Result · MIXTURE-RATIO-SCORE

Density ratios determine the mixture score

Derived from the literaturepublication: derived from published

Meaning

Component density ratios suffice for explicit score construction in a linear-mixture model.

Scientific context

For a mixture model, the score coordinates depend only on ratios of component densities to a reference component, so ratios to one reference component suffice after algebraic reconstruction. This is the direct density-ratio route from the same neighbouring literature, and it skips the classification step that CLASSIFIER-RATIO-ORACLE uses.

Statement

For p(x|theta)=Σ_alpha theta_alpha phi_alpha(x), score coordinates depend on phi_alpha(x)/Σ_beta theta0_beta phi_beta(x); ratios to one reference component suffice after algebraic reconstruction.

primary HEP template-fit interface

Relationships

Rests on

Local score can be obtained from a local density ratioRATIO-LOCAL-SCORE

Enables

Raises

Open next door

In the library

Carried by LinearComponentScore, scores_from_components. Reference (opens in a new tab).

Every object and refusal

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

O2. Linear-mixture component ratios suffice

For

p(x\mid\theta)=\sum_\alpha\theta_\alpha\phi_\alpha(x),

score coordinates depend on $\phi_\alpha(x)/\sum_\beta\theta_{0\beta}\phi_\beta(x)$ . Ratios to one reference component therefore suffice exactly after algebraic reconstruction.

From Score, ratio and classifier access · chapter contents