Intro to Causalitytoni/Courses/Fairness/Lectures/... · Quick Note on Fairness and Causality •...

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Intro to Causality David Madras October 22, 2019

Transcript of Intro to Causalitytoni/Courses/Fairness/Lectures/... · Quick Note on Fairness and Causality •...

Page 1: Intro to Causalitytoni/Courses/Fairness/Lectures/... · Quick Note on Fairness and Causality • Many fairness problems (e.g. loans, medical diagnosis) are actually causal inference

IntrotoCausalityDavidMadras

October22,2019

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Simpson’sParadox

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TheMontyHallProblem

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TheMontyHallProblem

1. Threedoors– 2havegoatsbehindthem,1hasacar(youwanttowinthecar)

2. Youchooseadoor,butdon’topenit3. Thehost,Monty,opensanother door(nottheoneyouchose),and

showsyouthatthereisagoatbehindthatdoor4. Younowhavetheoptiontoswitchyourdoorfromtheoneyou

chosetotheotherunopeneddoor5. Whatshouldyoudo?Shouldyouswitch?

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TheMontyHallProblem

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What’sGoingOn?

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Causation!=Correlation

• Inmachinelearning,wetrytolearncorrelationsfromdata• “WhencanwepredictXfromY?”

• Incausalinference,wetrytomodelcausation• “WhendoesXcause Y?”

• Thesearenotthesame!• Icecreamconsumptioncorrelateswithmurderrates• Icecreamdoesnotcausemurder(usually)

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CorrelationsCanBeMisleading

https://www.tylervigen.com/spurious-correlations

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CausalModelling

• Twooptions:1. Runarandomizedexperiment

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CausalModelling

• Twooptions:1. Runarandomizedexperiment2. Makeassumptionsabouthowourdataisgenerated

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CausalDAGs

• PioneeredbyJudeaPearl• Describesgenerativeprocessofdata

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CausalDAGs

• PioneeredbyJudeaPearl• Describes(stochastic)generativeprocessofdata

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CausalDAGs

• Tisamedicaltreatment• Yisadisease• Xareotherfeaturesaboutpatients(say,age)

• Wewanttoknowthecausaleffect ofourtreatmentonthedisease.

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CausalDAGs

• Experimentaldata:randomizedexperiment• WedecidewhichpeopleshouldtakeT

• Observationaldata:noexperiment• PeoplechosewhetherornottotakeT

• Experimentsareexpensiveandrare• Observationscanbebiased• E.g.WhatifmostlyyoungpeoplechooseT?

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AskingCausalQuestions• SupposeTisbinary(1:receivedtreatment,0:didnot)• SupposeY isbinary(1:diseasecured,0:diseasenotcured)• Wewanttoknow“Ifwegivesomeonethetreatment(T=1), whatistheprobabilitytheyarecured(Y=1)?”

• Thisisnot equaltoP(Y=1|T=1)• Supposemostlyyoungpeopletakethetreatment,andmostwerecured,i.e.P(Y=1|T=1)ishigh• Isthisbecausethetreatmentisgood?Orbecausetheyareyoung?

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Correlation vs.Causation

• Correlation

• Intheobserveddata,howoftendopeoplewhotakethetreatmentbecomecured?• Theobserveddatamaybebiased!!

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Correlationvs.Causation

• Let’ssimulate arandomizedexperiment• i.e.• CutthearrowfromXtoT• Thisiscalledado-operation

• Then,wecanestimatecausation:

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Correlationvs.Causation

• Correlation

• Causation– treatmentisindependent ofX

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InversePropensityWeighting

• Cancalculatethisusinginversepropensityscores• RatherthanadjustingforX,sufficienttoadjustforP(T|X)

P(T|X)

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InversePropensityWeighting

• Cancalculatethisusinginversepropensityscores• Thesearecalledstabilizedweights

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MatchingEstimators

• Matchupsampleswithdifferenttreatmentsthatareneartoeachother• Similartoreweighting

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Review:Whattodo withacausalDAG

ThecausaleffectofTonYis

Thisisgreat!Butwe’vemadesomeassumptions.

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Simpson’sParadox,Explained

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Simpson’sParadox,Explained

Size

Trmt Y

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Simpson’sParadox,Explained

Size

Trmt Y

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MontyHallProblem,Explained

Boringexplanation:

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MontyHallProblem,Explained

Causalexplanation:• Mydoorlocationis

correlatedwiththecarlocation,conditioned onwhichdoorMontyopens!

CarLocationMyDoor

OpenedDoor

https://twitter.com/EpiEllie/status/1020772459128197121

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MontyHallProblem,Explained

Causalexplanation:• Mydoorlocationis

correlatedwiththecarlocation,conditioned onwhichdoorMontyopens!

