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Causal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg [email protected]

Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg [email protected]

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Page 1: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

CausalInference:predic1on,explana1on,andinterven1on

Lecture5:CausalityandGraphicalModels

[email protected]

Page 2: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Nextfewweeks

•  October11(Tuesdayclass!):Timeseries•  October17:Lecture+midtermreview/Q&A•  October24:Midtermexam•  October31:Projectproposaldue

•  November29andDecember6:finalpresenta1ons

Page 3: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

FinalProject

•  Projecttypes(notexhaus1ve!)– Analyzedata,adaptcausalinferencemethodtopar1culardomain

–  Comparecausalinferencemethods–  Theore1calworkoncausality(methodsormeaning)

•  Proposal– What’sthegoal?Howwillyouaccomplishit?Howwillyouknowtheprojectwassuccessful?Whatresourcesareneeded(anddoyouhavethem)?1page

Page 4: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Today

•  Whatmakesagraphicalmodelcausal?•  Howtousegraphicalmodelstoanswercausalques1ons– Predic1ngeffectsofac1ons– Counterfactualqueries– Explana1on

Page 5: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Applica1on:infantmortality

Mani,S.,&Cooper,G.F.(2004).CausalDiscoveryUsingaBayesianLocalCausalDiscoveryAlgorithm.ProceedingsofMedInfo,731-735

Page 6: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Applica1on:Organizingevidence

Lagnado,D.(2011).ThinkingaboutEvidence.InProceedingsoftheBri2shAcademy(Vol.171,pp.183-223)

Page 7: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Applica1on:Causesandeffectsofpoverty

Bessler,D.A.(2003).Onworldpoverty:Itscausesandeffects.FoodandAgriculturalOrganiza2on(FAO)oftheUnitedNa2ons,ResearchBulle2n,Rome

Page 8: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Applica1onsofcausalBNs

•  Biomedicalinforma1cs–diagnosis,prognosis•  Psychology–representa1onofcausallearning•  Economics/finance

Page 9: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Markovcondi1on

(fromlastweek)Nodeindependentofnon-descendantsgivenitsparents

X

Y Z

Y ⊥ Z | X

Page 10: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

d-separa1on

X YZ

DAGGSetofindependencies

Y ⊥ Z | X

d-separa1on

Page 11: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

d-separa1on

Equivalentstatements,forsetsofnodesX,Y,ZingraphG:– XandYared-separatedbyZ(Zcanbenodeorsetofnodes)inG

– XandYarecondi1onallyindependentgivenZ– ZblocksallpathsbetweenXandY

Page 12: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

d-separa1onandMarkovblanketMarkovblanket:setofnodesthatseparateanodefromallothersd-separa3on:Methodfordeterminingwhetherapairofnodes(orsetsofnodes)areindependentcondi1onedonanotherset

Page 13: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Defini1on:d-separa1on•  Nodevisacollideriftwoarrowheadsmeetatv

•  XandYared-connectedbyZingraphGiff–  ExistsanundirectedpathbetweenavertexinXandvertexinYs.t.foreverycolliderConthepath,CordescendantofCisinZandnonon-collideronpathisinZ

•  XandYared-separatedbyZinGifftheyarenotd-connectedbyZinG

Z YX Z YX

✓✗

Page 14: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example1

•  X→Y→Z

•  XßY→Z

Inbothcases,X,Zd-separatedbyY:nocollidersonpathfromXtoZ,andXandZnotd-connectedbyY

Page 15: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example2

•  X→Y←Z

•  X,Zd-separatedbyasetofnodesonlyifYNOTinthatset.X,Zd-connectedbyY

Page 16: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example3

•  AreY,Zd-separatedbyW?

•  No,d-connectedbyXandWisdescendent

X

YZ

W

Page 17: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

But…

Indep->manynetworksNetwork->1setindep

X YZY ⊥ Z | X

X YZ

X

YZ

Page 18: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

But…

Canruleoutsome

X YZY ⊥ Z | X

X YZ

X

YZX

YZ

X

Page 19: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

…And

HDL

Heartdisease

Genes

Heartdisease HDL

Page 20: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

…AlsoCoin1 Coin2 #obs.

