The psychology of learning and motivation. Volume sixty one

328 Pages·2014·5.15 MB·English

by  Ross, Brian H

Series Editor
BRIAN H. ROSS
Beckman Institute and Department of Psychology
University of Illinois, Urbana, Illinois
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CONTRIBUTORS
JeffreyAnnis
DepartmentofPsychology,UniversityofSouthFlorida,Tampa,Florida,USA
PaulAtchley
DepartmentofPsychology,UniversityofKansas,Lawrence,Kansas,USA
WilliamR.Aue
DepartmentofPsychologicalSciences,PurdueUniversity,WestLafayette,Indiana,
andDepartmentofPsychology,SyracuseUniversity,Syracuse,NewYork,USA
ColinBla¨ttler
ResearchCenteroftheFrenchAirForce(CReA),Salon-de-Provence,France
GlenE.Bodner
DepartmentofPsychology,UniversityofCalgary,Calgary,Alberta,Canada
AmyH.Criss
DepartmentofPsychology,SyracuseUniversity,Syracuse,NewYork,USA
Andre´ Didierjean
UniversityofFranche-Comte´ &InstitutUniversitairedeFrance,Besanc¸on,France
VincentFerrari
ResearchCenteroftheFrenchAirForce(CReA),Salon-de-Provence,France
UlrikeHahn
DepartmentofPsychologicalSciences,Birkbeck,UniversityofLondon,London,
UnitedKingdom
AdamJ.L.Harris
DepartmentofCognitive,Perceptual&BrainSciences,UniversityCollegeLondon,
London,UnitedKingdom
GretaJames
DepartmentofPsychology,UniversityofWaterloo,Waterloo,Ontario,Canada
CharlesW.Kalish
DepartmentofEducationalPsychology,UniversityofWisconsin-Madison,Madison,
Wisconsin,USA
JeffreyD.Karpicke
DepartmentofPsychologicalSciences,PurdueUniversity,WestLafayette,Indiana,USA
DerekJ.Koehler
DepartmentofPsychology,UniversityofWaterloo,Waterloo,Ontario,Canada
SeanLane
DepartmentofPsychology,LouisianaStateUniversity,BatonRouge,Louisiana,USA
ix
x Contributors
MelissaLehman
DepartmentofPsychologicalSciences,PurdueUniversity,WestLafayette,Indiana,USA
KennethJ.Malmberg
DepartmentofPsychology,UniversityofSouthFlorida,Tampa,Florida,USA
MichaelE.J.Masson
DepartmentofPsychology,UniversityofVictoria,Victoria,BritishColumbia,Canada
RichardM.Shiffrin
DepartmentofBrainandPsychologicalSciences,IndianaUniversity,Bloomington,Indiana,
USA
JordanT.Thevenow-Harrison
DepartmentofEducationalPsychology,UniversityofWisconsin-Madison,Madison,
Wisconsin,USA
CHAPTER ONE
Descriptive and Inferential
Problems of Induction: Toward
a Common Framework
Charles W. Kalish1, Jordan T. Thevenow-Harrison
DepartmentofEducationalPsychology,UniversityofWisconsin-Madison,Madison,Wisconsin,USA
1Correspondingauthor:e-mailaddress:[email protected]
Contents
1. Introduction 2
2. Theory-BasedandSimilarity-BasedInductiveInference 3
3. InductionasStatisticalInference:DescriptiveandInferentialProblems 6
4. InductiveandTransductiveInference:SampleandPopulationStatistics 9
5. UsingTransductiveInference 12
6. Summary:TransductiveandEvidentialTheoriesofInference 16
7. DistinguishingTransductiveandEvidentialInferences 17
7.1 PeopleandStatistics 20
8. DevelopingSolutionstoDescriptiveProblems 21
8.1 CorrelationsandAssociations 22
8.2 ComponentialAnalysis 22
8.3 TransitionProbabilities 23
8.4 AbsolutetoRelationalStatistics 24
8.5 GlobaltoSpecificRelations 25
8.6 SimpletoComplex 26
8.7 SummaryofSolutionstoDescriptiveProblems 27
9. SolutionstoInferentialProblems 27
9.1 TransductiveInference 28
9.2 BayesianInference 28
9.3 BetweenTransductiveandEvidentialInference 29
9.4 CommunicativeBias 30
9.5 IntentionalVersusIncidentalLearning 31
9.6 SummaryofSolutionstoInferentialProblems 31
10. SummaryandConclusions 32
References 34
Abstract
Therearemanyaccountsofhowhumansmakeinductiveinferences.Twobroadclasses
ofaccountsarecharacterizedas“theorybased”or“similaritybased.”Thisdistinctionhas
PsychologyofLearningandMotivation,Volume61 #2014ElsevierInc. 1
ISSN0079-7421 Allrightsreserved.
