statistics アーカイブ - Data Processing Club

TwoNN Intrinsic Dimension Explained: Python and Visual Illustrations

Real-world data often live in a high-dimensional ambient space, but the points themselves concentrate near a much lower-dimensional manifold. The “visible” (ambient) dimension is easy to read off from the feature vector length, while the “intrinsic” dimension (the effective degrees of freedom) is much harder to estimate. Two Nearest Neighbors (TwoNN) is a simple yet […]

Fisher Information Explained: Python and Visual Illustrations

Definition of Fisher Information The Fisher information is defined as $$\mathrm{FisherInformation}(\theta_0)\stackrel{\text{def}}{=}-\mathbb{E}_{X\sim p(x\mid\theta_0)}\left[\frac{d^2}{d\theta^2}\log p(x\mid\theta)\bigg|_{\theta=\theta_0}\right].$$ Fisher information quantifies how precisely a model parameter can be estimated.A larger Fisher information means the parameter can be estimated more accurately,while a smaller Fisher information indicates that estimation is more difficult. Fisher information admits several equivalent interpretations. Equivalent Expressions $$\begin{align}&\mathrm{FisherInformation}(\theta_0) \\&\stackrel{\text{def}}{=}-\mathbb{E}_{X

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