Inductive Learning

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Inductive Learning

• A significant portion of human learning involves
  inductive learning.
• What is?
• Unlike deduction, inferences are not certain.
• Deduction
• All poodles are dogs.
• This animal is a poodle.
• The animal is a dog.

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• Induction
• This animal wags its tail.
• This animal eats bones.
• This animal is a dog. (But, it may not be.)
• Two inductive situations
• Categorization
• Causal inference

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Categorization

• How do we acquire concepts?
• animal, fruit, vegetable, furniture
• Concepts facilitate understanding of the world.
• A number of theories.

4
Associative view (Hull)

• We acquire concepts by associating the critical
  feature with a concept.
• Study
• Asked subjects to categorized Chinese characters.
• Each contained one critical feature, but subjects
  were not informed.
• Subjects gradually learned but were unable to
  identify the critical features.

5
Hypothesis testing (Bruner)

• Acquisition is more systematic.
• We test hypotheses.
• Study
• Subjects identified instances.
• Announce the concept when they identified.
• Much more conscious process than Hull thought.
• Also, the process is not continuous.

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But...

• Showed gradual improvement.
• Bower and Trabasso (1964)
• It is an artifact.
• Different subjects are acquiring the concepts at
  different trials.
• Graph - showing the percentage of subjects who
  are getting it rather than each individual is
  getting the concepts gradually.

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Backward learning curve

• New way of plotting data.
• The rate of success before the trial on which
  they made the last error.
• No gradual improvement.
• 50/50 success rate.
• Concept acquisition is all or none.

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Natural concepts

• But, we dont acquire natural concepts that way.
• We are not aware of critical features.
• E.g., Tomato - fruit? Vegetable? Why?
• In fact - McClosky Glucksberg (1978)
• Subjects disagreed each other.
• They changed their mind on retest (unreliable).

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• Also, there are degrees of belongingness
• Rosch (1973)
• Some are more typical than others.
• Natural categories are fuzzy categories.
• How do we learn?
• Schema theory
• Exemplar theory

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Schema theory

• Gluck and Bower (1988)
• Strengths of association are formed between
  stimulus features and categories according to
  Wagner Rescorla rule.
• Also, there is a corresponding reduction in
  strength for the alternative.
• Instances are seen as members to the extent that
  they display features associated with the
  category.

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Medin Schaffer (1978)

• 1. One large red triangle (is in category A).
• 4 A features and 0 B features.
• 2. Two small red triangles (is in category A).
• 2 A features and 2 B features
• 3. One large blue circle is (in category A).
• 2 A features and 2 B features
• 4. Two small blue circle is (in category B).
• 2 A features and 2 B features
• 5. One large red circle is (in category B).
• 3 A features and 1 B features
• 6. Two small blue circles (is in category B).
• 1 A features and 3 B features

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• 5 should be difficult for subjects, but not
  really.
• Additional assumption
• Subjects use configual cues.
• red circle

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Exemplar theory

• Medin and Schaffer (1978)
• Subjects remember some or all instances of
  various categories.
• So, given an instance
• determine which past instance is similar.
• if it is similar, it is an instance of the same
  category.

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Example

• Calculate similarity of component features
• Test stimulus One large blue triangle
• Retrieved One large red triangle
• Compute similarity using 0-1 scale
• Number Size Color Shape
• 1 x 1 x .2 x 1 .200

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Which one is correct?

• Estes et al. (1989)
• Categorizing patients symptoms into a rare or
  common disease.
• 240 cases
• Compared predictions made by the models and
  subjects performance.
• Both models fared well.

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Causal inferences

• How to make causal inferences?
• Animals do it in conditioning.
• We use a number of cues
• Statistical cues
• Spatial and temporal cues
• Kinematic cues

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Statistical cues

• Subjects are sensitive to statistical contingency

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Anderson Sheu (1994)

• But, they do not place equal weight to all the
  cells.
• So, they were not computing complete
  probabilities
• P(EC) a/ab P(EC) c/cd
• But, majority were. Minority ignored c d.

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Spatial and temporal cues

• Which is more important?
• Spatial or temporal
• Depending on the situations
• Bullock et al. (1982)
• jack-in-the-box paradigm
• two balls
• closer in space or closer in time
• 70 - relied on closer in space

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Not always.

• Anderson (1991)
• Varied time and distance
• Distance was important when time was short.
• More delay - no effect of distance
• Why the difference?
• Subjects actually think about the mechanism.
• Long delay with short distance?
• Unlikely the cause

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Kinematic cues

• Movement of objects
• One object hits the other.
• Subjects are very sensitive to how one object
  affects the movement of the other.
• But, subjects make errors.

22
Kaiser et al. (1985, 1986)

• How does a ball roll off a table?
• Errors
• straight down
• L-shapded
• How does a ball roll out of a curved tube?
• Error
• curved trajactory