http://dx.doi.org/10.1016/B978-0-12-800283-4.00001-0
2 CharlesW.KalishandJordanT.Thevenow-Harrison
organizedasubstantialamountofempiricalworkinthefield,buttheexactdimensions
ofcontrastbetweentheaccountsarenotalwaysclear.Recently,bothaccountshave
usedconceptsfromformalstatisticsandtheoriesofstatisticallearningtocharacterize
humaninductiveinference.Weextendtheselinkstoprovideaunifiedperspectiveon
inductionbasedontherelationbetweendescriptiveandinferentialstatistics.Mostwork
inPsychologyhasfocusedondescriptiveproblems:Whichpatternsdopeoplenoticeor
representinexperience?Wesuggestthatitissolutionstotheinferentialproblemof
generalizingorapplyingthosepatternsthatrevealsthemorefundamentaldistinction
between accounts of human induction. Specifically, similarity-based accounts imply
thatpeoplemaketransductiveinferences,whiletheory-basedaccountsimplythatpeo-
plemakeevidentialinferences.Incharacterizingclaimsaboutdescriptiveandinferential
components of induction, we highlight points of agreement and disagreement
betweenalternativeaccounts.Adoptingthecommonframeworkofstatisticalinference
alsomotivatesasetofempiricalhypothesesaboutinductiveinferenceanditsdevelop-
ment across age and experience. The common perspective of statistical inference
reframes debates between theory-based and similarity-based accounts: These are
notconflictingtheoreticalperspectives,butratherdifferentpredictionsaboutempirical
results.
1. INTRODUCTION
Inductionisafundamentalcognitiveprocess.Broadlyconstrued,any
predictionorexpectationaboutempiricalphenomenarepresentsaninduc-
tive inference. Within Psychology, learning, categorization, probability
judgments,anddecision-makingareallcentralformsofinductiveinference.
Other psychological processes may be treated as involving induction (e.g.,
perception,languagecomprehension).Therearelikelymanydifferentpsy-
chologicalmechanismsinvolvedinmakinginductiveinferences,manyways
people make predictions and form expectations. This chapter focuses on a
paradigmcase:Learningfromexamples.Basedonexperiencewithalimited
setofexamples,peoplegeneralizetonewexamples.Notallinductiveinfer-
encesneedtakethisform(thoughbybeinggenerousaboutwhatcountsas
an “example” and an “expectation” almost any induction may). However,
learningfromexamplescapturesanimportantsetofphenomena,andcovers
a broad enough range that characterizations may apply to other forms of
inductive inference.
This chapter further focuses on developmental questions. How do
infants and young children learn from examples, and what changes across
the lifespan? The development of inductive inference is a particularly
important question because induction is both (potentially) a subject of
DescriptiveandInferentialProblems 3
developmentandamechanismorsourceofdevelopmentalchange.Manyof
the changes that occur over the lifespan may reflect learning from experi-
ence: Children learn more about their world and culture and so become
more adult-like in their inferences (e.g., Carey, 1985).
Infantsclearlylearnfromexperience(e.g.,Rovee-Collier&Barr,2001).
Atthesametime,therearemanydevelopmentalprocessesthatlikelyaffect
the nature of such learning. As children acquire language, develop abstract
representations, and are exposed to formal instruction, what and how they
learn from examples changes. Whether there is continuity in processes of
inductive inference, or whether development involves the acquisition of
newformsofinferenceisamajorsourceofdebate.Debatesaboutthenature
ofinductiveinferencehavealonghistoryincognitivedevelopment.Alter-
native positions have been clearly articulated and defended with empirical
results. One of the primary goals of this chapter is to provide a unified
account of these alternatives.
2. THEORY-BASED AND SIMILARITY-BASED INDUCTIVE
INFERENCE
There are two primary approaches to inductive inference, similarity
based and theory based. This basic dichotomy appears in many forms, with
alternatives characterized in slightly different ways (e.g., “emergent” vs.
