Download Commentary on Nora Newcombe Neoconstructivism

Child Development Perspectives (In Press)
The theory theory 2.0: Probabilistic models and cognitive development
Commentary on Nora Newcombe Neoconstructivism
Alison Gopnik Dept. Of Psychology University of California at Berkeley, Berkeley, CA,
94704
[email protected]
Newcombe’s piece is a welcome attempt to reconcile the profusion of terrific
empirical work in cognitive development with the unsatisfactory traditional
theoretical positions. Most of her points are very well-taken, and define an emerging
empirical consensus. However, she doesn’t capture one important theoretical
dimension. Newcombe opposes nativism to everything else, combining
connectionist and dynamic systems theories, information processing theories, the
“theory theory”, statistical learning and Bayesian inference. But there is an
alternative split that is equally important and that carves up the theoretical territory
rather differently. This is a contrast between representational and nonrepresentational accounts of development. While almost all nativist approaches are
representational, 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 developmental cognitive science,
reflecting a deep tension in epistemology. Since Plato, two facts about human
knowledge. have clashed. We seem to have abstract, structured and accurate
representations of the world – representations that allow a wide range of new
inferences. But all that reaches us from the world are concrete, probabilistic
patterns of sensory stimuli. How do we get such powerful knowledge from such
impoverished data? Nativists, from Plato to “core knowledge” theorists, argue that
the abstract structure is actually innate, we only appear to learn it from experience.
Empiricists, from Aristotle to the connectionists, argue that we only appear to have
abstract, structured, representations – actually we just accumulate specific
associations.
The empirical accomplishments of the last thirty years have actually made the
theoretical tension worse. We might have thought, as Piaget did, that children begin
with concrete particular “sensorimotor” schemes and somehow gradually construct
more abstract representations. But, empirically, as Newcombe points out, one of the
most important discoveries of the last thirty years is that children—even young
infants—already have abstract, structured, representations of the world: intuitive
theories and grammars, conceptual hierarchies 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 even young infants learn in surprisingly 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 precursors, allow
learning but deny that there are abstract representations. Nativism allows
representation but denies that there is substantive learning. Many empirically
minded developmental psychologists, like those Newcombe describes, have been
dissatisfied with 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. However, until recently, there were no precise computational
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 changed 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 learning and is increasingly influential in
cognitive science (for recent reviews see Gopnik & Schulz, 2007 and Griffiths et al,
2010; for applications to cognitive development see Gopnik et al. 2004; Xu and
Tenenbaum, 2005 and special sections of Developmental Science (2007) and
Cognition (in press). )Probabilistic models promise a computationally precise
developmental cognitive science that can integrate structure and learning. Like
nativist approaches, but unlike traditional empiricist approaches, probabilistic
models propose that even very young infants have abstract, structured, hierarchical
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 recent 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. Unlike “core
knowledge”, learning in probabilistic models doesn’t require external
representations like language.
The central advance has been to formulate structured representations, such as
causal graphical models, or “Bayes nets” that can be easily combined with
probabilistic learning, such as Bayesian inference. “Theory theorists” proposed that
children learn by constructing hypotheses 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 contrast, if the child is a probabilistic learner, weighing
the evidence to strengthen or reduce support for one hypothesis over another, we
can help explain how children are gradually able to revise their initial theories in
favor of better ones. Young 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 data or fiddling with details 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 inferences that go beyond association (Sobel and Kirkham, 2007)
20-month-olds can infer a person’s desire from a non-random sampling pattern
(Kushnir, Xu and Wellman, in press) , and 4-year-olds discover new 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; Kushnir &
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 to infer simple
underlying patterns, as in data-mining. Developmentalists emphasize the
importance of framework theories, explanation and experimentation, and social
context. Computationalists are starting to tackle those problems, too, with some
success. Finally, but most important of all, the probabilistic 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.; Kushnir, 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 probabilistic 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. (2010). 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, 10451050
Xu, F. & Tenenbaum, J. B. (2007). Word learning as Bayesian inference. Psychological
Review, 245-272