Individual communication complexity
Journal of Computer and System Sciences
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Algorithmic Minimal Sufficient Statistic Revisited
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Kolmogorov Complexity and Model Selection
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
IEEE Transactions on Signal Processing
Approximation of the two-part MDL code
IEEE Transactions on Information Theory
Rate distortion and denoising of individual data using Kolmogorov complexity
IEEE Transactions on Information Theory
Using MDL for grammar induction
ICGI'06 Proceedings of the 8th international conference on Grammatical Inference: algorithms and applications
The long and the short of it: summarising event sequences with serial episodes
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Summarizing categorical data by clustering attributes
Data Mining and Knowledge Discovery
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In 1974, Kolmogorov proposed a nonprobabilistic approach to statistics and model selection. Let data be finite binary strings and models be finite sets of binary strings. Consider model classes consisting of models of given maximal (Kolmogorov) complexity. The "structure function" of the given data expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data. We show that the structure function determines all stochastic properties of the data: for every constrained model class it determines the individual best fitting model in the class irrespective of whether the "true" model is in the model class considered or not. In this setting, this happens with certainty, rather than with high probability as is in the classical case. We precisely quantify the goodness-of-fit of an individual model with respect to individual data. We show that-within the obvious constraints-every graph is realized by the structure function of some data. We determine the (un)computability properties of the various functions contemplated and of the "algorithmic minimal sufficient statistic.".