The Generalized Universal Law of Generalization

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dc.creatorChater, Nick
dc.creatorVitanyi, Paul
dc.date2001-01-29
dc.date.accessioned2026-07-07T03:16:54Z
dc.date.available2026-07-07T03:16:54Z
dc.descriptionIt 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
dc.description17 pages LaTeX, Submitted
dc.identifierhttps://arxiv.org/abs/cs/0101036
dc.identifierhttp://arxiv.org/abs/cs/0101036
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/30531
dc.subjectComputer Vision and Pattern Recognition
dc.subjectArtificial Intelligence
dc.subjectProbability
dc.subjectPhysics and Society
dc.subjectJ.4
dc.titleThe Generalized Universal Law of Generalization
dc.typetext

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