Child Development Perspectives (In Press) The theory theory 2.0: Probabilistic models and cognitive development Commentary on Nora Newcombe Neoconstructivism

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Child Development Perspectives

(In Press)


The theory the
ory 2.0: P
robabilistic models

and cognitive development



Commentary on Nora Newcombe Neoconstructivism



Alison Gopnik Dept. Of Psychology University of California at Berkeley, Berkeley, CA,
94704


Gopnik@berkeley.edu


Newcombe’s piece is a
welcome attempt to
reconcile the profusion of terrific

empirical work in cogn
itive development with the
unsatisfactory

traditional
theoretical

positions
. M
ost

of her points are
very
well
-
taken
, and

define an
emer
ging
empirical consensus
. However,
she doesn’t capture one

important
theoretical
dimension
.
Newcombe opposes nativism to everything els
e, combining
connectionist and dynamic systems theories, in
formation processing theories,
the
“theory theory”
,

statistica
l learning a
nd Bayesian inference. But
there is an
alternative split that is equally i
mportant and that
carve
s

up the theoretical territory
rather differently. This is a contrast between representational and non
-
representational accounts of development.

Wh
ile almost all nativist approaches are
representationa
l, among empiricists there is an important divide between those
who, like nativists, embrace representation
,

and those who deny it.



A deep theoretical tension lies at the heart of develo
pmental cognit
ive science,
reflecting a deep
tension in epistemology.

Since

Plato
,

two facts about
human
knowledge.

have clashed.

We
seem to have
abstract,
structured and accurate
rep
resentations of the world



representations that allow a wide range of new
inferences
.
But

all that reaches u
s
from the world

are
concrete
,

prob
abilistic
patterns of sensory stimuli
.
How do we get such powerful knowledge from such
impoverished data?
N
ativists
,

from Plato

to “core knowledge” theorists
,

argue
that
the
abstr
act structure is act
ually innate, we only appear to learn it from experience
.
E
mpiricists
,

from Aristotle to the connectionists
, argue
that we only appear

to have
abstract
,

structured
,

representations


actually we just
ac
cumulate specific
associations.


The empirical
accom
plishments

of the last thirty yea
rs have

actually made the
theoretical tension

worse. We might have thought
,

as Piaget did
,

that children begin
with concr
ete particular “sensorimotor”

schemes and somehow gradually

construct
more abstract representations
.
B
ut
,

e
mpirically
,

as Newcombe points out,
o
ne of the
most important
discoveries o
f the last thirty years is that

children

even young

infants

already
have abstract, structured, representations of the world: intuitive
theories and grammars, conceptual hierar
chies and phonological
and spatial
maps.
But, as she also
points out,
we have

accumulated equally compelling evidence that
those representations change as a result of experience and learning. In fact,
we’ve
discovered that
e
ven young infants
learn

in surpr
isingly complex and sophisticated
ways.

They transform their representations based on concrete experiences
--

the
contingent, probabilistic evidence of their senses.
How is this possible?


Connectionist and

dynamic

theories
, like their associationist precu
rsors,

allow
learning but deny that there ar
e abstract representations. N
ativism
allows
representation but denies that there is substantive learning.
Many e
mpirically
minded de
velopmental psychologists,
like those
Newcombe

describes
,
have been
dissatisfied

w
ith both those options. In fact
,

for that very reason
,

many of us

have
advocated the “theory theory”


the idea that children’s learning is like theory
change in science

because in science we also see both rich structure and
significant learning.


H
owev
er, until recently, there were no
precise
computati
onal
accounts of theories or theory

change. Connectionism
, in particular, could
characterize some types of learning but only at the cost of eschewing
representation.


Fortunately
,

that situation has chan
g
ed dramatically in the past decade
. Newcombe
mentions Bayesian learning as an alternative to association, but Bayesian learning is
just one part of a broader approach
,
sometimes called the “probabilistic model”
approach
,

that dominates
machine lear
ning and

is
increasing
ly

influential in
cognitive science

(for
recent review
s

see
Gopnik & Schulz, 2007 and
Griffiths et al,
2010; for applications to cognitive development see Gopnik et al
.

2004;

Xu and
Tenenbau
m, 2005
and special sections of Developmental Scienc
e (2007) and
Cognition (in press).

)
P
robabilist
ic models
promise

a computationally precise
developmental cognitive science that can integrate structure and learning.
Like

n
ativist approaches, but unlike traditional empiricist approaches
, probabilistic
mode
ls propose that even very young infants have abstract
, structured, hierar
chical

representations
--

representations that we can think of as hypotheses about

objects,
people or language. Unlike nativism, however, the probabilistic models approach
allows for
learning and even
, in the most recent formulations, for

radical theory

change as a result of evidence

(for
a
r
ecent example

see
Kemp et al, 2010
)
.

