Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise
<|reference_start|>Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise: 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.<|reference_end|>
@article{crowley2024submodularity,
    title={Submodularity of Mutual Information for Multivariate Gaussian Sources
  with Additive Noise},
    author={George Crowley and Inaki Esnaola},
    journal={arXiv preprint arXiv:2409.03541},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03541},
    primaryClass={cs.IT math.IT}
}