Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913492321173504 |
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| author | Crowley, George Esnaola, Inaki |
| author_facet | Crowley, George Esnaola, Inaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise Crowley, George Esnaola, Inaki Information Theory 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. |
| title | Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise |
| topic | Information Theory |
| url | https://arxiv.org/abs/2409.03541 |