• ThisisbecauseMontywon’tshowmethecar

• Ifhe’sguessingalso,thencorrelationdisappears

CarLocationMyDoor

Monty’sDoor

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StructuralAssumptions

• AllofthisassumesthatourassumptionsabouttheDAGthatgeneratedourdataarecorrect

• Specifically,weassumethattherearenohiddenconfounders• Confounder:avariablewhichcausallyeffectsboththetreatment(T)andtheoutcome(Y)• No hiddenconfoundersmeansthatwehaveobservedallconfounders

• Thisisastrongassumption!

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HiddenConfounders

• CannotcalculateP(Y|do(T))here,sinceUisunobserved

• Wesayinthiscasethatthecausaleffectisunidentifiable• Eveninthecaseofinfinitedataandcomputation,wecannevercalculatethisquantity

X

T Y

U

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WhatCanWeDowithHiddenConfounders?

• Instrumentalvariables• Findsomevariablewhicheffectsonly thetreatment

• Sensitivityanalysis• Essentially,assumesomemaximumamountofconfounding• Yieldsconfidenceinterval

• Proxies• Otherobservedfeaturesgiveusinformationaboutthehiddenconfounder

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InstrumentalVariables

• Findaninstrument – variablewhichonlyaffectstreatment• Decouplestreatmentandoutcomevariation

• Withlinearfunctions,solveanalytically• Butcanalsouseanyfunctionapproximators

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SensitivityAnalysis

• Determinetherelationshipbetweenstrengthofconfoundingandcausaleffect• Example:Doessmokingcauselungcancer?(wenowknow,yes)• Theremay beagenethatcauseslungcancerand smoking• Wecan’tknowforsure!• However,wecanfigureouthowstrongthisgenewouldneedtobetoresultintheobservedeffect• Turnsout– verystrong

X Gene

Smoking Cancer

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SensitivityAnalysis

• Theideais:parametrizeyouruncertainty,andthendecidewhichvaluesofthatparameterarereasonable

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UsingProxies

• Insteadofmeasuringthehiddenconfounder,measuresomeproxies(V=fprox(U))• Proxies:variablesthatarecausedbytheconfounder• IfUisachild’sage,Vmightbeheight

• Iffprox isknownorlinear,wecanestimatethiseffect

X

T

U

Y V

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UsingProxies

• Iffprox isnon-linear,wemighttrytheCausalEffectVAE• LearnaposteriordistributionP(U|V)withvariationalmethods• However,thismethoddoesnotprovidetheoreticalguarantees• Resultsmaybeunverifiable:proceedwithcaution!

X

T

U

Y V

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CausalityandOtherAreasofML

• ReinforcementLearning• Naturalcombination– RLisallabouttakingactionsintheworld• Off-policylearningalreadyhaselementsofcausalinference

• Robustclassification• Causalitycanbenaturallanguageforspecifyingdistributionalrobustness

• Fairness• Ifdatasetisbiased,MLoutputsmightbeunfair• Causalityhelpsusthinkaboutdatasetbias,andmitigateunfaireffects

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QuickNoteonFairnessandCausality

• Manyfairnessproblems(e.g.loans,medicaldiagnosis)areactuallycausalinferenceproblems!• WetalkaboutthelabelY– however,thisisnotalwaysobservable• Forinstance,wecan’tknowifsomeonewould returnaloanifwedon’tgiveonetothem!• Thismeansifwejusttrainaclassifieronhistoricaldata,ourestimatewillbebiased• Biasedinthefairnesssenseand thetechnicalsense

• Generaltakeaway:ifyourdataisgeneratedbypastdecisions,thinkveryhardabouttheoutputofyourMLmodel!

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FeedbackLoops

• Takesustopart2…feedbackloops• WhenMLsystemsaredeployed,theymakemanydecisionsovertime• Soourpastpredictionscanimpactourfuturepredictions!• Notgood

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UnfairFeedbackLoops

• We’lllookat“FairnessWithoutDemographicsinRepeatedLossMinimization”(Hashimotoetal,ICML2018)• Domain:recommendersystems• Supposewehaveamajoritygroup(A=1)andminoritygroup(A=0)• Ourrecommendersystemmayhavehighoverallaccuracybutlowaccuracyontheminoritygroup• Thiscanhappenduetoempiricalriskminimization(ERM)

• Canalsobeduetorepeateddecision-making

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RepeatedLossMinimization

• Whenwegivebadrecommendations,peopleleaveoursystem• Overtime,thelow-accuracygroupwillshrink

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Distributionally RobustOptimization

• Upweight exampleswithhighlossinordertoimprovetheworstcase• Inthelongrun,thiswillpreventclustersfrombeingunderserved

• Thisendsupbeingequalto

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Distributionally RobustOptimization

• Upweight exampleswithhighlossinordertoimprovetheworstcase• Inthelongrun,thiswillpreventclustersfrombeingunderserved

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Conclusion

• Yourdataisnotwhatitseems• MLmodelsonlyworkifyourtraining/testsetactuallylookliketheenvironmentyoudeploythemin• Thiscanmakeyourresultsunfair• Orjustincorrect

• Soexamineyourmodelassumptionsanddatacollectioncarefully!


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