H H 5

T T 3

H T 1

T H 1

P(C1 = H ^C2 = H )> P(C1 = H )P(C2 = H )5 /10 > 6 /10*6 /10

C1 /⊥C2

Page 21: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Causalinterpreta1on

•  CausalMarkovcondi1on•  Faithfulness•  Causalsufficiency

+afewothers,e.g.variables“correctly”specified

Page 22: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Causalgraph

•  Arrowsdenotedirectcauses– EdgefromXtoYmeansXcausesY

•  DAG

ads buy weather

Page 23: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

CausalMarkovcondi1on(CMC)

Nodeinthegraphisindependentofallofitsnon-descendants(directandindirecteffects)givenitsdirectcauses

Page 24: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

CMCandscreeningoff

RecallCommonCausePrinciple(CCP)IfP(X^Y)>P(X)P(Y)theneitherXcausesY(orviceversa)ortheyhaveacommoncause

Now:ifP(X^Y)>P(X)P(Y)andtheyhaveacommoncauseC,itmeansXindY|CNotethatCCPseekssinglecommoncause.CMCallowsforsetsofnodes.

Page 25: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Problems:feedback

Supply

Demand

Page 26: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Problems:Indeterminism

P(picture|switch)<P(picture|switch,sound)

TVswitch

Picture Sound

TVswitch

Picture Sound

ClosedCircuit

Spirtes,P.,Glymour,C.,&Scheines,R.(2000).Causa2on,predic2on,andsearch.MITPress

Page 27: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Problems:hiddencommoncauses

CFS

Tired Achy

Flu

Page 28: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Completenessofgraph

•  Complete:allcommoncausesincluded,allcausalrela1onsamongvariablesincluded

•  Incomplete:notallintermediatefactorsnecessarilyincluded

Page 29: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Faithfulness

Exactlythedependenciesintheunderlyingstructureholdinthedata–  i.e.Independencerela1onsnotfromchancebutfromstructure

– Nocancelingout

Page 30: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example

Smoking

Exercise

Health

- +

+

Page 31: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Anotherexample

GeneA

GeneB Phenotype

- +

+

Page 32: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Afinalexample(determinis1cchain)

X Y Z

X ⊥ Z |Y

Page 33: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Selec1onbias

fever Abdominalpain F+A

GotohospitalStayhome

Cooper,G.F.(1999).Anoverviewoftherepresenta1onanddiscoveryofcausalrela1onshipsusingbayesiannetworks.InC.Glymour&G.F.Cooper(Eds.),Computa2on,causa2on,anddiscovery.AAAIPressandMITPress

Page 34: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Howbigofaproblemisthis?

Page 35: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Recapofproblemsforfaithfulness

•  Onlytrueinlargesamplelimit•  Simpson’sparadox•  Selec1onbias•  Sta1s1caltests

Page 36: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Quickrecap

•  CMC:popula1onproducedbystructurehastheseindependencies

•  Faithfulness:popula1onhasonlytheseindependenciesWhydoweneedboth?

X Y Z

Page 37: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Causalsufficiency

•  Allcommoncausesofpairsofvariablesmeasured

•  NotsufficientifYnotmeasured

X

Y

Z

Page 38: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Completenessvs.sufficiency

Completeness:commoncausesareincludedincausalgraphSufficiency:allcommoncauseshavebeenmeasured

Page 39: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example

Intelligence

X Y Z

Scheines,R.(1997).Anintroduc1ontocausalinference.CausalityinCrisis,185-99

Page 40: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Whatifnocausalsufficiency?

•  Needtoincludeallgraphswithunmeasuredcommoncauses.

•  Ex:measuredA,B,C.FoundA�C.WithCMC,faithfulnessbutnocausalsufficiency,thefollowinggraphsareallpossible(Xisunmeasured):

A

B

C A

B

C

X

A

B

C

X ...

