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)

PDF Abstract
No code implementations yet. Submit your code now

Categories


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