“structured probability,” Griffiths, Chater, Kemp, Perfors, & Tenenbaum,
2010;McClellandetal.,2010).Insimilaritytheories,learningfromexamples
involves forming associations or other representations of patterns of
co-occurrence (e.g., Hampton, 2006, see papers in Hahn & Ramscar,
2001). Such accounts typically posit continuity in inductive inference, both
phylogenetically and ontogenetically. They tend to invoke domain-general
mechanisms and emphasize internalizing structure from environment.
Changes in inductive inference are a result of changing experience: As the
childformsdifferentassociations,comestorepresentmoreormorecomplex
patterns in experience, their thinking changes. Alternative, theory-based
approaches treat learning from examples as a form of hypothesis testing
(Chater, 2010; Gelman & Koenig, 2003; Gopnik et al., 2004; Murphy &
Medin, 1985). Such accounts often emphasize domain-specificity (in the
hypotheses available) and are congenial to nativists (e.g., innate sources of
hypotheses). Theory-based views involve some developmental discontinu-
ities,atleastphylogenetically(itisunlikelythatsimpleorganismstesthypoth-
eses). As hypothesis-testing seems to be a more complex cognitive process
4 CharlesW.KalishandJordanT.Thevenow-Harrison
thanassociationformation,anaturaldevelopmentalhypothesisisthatinfants
maystartmakingsimilarity-basedinductionsbutacquiretheory-basedinduc-
tion at some point.
Asthedescriptionsofferedaboveillustrate,similarity-basedandtheory-
based views differ on a number of dimensions. While distinctions between
the two approaches have organized much of contemporary research (see
Feeney & Wilburn, 2008; Gelman & Medin, 1993; Pothos, 2005;
Sloutsky&Fisher,2008;Smith,Jones,&Landau,1996),itisnotalwaysclear
just where the critical differences lie. For example, similarity-based
approaches tend to emphasize domain generality and continuity across
development,butneednotdoso.Inmotivatingourproposalforaunifying
framework,wefirstconsidersomealternativewaysofcharacterizingthetwo
approaches to inductive inference.
Similarity-basedtheoriesareoftencharacterizedby“bottom-up”build-
ing of associations from basic, perceptual, experience (Smith et al., 1996).
Theory-based accounts emphasize “top-down” application of conceptual
structures or constraints to organize experience (Wellman & Gelman,
1992). In the developmental literature, similarity-based theories are often
associatedwiththeviewthatyoungchildren’sinductiveinferencesarebased
on apparent, perceptual features (see Keil, Smith, Simons, & Levin, 1998;
Springer, 2001). Children learn from examples by forming associations
between perceptual features. Theory-based views hold that even young
children organize experience using abstract, theoretical, concepts, such as
“cause” or “belief” (Carey, 1995; Wellman & Gelman, 1992). Children
canlearnnotjustperceptualassociationsinexperience,butrelationsinvolv-
ing nonperceptual properties as well (Mandler, 2004). This framing of the
alternatives has led to substantial research about children’s representations
of nonperceptual information (e.g., Gelman & Markman, 1986; Kalish,
1996;Wellman&Estes,1986;butseeSloutsky&Fisher,2008).However,
we suggest that the perceptual versus abstract features distinction is largely
orthogonaltowhetherinductionisbestcharacterizedassimilarityortheory
based. For example, it is quite possible to learn similarity relations among
abstract features.
Aseconddimensionofdistinctionisrulesversusgradedrepresentations.
Theory-based inferences are characterized as all-or-none judgments based
on rules or criterial features (Sloutsky, Lo, & Fisher, 2001). For example,
indeterminingthecategorymembership(andthusthebasisforfuturepre-
dictions) of an animal, its parentage is particularly informative and other
information (e.g., location) is largely irrelevant. The critical features may
DescriptiveandInferentialProblems 5
be unknown: An underlying “essence” determines category membership
and forms the basis for inductive inferences (Gelman, 2003). The point is
that adistinctionis madebetweenthosefeatures that truly determinecate-
gorymembership,orcauseobjectstohavethepropertiestheydo,andthose
featuresthataremerelyassociatedwithotherfeatures.Theory-basedinduc-
tiveinferencedependsonidentifyingthecritical(causal,essential)features.
