Average entropy of Gaussian mixtures
<|reference_start|>Average entropy of Gaussian mixtures: We calculate the average differential entropy of a $q$-component Gaussian mixture in $\mathbb R^n$. For simplicity, all components have covariance matrix $\sigma^2 {\mathbf 1}$, while the means $\{\mathbf{W}_i\}_{i=1}^{q}$ are i.i.d. Gaussian vectors with zero mean and covariance $s^2 {\mathbf 1}$. We obtain a series expansion in $\mu=s^2/\sigma^2$ for the average differential entropy up to order $\mathcal{O}(\mu^2)$, and we provide a recipe to calculate higher order terms. Our result provides an analytic approximation with a quantifiable order of magnitude for the error, which is not achieved in previous literature.<|reference_end|>
@article{joudeh2024average,
    title={Average entropy of Gaussian mixtures},
    author={Basheer Joudeh and Boris v{S}kori'c},
    journal={arXiv preprint arXiv:2404.07311},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.07311},
    primaryClass={cs.IT math.IT}
}