Rényi’s Information Dimension Beyond I.I.D.

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• Tobias Koch (Universidad Carlos III de Madrid)
• Tuesday 24 July 2018, 09:00-09:45
• Seminar Room 1, Newton Institute.

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Co-author: Bernhard C. Geiger (Graz University of Technology)

In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. Since then, it was shown that the information dimension is of relevance in various areas of information theory, including rate-distortion theory, almost lossless analog compression, or the analysis of interference channels. In this talk, I will propose a generalization of information dimension to stochastic processes, termed information dimension rate. I will then discuss some of its properties and compare it with other generalizations of information dimension available in the literature. I will further show that for Gaussian processes the information dimension rate permits a simple and intuitive characterization in terms of its spectral distribution function.Joint work with Bernhard Geiger (Graz University of Technology).

Related Links

• https://arxiv.org/abs/1702.00645  Link to relevant Arxiv preprint
• https://arxiv.org/abs/1712.07863  Link to relevant Arxiv preprint

This talk is part of the Isaac Newton Institute Seminar Series series.

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