Technical Program

Paper Detail

Paper IDO.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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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