Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise

George Crowley; Inaki Esnaola

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arXiv · 2409.03541

Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise

George Crowley·Inaki Esnaola

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Abstract

Sensor placement approaches in networks often involve using information-theoretic measures such as entropy and mutual information. We prove that mutual information abides by submodularity and is non-decreasing when considering the mutual information between the states of the network and a subset of $k$ nodes subjected to additive white Gaussian noise. We prove this under the assumption that the states follow a non-degenerate multivariate Gaussian distribution.

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George Crowley, Inaki Esnaola. 2024-09-05. Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise. https://arxiv.org/abs/2409.03541

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