Unlike
the connectionist or dynamic picture, learning

is rational
. Probabilistic models stem
from work in the

philosophy of science and machine learning
that outlines how a
system could
,

in principle, make the best inferences from data.
U
nlike “core
knowledge”
,

learning in probabilistic models

doesn’t require external
r
epresen
tations

like language
.


The central a
dvance has been to formulate structured representations, such as
causal graphical models,

or “Bayes nets”

that can be easily combined with
probabilistic learning, such as Baye
sian inference. “T
heory theorists” proposed that
children learn by constructing h
ypotheses and testing them against evidence. But if
this is a deterministic process then the “poverty of the stimulus” problem becomes
acute


there will never be enough data to definitively prove that one hypothesis is
right
and reject the rest. In contra
st, i
f the
child is a probabilistic learner, weighing
the evidence to strengthen or reduce support for one hypothesis ov
er another, we

can help explain how children are gradually able to revise their initial theories

in
favor of better ones. Y
oung children

do indeed behave like probabilistic learners


entertaining multiple hypotheses, weighing new possibilities against prior beliefs,
experimenting and explaining


rather than simply using associationist mechanisms
to match the patterns in the dat
a
or fiddl
ing with d
etails of innate core knowledge
.


The ultimate test of any perspective is whether it generates new and interesting
empirical research. Researchers inspired by the probabilistic models approach have
already begun to make important developmental

discoveries, discoveries that don’t
fit
either
a connectionist
/dynamic

or nativist
picture.

9
-
month
-
olds
, for example,

can make causal inferen
ces that go beyond association

(Sobel and Kirkham
,

2007)

20
-
month
-
olds can infer a person’s desire from a no
n
-
r
andom sampling pattern

(Kushnir, Xu and Wellman, in press)
,

and 4
-
year
-
olds

discover n
ew abstract
variables and rules from only a few data points

(Schulz et al. 2008; Lucas et al,
2010
)
,
integrate new evidence and prior knowledge

(Schulz et al. 2007; Kush
nir &
Gopnik 2007, Sobel et al, 2004)

and
rationally experiment to uncover
new
causal
structure

(Schulz & Bonawitz, 2007)
.



Developmental evidence has also inspired computational advances. The
computational

framework
began by using statistical patterns t
o

infer simple
underlying
patterns, as in data
-
mining. Developmentalists emphasize the
importance of framework theories, explanation and experi
mentation, and social
context. C
omputationalists are starting to tackle those problems, too
, with some
success
.

F
inally, but most important of all,

t
he prob
abilistic models approach is

broad enough that there are
many theoretical specifics to be worked out and many
exciting empirical questions to ask.


References


Gopnik, A,; Glymour, C.; Sobel, D.; Schulz, L.; Kush
nir, T.; Danks, D. (2004). A theory
of causal learning in children: Causal maps and Bayes nets.
Psychological Review
,
111(1),3
-
32


Gopnik, A. & Schulz L. (eds). (2007).
Causal learning: Philosophy, psychology and
computation.

NY,: Oxford University Press.


Griffiths. T.; Chater, N.; Kemp, C.; Perfors, A., & Tenenbaum, J. (2010). Probabilistic
models of cognition: Exploring representations and inductive biases.
Trends in
Cognitive Sciences,


Kemp, C.; Tenenbaum, J. B, Niyogi, S. & Griffiths, T. (2010).
A p
robabilistic model of
theory formation. Cognition, 114, 2

, 165
-
196.


Kirkham, N., & Sobel, D. (2006). Blicket and babies: The development of causal
reasoning in toddlers and infants.
Developmental Psychology.

42(6), 1103
-
1115.


Kushnir, T., & Gopnik, A. (
2007).
Conditional probability versus spatial contiguity in
causal learning: Preschoolers use new contingency evidence to overcome prior
spatial assumptions.

Developmental Psychology,

Vol 43(1), 186
-
196


Kushnir, T., Xu, F., & Wellman, H. (in press). Young children use statistical sampling to
infer the preferences of others.
Psychological Science.


Lucas C.; Gopnik, A. & Griffiths, T. (201
0). Developmental differences in learning the
form of causal relationships. Proceedings of the Cognitive Science Society.


Schulz, L.; Goodman, N.; Tenenbaum, J.; & Jenkins, A. (2008). Going beyond the
evidence: Abstract laws and preschoolers' responses to

anomalous data.
Cognition

109(2), 211
-
223.


Schulz, L.; Bonawitz, E.; & Griffiths, T. (2007). Can being scared cause tummy aches?
Naive theories, ambiguous evidence, and preschoolers' causal inferences.
Developmental
Psychology,
43(5), 1124
-
1139.


Schulz
, L. E. & Bonawitz, E. B. (2007). Serious fun: Preschoolers engage in more
exploratory play when evidence is confounded.
Developmental Psychology
, 43, 1045
-
1050


Xu, F. & Tenenbaum, J. B. (2007). Word learning as Bayesian inference.
Psychol
ogical

Rev
iew
,

245
-
272