An Alphabet-Size Bound for the Information Bottleneck Function
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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 |\mathcal{W}| \leq |\mathcal{X}| + 1 which makes the calculation possible for finite |\mathcal{X}|. 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 (\varepsilon,\;|\mathcal{Y}|) with a cardinality |\mathcal{W}| \leq f( \in,\;|\mathcal{Y}|), for explicitly given functions δ and f of an approximation parameter ϵ > 0 and the cardinality of \mathcal{Y}.Finally, we generalize the known cardinality boundsY to the case were some of the random variables represent quantum information.
Original language | English |
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Title of host publication | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings |
Publisher | IEEE |
Publication date | 2020 |
Pages | 2383-2388 |
Article number | 9174416 |
ISBN (Electronic) | 9781728164328 |
DOIs | |
Publication status | Published - 2020 |
Event | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020 |
Conference
Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
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Land | United States |
By | Los Angeles |
Periode | 21/07/2020 → 26/07/2020 |
Sponsor | IEEE Information Theory Society, The Institute of Electrical and Electronics Engineers |
ID: 256725258