Page 41: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Inabsenceofsufficiency…

•  Cans1lllearnsomething– Somerela1onshipsmayappearinallgraphs– Canfindsetofallgraphsrepresen1ngindependencerela1ons,withnodesforpossiblehiddenvariables

•  Timinginforma1onhelps

Page 42: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Thingstobewareofwithinference

•  Samplesize•  Missingdata(notjustvariables)•  Mul1pletes1ng(andFDR)•  WhatstructuresDAGcan/cannotrepresent(e.g.1meseriesandfeedback)

•  Variablerepresenta1on

Page 43: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Thegoodnews

•  Canadd1me•  Canexperiment•  Methodsfortes1ngassump1ons

Page 44: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

RecapofcausalinferencewithBN

WhatmakesaBayesiannetworkcausal?Theassump1ons:CMC,sufficiency,faithfulness

Assump1ons+DataàIndependenciesàCausalBN(s)àeffectsofinterven1ons

Page 45: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

LearningBN

Samemethodswediscussedlastweek– Searchandscore– Constraintbased(e.g.PCalgorithm)

Page 46: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

UsesforBNs

•  Ac1ons– WhathappensifwedoX?

•  Counterfactuals– Whatifthingshappeneddifferently?

•  Explana1ons– WhydidXhappen?

Page 47: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Manipulability

BPA

Obesity

Page 48: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Idealmanipula1ons

•  Defini1on:changeinvalueofavariablethatdoesnotintroduceanyotherchanges(exceptthoseproducedbythechangeinvariable)

Weather

Runningspeed Aircondi1oner

Page 49: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Speeches

Popularity Dona1ons

Tes1ngpopularity,howdowemanipulateit’svalue?

Page 50: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Seeingversusdoing

Disease

Treatment

Doctor

Outcome

Hospital

Page 51: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

What’sP(C)ifIturnthesprinkleron? IsthisthesameasP(C|S=T)?

Cloudy

Sprinkler Rain

Wetgrass

Page 52: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Interven1onandjointprobability

!=justincorpora1ngevidence– Lastweek:setvalueofobservedvalues– Thisweek:setvaluebyforcingvariabletotakevalueindependentofitsparents’values

Cloudy

Sprinkler Rain

Wetgrass

Ifturnonsprinkler,thefactthatit’sonnolongergivesinfoaboutC

Page 53: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Interven1onandjointprobability

Cloudy

Sprinkler Rain

Wetgrass

P(C,S,W,R) = P(c)P(s | c)P(r | c)P(w | s, r)C,S,W ,R∑

P(C,W,R | do(s)) = P(c)P(s)P(r | c)P(w | s, r)C,W ,R∑

Page 54: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

do()operator

Modelcanhelpusdeterminetheeffectofinterven1onsP(X=x|Y=y)!=P(X=x|setY=y)Bigassump1on:cansetvariableT/F!

Page 55: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Example

P(S|do(M))

Disease

Medica1on

Sideeffect

Page 56: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

ExampleDisease

Medica1on

Sideeffect

XP(s | do(m)) = P(s | m̂))

= P(s,d, m̂d∑ ) / P(m̂) = P(s | d, m̂

d∑ )P(d | m̂)P(m̂) / P(m̂)

= P(s | d, m̂d∑ )P(d)

BUT!P(d | m̂) = P(d)P(m) / P(m) =1

SO

Page 57: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

do-calculusrules

1.  Inser1on/dele1onofobserva1ons

P(y | do(x), z,w) = P(y | do(x),w) if (Y⊥ Z|X,W)GX

Disease

Medica1on

Sideeffect

GX MeansedgesintoXdeleted

Page 58: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

do-calculusrule1examples

1.  Inser1on/dele1onofobserva1ons

P(y | do(x), z,w) = P(y | do(x),w) if (Y⊥ Z|X,W)GX

D

M

S

G GS

D

M

S

X

W

Y

Z

G

X

W

Y

Z

GX

Page 59: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

do-calculusrules

2.Ac1on/Observa1onexchangeIfremoveedgesfromZ,andindependent,canreplacedoingwithobserving

P(y | do(x),do(z),w) = P(y | do(x), z,w) if (Y⊥ Z | X,W)GXZ

X YZ

W

X YZ

W

GG-XZ

Page 60: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

do-calculusrules

3.Inser1on/dele1onofac1onsZ(W)issetofZnodesthatarenotancestorsofW-nodesin

P(y | do(x),do(z),w) = P(y | do(x),w) if (Y ⊥ Z | X,W )GX,Z (W )

X YQ

W

Z X YQ

W

Z

GX

G G–X,Z(W)

Page 61: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Summaryofdo-calculus

