ConceptLearningOckhamsRazor

ConceptLearningOckhamsRazor - Tenenbaum (1999) Concept...

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Tenenbaum (1999) Concept learning E.g., glorch vs. not glorch E.g., word meanings E.g., edible food Focus on Learning concepts from positive examples Learning from a small number of examples Contrast with machine learning approaches and psychological models at the time glorch glorch not glorch not glorch
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Domain Two dimensional continuous feature space Categories defined by axis-parallel rectangles e.g., feature dimensions cholesterol level ( x 1 ) insulin level ( x 2 ) e.g., concept healthy ( C )
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Hypothesis (Model) Space H: all rectangles on the plane, parameterized by (l 1 , l 2 , s 1 , s 2 ) h: one particular hypothesis Consider all hypotheses in parallel In contrast to non-Bayesian approach of maintaining only the best hypothesis at any point in time.
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Prediction via Model Averaging Generalization function for unknown input y given a set of n examples X = {x 1 , x 2 , x 3 , …, x n } p(y | X) = ⌠ h p(y & h | X) = p(y | h, X) p(h | X) p(y | h, X) = p(y | h) = 1 if y is in h p(h | X) ~ p(X | h) p(h) prior likelihood
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Priors and Likelihood Functions Priors, p(h) Location invariant Uninformative prior (prior depends only on area of rectangle) Expected size prior Likelihood function, p(X|h) X = set of n examples Size principle x
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Expected size prior
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Generalization Gradients MIN: smallest hypothesis consistent with data weak Bayes: instead of using size principle, assumes examples are produced by process independent of the true class Dark line = 50% prob.
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This note was uploaded on 10/24/2010 for the course CSCI 4202 at Colorado.

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ConceptLearningOckhamsRazor - Tenenbaum (1999) Concept...

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