2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | O.2.1 | ||
| Paper Title | An Alphabet-Size Bound for the Information Bottleneck Function | ||
| Authors | Christoph Hirche, University of Copenhagen, Denmark; Andreas Winter, Universitat Autonoma de Barcelona, Spain | ||
| Session | O.2: Lossy Source Coding | ||
| Presentation | Lecture | ||
| Track | Source Coding | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | The information bottleneck function gives a measure of optimal preservation of correlation between some random variable $X$ and some side information $Y$ while compressing $X$ into a new random variable $W$ with bounded remaining correlation to $X$. As such, the information bottleneck has found many natural applications in machine learning, coding and video compression. The main objective in order to calculate the information bottleneck is to find the optimal representation on $W$. This could in principle be arbitrarily complicated, but fortunately it is known that the cardinality of $W$ can be restricted as $|\cW|\leq|\cX|+1$ which makes the calculation possible for finite $|\cX|$. Now, for many practical applications, e.g. in machine learning, $X$ represents a potentially very large data space, while $Y$ is from a comparably small set of labels. This raises the question whether the known cardinality bound can be improved in such situations. We show that the information bottleneck function can always be approximated up to an error $\delta(\epsilon,|\cY|)$ with a cardinality $|\cW| \leq f(\epsilon,|\cY|)$, for explicitly given functions $\delta$ and $f$ of an approximation parameter $\epsilon>0$ and the cardinality of $\cY$. Finally, we generalize the known cardinality bounds to the case were some of the random variables represent quantum information. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
