Elements of information theory
Elements of information theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Minimum Description Length Principle (Adaptive Computation and Machine Learning)
The Minimum Description Length Principle (Adaptive Computation and Machine Learning)
On a definition of random sequences with respect to conditional probability
Information and Computation
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Minimum description length induction, Bayesianism, and Kolmogorov complexity
IEEE Transactions on Information Theory
Iterated logarithmic expansions of the pathwise code lengths for exponential families
IEEE Transactions on Information Theory
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Supplementing Vovk and V'yugin's 'if' statement, we show that Bayesian compression provides the best enumerable compression for parameter-typical data if and only if the parameter is Martin-Löf random with respect to the prior. The result is derived for uniformly discretizable statistical models, introduced here. They feature the crucial property that given a discretized parameter, we can compute how much data is needed to learn its value with little uncertainty. Exponential families and certain nonparametric models are shown to be uniformly discretizable.