ScoreQuant

Result · RATIO-LOCAL-SCORE

Density ratios determine the local score

Derived from the literaturepublication: derived from published

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Meaning

Differentiating a local model density ratio yields the local score under the stated regularity conditions.

Scientific context

The local score is the gradient of a log density ratio, so absolute normalized densities are unnecessary when the relevant local density ratio is available. This is direct prior art from the simulation-based-inference literature, which supplies the local score as a learned summary built on calibrated classifier likelihood ratios.

Statement

s(x)=∇_theta log[p(x|theta)/p(x|theta0)]|theta0; absolute normalized densities are unnecessary if the relevant local density ratio is available.

Relationships

Enables

In the library

Carried by DensityRatioScore, CentralLogRatioScore. Reference.

Every object and refusal

Local graph
Local map of Local score can be obtained from a local density ratio0 prerequisites to the left, 1 results it enables or questions it raises to the right, 0 boundary cases below.Linear-mixture component ratios suffice for score constructionLinear-mixture compon…Local score can be obtained from a local density ratioLocal score can be ob…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

O1. Density ratios suffice for local scores
s(x)=∇θlog⁡p(x∣θ)p(x∣θ0)∣θ0.s(x)=\left.\nabla_\theta\log\frac{p(x\mid\theta)}{p(x\mid\theta_0)}\right|_{\theta_0}.

Full absolute densities are not required if the relevant local density ratio is available.

From Score, ratio and classifier access · chapter contents