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The Generalized Universal Law of Generalization
Nick Chater,Paul M. B. Vitányi +1 more
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In this paper, the authors show that the universal law of generalization holds with probability going to one-provided the confusion probabilities are computable, and they also give a mathematically more appealing form.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 formread more
Citations
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Bayesian models of cognition revisited: Setting optimality aside and letting data drive psychological theory.
TL;DR: This paper argues that there are 2 qualitatively different ways in which a Bayesian model could be constructed, and demonstrates how the descriptive Bayesian approach can be used to answer different sorts of questions than the optimal approach, especially when combined with principled tools for model evaluation and model selection.
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Evolution of protolinguistic abilities as a by-product of learning to forage in structured environments
TL;DR: Using agent-based simulations in a range of virtual environments, it is demonstrated that challenges of foraging for food can select for cognitive mechanisms supporting complex, hierarchical, sequential learning, the need for which arises in language acquisition.
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Lure similarity affects visual episodic recognition: Detailed tests of a noisy exemplar model
TL;DR: Fitting each of four summed-similarity models of visual episodic recognition memory to the individual subjects’ data demonstrated a clear superiority for models that take account of interitem similarity on a trialwise basis.
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Renewing the respect for similarity
Shimon Edelman,Reza Shahbazi +1 more
TL;DR: It is argued for a renewed focus on similarity as an explanatory concept, by surveying established results and new developments in the theory and methods of similarity-preserving associative lookup and dimensionality reduction—critical components of many cognitive functions, as well as of intelligent data management in computer vision.
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Similarity, Kernels, and the Triangle Inequality
TL;DR: In this article, it was shown that similarity measures based on Shepard's universal law of generalization lead to an inner product representation in a reproducing kernel Hilbert space, which has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli.
References
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Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Book
The Mathematical Theory of Communication
TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.
Journal ArticleDOI
On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.