Fisher Information
From the book
Chapter 14: Information Theory. In the chapter mind map this icon labels Info Geometry: Fisher Info Metric. The discussion below is excerpted and lightly edited from § Definition: Fisher Information (Scalar) in Mathematics for AI and Machine Learning.
For a parametric probability distribution $p_{\theta}(x)$ with a single parameter $\theta \in \mathbb{R}$, the Fisher information is a scalar that measures the amount of information that data provides about the parameter:
Intuitively, the Fisher information measures how sensitive the log-probability of the data is to changes in the parameter $\theta$. Higher values indicate that the parameter can be estimated more precisely.
What this drawing shows
What you see. Represents curvature of the log-likelihood or score variance, measuring how much data informs a parameter.
In the mind map. Chapter 14 — Info Geometry: Fisher Info Metric. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 14: Information Theory — see the mind-map node Info Geometry: Fisher Info Metric.