Troy Lee, Andrei Romashchenko

The information contained in a string $x$ about a string $y$

is defined as the difference between the Kolmogorov complexity

of $y$ and the conditional Kolmogorov complexity of $y$ given $x$,

i.e., $I(x:y)=\C(y)-\C(y|x)$. From the well-known Kolmogorov--Levin Theorem it follows that $I(x:y)$ is symmetric up to a small ...
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Alexey Milovanov, Nikolay Vereshchagin

A fundamental notion in Algorithmic Statistics is that of a stochastic object, i.e., an object having a simple plausible explanation. Informally, a probability distribution is a plausible explanation for $x$ if it looks likely that $x$ was drawn at random with respect to that distribution. In this paper, we ... more >>>