1.  Inser1on/dele1onofobserva1ons2.  Ac1on/Observa1onexchange3.  Inser1on/dele1onofac1ons

Ingeneral,mayhaveunobserved/hiddenvariables

Page 62: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Somecaveats

•  Time•  Modularity•  Possibilityofintervening•  Efficacy

Page 63: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Counterfactualsreminder

•  IfIhadnotgonerunning,Iwouldnothavego|enasunburn

•  Ifthepa1enthadtakenthedrug,shewouldhaverecovered

•  HadIboughtsharesofApplestockin2004,Iwouldhavemadealargeprofit

Page 64: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

PearlonCounterfactuals

Likedo(),exceptbackwardlookingandchangingvalueofvariableThreesteps

1.  Abduc1on:useevidencetointerpretpast

2.  Ac1on:changetohypothe1calvalues

3.  Predic1on:seeconsequencesofac1ons

Disease(D)

Medica1on(M)

Sideeffect(S)

Page 65: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

ExamplefromPearlIfD,thenDwoulds1llbetrueifAwerefalseDàD¬A

Court(U)

Captain(C)

A B

Death(D)

Abduc1on

Captain(C)

A B

Death(D)

Ac1on

Court(U)

Captain(C)

A B

Death(D)

Predic1on

Court(U)

Pearl,J.(2000).Causality:Models,reasoning,andinference.CambridgeUniversityPress

Page 66: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Actualcausality

Pearl:tokencause=actualcause– Whatcausedaperson’slungcancer?– Whoisresponsibleforanaccident

Page 67: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Graphicalmodelsandexplana1on

•  Graphicalmodelrepresentsrela1onshipsbetweenvariables

•  Observa1onsgivetruthvalueofvariablesinpar1cularscenario

•  Evaluatecounterfactualqueriesusingmodel+observa1ons

Page 68: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Pearl’sapproachtoactualcause

•  Basedonbuta|emptstosolveproblemswithcounterfactuals– BobandSusieandthebrokenbo|le

•  Keyidea:sustenance(mixofnecessityandsufficiency)–  IfBob’srockmissed,wouldSusie’ssustaintheglassbreaking?

Page 69: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Defini1ons

•  Depends(necessity)–  ydependsonx,ifxisnecessarytomaintainvalueofy

•  Produces(sufficiency)–  xcanproduceyifitcanbringabouteffectwhenneitherarepresent

•  Sustains–  xsustainsyifthereisatleastonecondi1onwhereYwilldifferfromyinabsenceofxANDY=yismaintainedinpresenceofxunderanysetofcondi1ons

Page 70: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

CausalBeams

•  Causalbeam:Newmodel,whereweremoveallparentsexceptthosethatminimallysustaintheirchildren.Setotherparentstosomew’.

•  xisactualcauseofyifxisnecessaryforyinthatcausalbeamforsomew’

Page 71: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Exampleofcausalbeam

•  Didthetravelerdieofthirstorpoisoning?

•  Death=CvD

X(enemy2shootscanteen)

D(dehydra1on)

p(enemy1Poisonswater)

C(cyanideIntake)

Y(death)

Pearl,J.(2000).Causality:Models,reasoning,andinference.CambridgeUniversityPress

Page 72: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Construc1ngthecausalbeam

•  True:X,D,Y,P•  False:C

•  Note:C=¬X^P

X=1

D=1

P=1

C=0

Y=1

X=shootscanteen,D=dehydra1on,Y=Death,C=cyanideintake,P=poisonswater

Sustaining

Inac1ve

Page 73: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Construc1ngthecausalbeam

•  True:X,D,Y,P•  False:C

•  Now:C=¬X

X=1

D=1

P=1

C=0

Y=1

X=shootscanteen,D=dehydra1on,Y=Death,C=cyanideintake,P=poisonswater

Sustaining

Page 74: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Construc1ngthecausalbeam

•  True:X,D,Y,P•  False:C

•  Next:Y=DvC

X=1

D=1

P=1

C=0

Y=1

X=shootscanteen,D=dehydra1on,Y=Death,C=cyanideintake,P=poisonswater

Sustaining

SustainingInac1ve

Page 75: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Construc1ngthecausalbeam

•  True:X,D,Y,P•  False:C

•  Finally:Y=D,Y=X

X=1

D=1

P=1

C=0

Y=1

X=shootscanteen,D=dehydra1on,Y=Death,C=cyanideintake,P=poisonswater

Sustaining

Sustaining

Page 76: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Whatifweareuncertain?

