On Algorithmic Statistics for space-bounded algorithms
Information Theory
2017-07-14 v2 Computational Complexity
math.IT
Abstract
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice because Kolmogorov complexity is not computable. In this paper we develop algorithmic statistics using space-bounded Kolmogorov complexity. We prove an analogue of one of the main result of `classic' algorithmic statistics (about the connection between optimality and randomness deficiences). The main tool of our proof is the Nisan-Wigderson generator.
Cite
@article{arxiv.1702.08084,
title = {On Algorithmic Statistics for space-bounded algorithms},
author = {Alexey Milovanov},
journal= {arXiv preprint arXiv:1702.08084},
year = {2017}
}
Comments
accepted to CSR 2017 conference