On Information Bottleneck for Gaussian Processes

Michael Dikshtein; Nir Weinberger; Shlomo Shamai

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arXiv · 2208.10136

On Information Bottleneck for Gaussian Processes

Michael Dikshtein·Nir Weinberger·Shlomo Shamai

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Abstract

The information bottleneck problem (IB) of jointly stationary Gaussian sources is considered. A water-filling solution for the IB rate is given in terms of its SNR spectrum and whose rate is attained via frequency domain test-channel realization. A time-domain realization of the IB rate, based on linear prediction, is also proposed, which lends itself to an efficient implementation of the corresponding remote source-coding problem. A compound version of the problem is addressed, in which the joint distribution of the source is not precisely specified but rather in terms of a lower bound on the guaranteed mutual information. It is proved that a white SNR spectrum is optimal for this setting.

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Michael Dikshtein, Nir Weinberger, Shlomo Shamai. 2022-08-22. On Information Bottleneck for Gaussian Processes. https://arxiv.org/abs/2208.10136

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