting the future with the right model Stijn Meganck Vrije Universiteit Brussel Department of Electronics and Informatics (ETRO)

3. Inference Inference = Predicting the future Probabilistic Inference –What would be if we observed that … –P(Y|X) Causal Inference –What would be the effect of performing an intervention on… –P(Y|do(X=x)) 3Causal Inference and the KMSS

4. Causal Bayesian Network Graphical Model –Nodes = variables –Edges = cause-effect relationships Example –Season: summer/winter/spring/fall –Rain, Sprinkler, Wet, Slippery: yes/no –Sprinkler setting depends on season –Chance of rain depends on season –… Season Sprinkler Rain Wet dog Smelly

5. Causal Bayesian Network Probability Theory –Conditional probability of each variable given its parents in the graph P(X|Pa(X)) Example P(Rain=yes|Season=Summer)=0.2 P(Rain=yes|Season=Fall)=0.8 P(Smelly=yes|Wet dog=yes)=0.75 … P(Season) P(Sprinkler|Season) P(Rain|Season) P(Wet dog|Sprinkler,Season) P(Smelly|Wet dog)

6. Causal Inference Interventions –Manipulation of the causal system Causal Inference –What is the effect of this manipulation Example –How likely is it that the dog smells if the sprinkler was forced to be turned off? –…

7. Probabilistic/Causal Inference P(Wet dog=yes)=1/2

8. Probabilistic/Causal Inference P(Wet dog=yes|Smelly=yes)=3/4

9. Probabilistic/Causal Inference Forcing all dogs to be smelly by spraying them with stinky sweat spray

10. Probabilistic/Causal Inference P(Wet dog=yes|do(Smelly=yes))=1/2

11. Probabilistic/Causal Inference P(Wet dog=yes|do(Smelly=yes))=1/2 ≠ P(Wet dog=yes|Smelly=yes)=3/4

12. Probabilistic/Causal Inference So why was the answer different? –We manipulated the effect! –Manipulation of an effect does not change the probability of the cause

13. Probabilistic/Causal Inference Model –(causal) DAG Inference engine / Mathematical theory –Probabilistic Lambda-pi Junction Tree Variable Elimination –Causal do-calculus 13Causal Inference and the KMSS

14. Causal Inference do-calculus (Pearl, 2000) –Transform P(Y|do(X=x)) into P(Y|something without do()) –P(Y|something without do()) can be calculated! –Probabilistic inference 14Causal Inference and the KMSS One less do()

15. Oke. Cool! Now, let’s try it on my relationship! (Stijn Meganck, anno 2004) 15Causal Inference and the KMSS

16. Relationship CBN for dummies

18. Predict the future with the RIGHT model!

19. Example Model ABCDE …………… …………… 11.42120.310 …………… …………… …………… ……………

20. Example PC [Spirtes et al. 1993] –Initialize –Complete undirected graph

21. Example PC [Spirtes et al. 1993] –Skeleton discovery –Independencies –A || D | Ø –B || D | Ø –A || C | B –B || E | C –… –Sepset AD = Ø –Sepset AC = B

22. Example PC [Spirtes et al. 1993] –Orientation phase –Pattern –C – E – D –E not in Sepset CD

23. Assumptions Minimality –X  Y => X ~ Y | OthPa(Y) Causal Markov Condition –Each variable is independent of its non-effects given its direct causes Faithfulness –All independencies follow from the Causal Markov Condition Causal Sufficiency –No latent variables No feedback loops Oracle for independencies Accept Graphoid Axioms ( needed in proof )

24. Assumptions Faithfulness –Adjacency Faithfulness –X – Y => X ~ Y | all subsets –Orientation Faithfulness –Given an unshielded triple X - Z – Y, if X-> Z <- Y: X ~ Y | all subsets containing Z Otherwise: X ~ Y | all subsets not containing Z

25. Violation of Orientation Faithfulness Assume adjacency faithfulness X – Z –Y E not in Sepset CD C || D | E  Unfaithful triple CPC-algorithm Ramsey et al.

26. Violations of Adjacency Faithfulness Detectable violations #byte s #bits Time

27. Violation of Orientation Faithfulness Undetectable violations –Distribution not faithful to correct graph –Distribution faithful to other graph –Only happens when triangle faithfulness is violated! 27Causal Inference and the KMSS Given a set of variables with true causal DAG G, let X, Y, Z form a triangle in G: If Y is a non-collider on the path X – Y – Z, then X ~Z | all subsets not including Y If Y is collider on X – Y – Z, then X ~ Z |all subsets including Y Given a set of variables with true causal DAG G, let X, Y, Z form a triangle in G: If Y is a non-collider on the path X – Y – Z, then X ~Z | all subsets not including Y If Y is collider on X – Y – Z, then X ~ Z |all subsets including Y

28. Violations of Adjacency Faithfulness Violation of triangle faithfulness X || Y X || Z | Y

29. Where does your model come from? Expert? Experimental / Observational data? A vision? Does the system adhere to your assumptions? 29Causal Inference and the KMSS

30. Questions? 30Causal Inference and the KMSS