Babies Do Not Play Dice Either

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Babies Do Not Play Dice Either!

• Marzieh Asgari-Targhi

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Overview

• I will briefly explain Gopnik et als idea
  presented in their 2004 paper.
• I shall call into question the key assumptions
  underlying Gopnik et als work.
• I will then suggest a solution by considering
  causality as a non- monolithic notion.

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Gopnik et als claim

• Infants and children have the prerequisites for
  making causal inferences consistent with causal
  Bayes net learning algorithms.
• Infants and children learn from evidence in the
  form of conditional probabilities, interventions
  and combinations of the two.

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Causal Bayes nets

• A Bayesian network is a set of random variables
  with a joint distribution, arranged in a network
  (graph), and satisfying the Markov Condition.
• Causal relations are represented by directed
  acyclic graphs. The graphs consists of variables,
  representing types of events or states of the
  world, and directed edges (arrows) representing
  the causal relations between those variables.

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A Causal Bayes net
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Causal Markov Condition

• The structure of a causal graph constrains the
  probability of the variables in that graph. In
  particular, it constrains the Conditional
  Independencies among those variables. These
  constrains are captured by the Causal Markov
  Condition.
• Causal Markov Condition For any variable X in a
  causal graph, X is independent of all other
  variables in the graph (except for its own direct
  and indirect effects) conditional on its own
  direct causes.

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Learning from conditional Probability

• Two-and-half-year-olds can discriminate
  conditional independence and dependence, that is
  conditional probabilities with controls for
  frequency, and can use that information to make
  judgments about causation.
• Experiments (a) one-cause condition
• Children choose A rather than B.
• (b) Two-cause condition
• Children choose equally between A and B.

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Children using principle of Bayesian inference.

• In experiments (c) Inference condition and (d)
  Backward blocking condition, four-year-old
  children used principles of Bayesian inference to
  combine prior probability information with
  information about the conditional probability of
  events.
• Four-year-olds can also perform even more complex
  kinds of reasoning about conditional
  dependencies, and they do so in many domains,
  biological and psychological as well as physical.
  Monkey and Flowers Experiment.

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Monkey and the Flowers
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Learning from Interventions

• The intervention Assumption A variable x is an
  intervention on a variable Y in a causal graph if
  and only if (1) x is not caused by any other
  variables in the graph (2) directly fixes the
  value of Y to y and (3) does not affect the
  values of any other variables in the graph except
  through its influence on Y.
• The underlying concept is actually very
  intuitive, eg, (2) is basic to understanding
  goal-directed action, (3) is essential to
  understanding means-ends relations.

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Intervention is one basic type of evidence for
causation.

• Extensive literature on early imitations show
  that nine-month-old infants who see another
  person perform a novel intervention ( ie, an
  experimenter touching the top of the box with his
  head to make the box light up) will adopt that
  intervention themselves-the babies will put their
  own heads on the box.
• I agree with Gopnik that infants and children
  learn from intervention but

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Key assumptions questioned

• How do Gopnik et al arrive from childrens
  frequency information to their judgments of
  conditional probability?
• The children in Gopnik et als experiments gave
  answers similar to what would be produced by a
  Bayes net, how is it justified to say that they
  used the Bayes net approach? Dont children use
  some form of Humean regularity theory?
• Why causation is identified with probability?

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Whats Gopnik getting at?

• If the suggestion is that young children have
  some kind of causal Bayes net learning mechanism
  programmed into their brains, then these
  experiments do no prove this.
• If the suggestion is that young children can
  actually be taught the theory of Bayes nets, then
  that is even less plausible, because the very
  basic concept in Bayes net is probability, and
  there are suggestions that children and young
  adults find probability concepts difficult to
  learn. See Peter Cheng 2003.

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Causation is a multi-faceted concept.

• Causes almost always proceed their effects.
  Humes Regularity theory of causation.
• Causation has uncertainty or probabilistic
  aspect. Advocates Suppes, Shafer
• Causation has counterfactual facet. Ad Lewis,
  Ramachandran,
• It has logical facet, causes can be necessary and
  sufficient for their effects. Mackie, Bell
• Causal Bayesian Networks Glymour, Cooper
• Causality has manipulability aspect. Ad
  Collingwood. Menzies, Price

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Non-monolithic Approch to Causality

• Causality has many different facets. I argue for
  a pluralistic model of causality which involves
  accepting all the characteristics of causation
  and using them in different situation.
• Humean regularity theory is our very basic method
  for causal inference. The probability models
  might be more appropriate in more sophisticated
  and developed knowledge situations.

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• Counterfactual causal models are useful in
  situations which we can envisage or indeed build
  a possible world in which the existence or
  non-existence of causes and their possible
  effects can be examined thoroughly. Logical
  causal models are used in conceptually difficult
  situations, where causes have been identified but
  the cause cannot be identified.

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• Children learn causality from intervention and
  they employ Humean regularity theory of
  causality. As we grow older and become
  sophisticated agents with language skills who can
  understand many aspects of causality, we use
  various causal tool available to us depending on
  contexts we are in.
• Pluralistic view of causality suggests a way as
  how to strike a good balance between precise
  formalism and commonsense reality of causal
  contexts.

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Thank you!