In contrast, similarity-based theories emphasize patterns of associations
acrossanumberoffeatures.Anypatternofassociationcanbeusefulforpre-
diction and inference: There is no distinction between “really” and
“merely”associated.Featuresareusefulforpredictionbecauseoftheirinfor-
mationalvalue:Doesobservingonefeatureaffecttheprobabilityofobserv-
ing another? This perspective tends to emphasize graded or probabilistic
judgments (Yurovsky, Fricker, Yu, & Smith, 2013). Multiple features or
patternsofassociationcanbepresentatanyonetime(e.g.,ananimallooks
likeadogbuthadbearparents).Inferenceinvolvescombiningthesefeatures
(e.g.,weighting bypastdiagnosticity;see Younger,2003). Researchmoti-
vatedbythiscontrastaddressesselectivityininductivejudgments(Kloos&
Sloutsky, 2008; Sloutsky et al., 2001). Do children privilege some features
over others when making inductive inferences? Can such preferences be
tracedbacktopatternsofassociationordotheyinvolvebeliefsaboutcauses
and essences (Gelman & Wellman, 1991; Kalish & Gelman, 1992)? For
example, when a child judges that an animal that looks like a dog but has
bear parents will have internal organs of a bear rather than a dog, are they
usingaruleorprinciplethat“parentsmatter”oraretheybasingtheirjudg-
ment on the past reliability of parentage over appearance? The question of
thegradedversuscriterialbasisofchildren’sinferenceshasmotivatedsignif-
icant research but is also largely orthogonal to the distinction we wish
to draw.
There are a number of other ways of distinguishing between theory-
based and similarity-based inductive inference. For example, theories may
involve conscious deliberate judgment, while similarity is unconscious
andautomatic(seeSmith&Grossman,2008).Wesuggestthatallthesedis-
tinctionsaresymptomsorconsequencesof amorefundamentaldifference.
Theory-based accounts treat examples as evidential; similarity-based
accounts treat examples as constitutive. In theory-based inference, the
examples a person has encountered provide evidence for a relation
(Gelman,2003;Gopnik&Wellman,1994;Murphy&Medin,1985).That
allthedogsonehasseensofarhavebarkedprovidesevidencethatthenext
dog observed will also bark. In contrast, for similarity-based views, the
6 CharlesW.KalishandJordanT.Thevenow-Harrison
predictionaboutthenextdogisakindofreportofthatpastexperience.The
characterizations of theory-based inference discussed above are a conse-
quence of attempts to explicate evidential inferences in terms of scientific
theories (see Gopnik & Wellman, 1992, 1994). Scientists use theories to
interpret evidence, and evidence is used to develop and refine theories.
Toassertthatyoungchildrentreatexamplesasevidenceistoassertthatthey
dowhat scientists do.There is also atradition of formal approaches to evi-
denceevaluationinthestatisticalandphilosophicalliterature.Aspsycholo-
gists have adopted these formal approaches, a new characterization of
theory-based inference has been developed (Gopnik et al., 2004; see
Oaksford & Chater, 2007; Tenenbaum & Griffiths, 2001; Xu &
Tenenbaum, 2007a). Theory-based inference is a type of statistical infer-
ence. Similarity-based inference is also a type of statistical inference. This
common grounding in statistical theory, induction as statistical inference,
provides a unified perspective on theory-based and similarity-based
accounts. We develop this unified perspective below and use it to identify
justwhatisatissueinthedebatebetweentheory-basedandsimilarity-based
views. This perspective leads directly to empirical tests of the two views.
3. INDUCTION AS STATISTICAL INFERENCE:
DESCRIPTIVE AND INFERENTIAL PROBLEMS
Makingastatisticalinferenceinvolvestwosteps:describingtheavail-
able data and then generalizing. For example, after conducting an experi-
ment, a researcher needs to describe her results. She may compute the
mean and standard deviations of observations in the various conditions.
Thosedescriptivestatisticsconveyinformationaboutpatternsinthesample,
in the observed data. The researcher’s next step is to make some general
claims basedon those descriptivestatistics. Shewants to estimatea popula-
tion parameter or identify the generative process that produced the obser-
vations.Thisstepinvolvescomputinginferentialstatistics(e.g.,at-test).Ina
nutshell,similarity-basedapproachestoinductiveinferencefocusonthefirst
step:Thedescriptiveproblemofcharacterizingpatternsinthedata.Theory-
basedapproachesfocusonthesecondstep:Theinferentialproblemofesti-
matingagenerativeprocess.Infleshingoutthischaracterizationofinductive
inference,weintroduceanumbertermsanddistinctions,manyofwhichare
illustrated in Fig. 1.1.
The descriptive problem in inductive inference is noticing patterns in
experience. Some patterns may be obvious, some less so. Children may