The Generalized Universal Law of Generalization
release_pvamwtnizfbetmt6u56au5ayqy
by
Nick Chater
2001
Abstract
It has been argued by Shepard that there is a robust psychological law that
relates the distance between a pair of items in psychological space and the
probability that they will be confused with each other. Specifically, the
probability of confusion is a negative exponential function of the distance
between the pair of items. In experimental contexts, distance is typically
defined in terms of a multidimensional Euclidean space-but this assumption
seems unlikely to hold for complex stimuli. We show that, nonetheless, the
Universal Law of Generalization can be derived in the more complex setting of
arbitrary stimuli, using a much more universal measure of distance. This
universal distance is defined as the length of the shortest program that
transforms the representations of the two items of interest into one another:
the algorithmic information distance. It is universal in the sense that it
minorizes every computable distance: it is the smallest computable distance. We
show that the universal law of generalization holds with probability going to
one-provided the confusion probabilities are computable. We also give a
mathematically more appealing form
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