Global ETD Search
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Showing 1 to 8 of 8 for “"Kolmogorov complexity."”.
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Kolmogorov Complexity, Strong Reducibilities, and Computably Enumerable Sets
We also study connections between strong reducibilities and properties of computably enumerable sets such as simplicity. We call a class S of computably enumerable sets bounded if there is an m-incomplete computably enumerable set A such that every set in S is m-reducible to A. For example, we show …
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Algorithmic specified complexity.
… not all improbable events convey information. Kolmogorov complexity captures the idea of information as something easily described. But not all easily described objects are information. The proposed Algorithmic Specified Complexity takes into account both Shannon Information and Kolmogorov …
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Methods for Constructing and Exploiting Information Measures for Neural Networks
… is the algorithmic notion of information (Kolmogorov complexity) along with related topics such as algorithmic probability which, together, have laid important theoretical foundations for machine learning. While practical results are elusive due to the uncomputability of Kolmogorov …
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Approximation algorithms for grammar-based data compression
… can be regarded as a computable relaxation of Kolmogorov complexity. Finally, work on the smallest grammar problem qualitatively extends the study of approximation algorithms to hierarchically-structured objects. In this thesis, we establish hardness results, evaluate several previously …
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Competitive regression.
This thesis is about investigating the predictive complexity of online regression. In essence, supervised learning from a data sequence consisting of n-dimensional input and the corresponding output is considered. In this work online learning scenario considered consists of sequential arrival of …
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Landscapes of Finite Information
… the set of distributions with finite mean Kolmogorov complexity. In addition, we prove that this result cannot be strengthened; thus, the PLUB condition is, in a precise sense, optimal. If $X$ is a finite binary string, then $\log N(X)$ is essentially its length, where $N(X)$ denotes the …
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Computability and Fractal Dimension
… to algorithmic information theory developed by Kolmogorov and his students. We are able to give a new and much easier proof of a central result of the effective theory: Effective Hausdorff dimension coincides with the lower asymptotic algorithmic entropy, defined in terms of Kolmogorov …
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A Dynamic and Thermodynamic Approach to Complexity.
… problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, …