
Equivalences between learning of data and probability distributions, and their applications
Algorithmic learning theory traditionally studies the learnability of ef...
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The cut metric for probability distributions
Guided by the theory of graph limits, we investigate a variant of the cu...
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On the Computability of AIXI
How could we solve the machine learning and the artificial intelligence ...
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An equivalence between learning of data and probability distributions, and some applications
Algorithmic learning theory traditionally studies the learnability of ef...
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Randomized Computation of Continuous Data: Is Brownian Motion Computable?
We consider randomized computation of continuous data in the sense of Co...
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An Application of Computable Distributions to the Semantics of Probabilistic Programs
In this chapter, we explore how (Type2) computable distributions can be...
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Algorithmic Theories of Everything
The probability distribution P from which the history of our universe is...
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Algorithmic learning of probability distributions from random data in the limit
We study the problem of identifying a probability distribution for some given randomly sampled data in the limit, in the context of algorithmic learning theory as proposed recently by Vinanyi and Chater. We show that there exists a computable partial learner for the computable probability measures, while by Bienvenu, Monin and Shen it is known that there is no computable learner for the computable probability measures. Our main result is the characterization of the oracles that compute explanatory learners for the computable (continuous) probability measures as the high oracles. This provides an analogue of a wellknown result of Adleman and Blum in the context of learning computable probability distributions. We also discuss related learning notions such as behaviorally correct learning and orther variations of explanatory learning, in the context of learning probability distributions from data.
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