# On Algorithmic Statistics for space-bounded algorithms

## TL;DR

This paper extends algorithmic statistics to space-bounded algorithms by using space-bounded Kolmogorov complexity, establishing key theoretical results with the Nisan-Wigderson generator.

## Contribution

It develops a space-bounded version of algorithmic statistics and proves an analogue of a main classical result using the Nisan-Wigderson generator.

## Key findings

- Established a connection between optimality and randomness deficiencies in space-bounded setting.
- Proved an analogue of a key classical result in algorithmic statistics.
- Utilized the Nisan-Wigderson generator as a main proof tool.

## 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.