# Fisher Information and Mutual Information Constraints

11 Feb 2021 Leighton Pate Barnes Ayfer Ozgur

We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual information or capacity of the channel. We show that if the statistical model has a sub-Gaussian score function, then the trace of the Fisher information matrix for estimating $\theta$ from $Y$ can scale at most linearly with the mutual information between $X$ and $Y$... (read more)

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# Categories

• INFORMATION THEORY
• INFORMATION THEORY
• STATISTICS THEORY
• STATISTICS THEORY