•  Urepresents1me1llfirstdrink

•  U=1ifcanteenemp1edbeforedrink

•  U=0otherwise

X=1

D

P=1

C

Y

u

Page 77: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Case1:u=1

•  Canteenemp1edbeforetravelerdrinks

•  Samebeamasbefore

X=1

D=1 C=0

Y=1

P=1U=1

Page 78: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Case2:u=0

•  Drinksbeforecanteenisemp1ed

•  WhatifUisuncertain?•  UseP(u)tocalculate•  P(xcausedy)=– SumofP(u)overuwherexcausedyinu

X=1

D=0

P=1

C=1

Y=1

U=0

Page 79: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Problem:Over-determina1on

•  Whichriflemancausedthedeath?

•  Counterfactual:–  IfnotA,thenBwouldhavecausedD

Court(U)

Captain(C)

A B

Death(D)

Page 80: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Problem:Over-determina1on

•  Whichriflemancausedthedeath?

•  Counterfactual:–  IfnotA,thenBwouldhavecausedD

•  Structural:– AsustainsDagainstB

Court(U)

Captain(C)

A

Death(D)

B=False

Page 81: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Par1alsolu1on:defaults

Example:NeitherJacknorJillwateraplant,andtheplantdies.Jillusuallywatersit,JackneverdoesWho’satfault?

Halpern,JosephY."DefaultsandNormalityinCausalStructures."KR.2008.JosephY.HalpernandChristopherHitchcock.GradedCausa1onandDefaults.TheBri1shJournalforthePhilosophyofScience,66(2):413–457,2015.

Page 82: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

•  Default:whatwethinkistruemostofthe1me•  Typicality:whatusuallyhappens(frequency)•  Norms:judgmentofwhatshouldusuallyhappen

•  Mainidea:forcounterfactualswecomparepossibleworlds,nowwerankthem

•  Recallpenproblem!

Page 83: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Challengesfortheactualcause

•  Type!=Token•  Subjec1vity•  Timing•  Limitedbycompletenessofmodel

Page 84: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Challenge:subjec1vity

•  Variableschosenandwhatvaluestheyaresettoaffectoutcome– Smokingvs.dura1onofsmoking

•  Note:bothqueriesandtheiranswersmaythendiffer

Intoxica1on

CarAccident

WeatherEmo1onalstate

Page 85: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Challenge:1me

•  Bobstartssmoking(S)Wednesday.He’sdiagnosedwithlungcancer(LC)onFriday.DidhisScausehisLC?

•  Boblaterdies.WasLCthecause?

Smoking

Lungcancer

Death

Page 86: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

InferencerecapBN DBN Granger Temporallogic

Results Graph

Time No

Data C/D/M

Cycles No

Latentvars. Yes

Predic1on Yes

Tokencause

Counterfactual-based

BN DBN Granger Temporallogic

Results Graph Graph Rela1onships Rela1onships

Time No Setoflags Singlelag* Window

Data C/D/M C/D/M* C D/M

Cycles No Yes Yes Yes

Latentvars

Yes Yes No No

Predic1on

Yes Yes No No

Tokencause

Counterfactual-based

No No Probabilis1c

Page 87: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Furtherreading•  Graphicalmodelsandcausality–  Spirtes,P.,Glymour,C.,&Scheines,R.(2000).Causa2on,predic2on,andsearch.MITPress

–  Pearl,J.(2000/2009).Causality:Models,reasoning,andinference.CambridgeUniversityPress.

•  Actualcause–  Pearl’sbook– Halpern,J.Y.,&Pearl,J.(2005).Causesandexplana1ons:Astructural-modelapproach.PartI:Causes.TheBri2shJournalforthePhilosophyofScience,56(4),843-887.

Page 88: Causal Inference: predic1on, explana1on, and interven1onCausal Inference: predic1on, explana1on, and interven1on Lecture 5: Causality and Graphical Models Samantha Kleinberg samantha.kleinberg@stevens.edu

Fornextweek

•  Howcanwefindhowlongittakesforsmokingtocauselungcancer?

•  Whentobuy/sellastockaÇeryouhearsomenews?

•  ReadCPT2.4.2


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