DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Finite linear-score classifiers with a deterministic tie rule

Definition

Let $d \geq 1$ and $K \geq 2$ be finite integers, with ordered labels $1 < 2 < \dots < K$ . A finite linear-score classifier on $R^{d}$ is specified by vectors $a_{k} \in R^{d}$ and constants $b_{k} \in R$ , one pair for each label, and assigns score $s_{k} (x) = a_{k}^{T} x + b_{k}$ to $x \in R^{d}$ . Its predicted label is the smallest index attaining $\max_{1 \leq j \leq K} s_{j} (x)$ . This rule is single-valued, including when two or more scores tie.

Definition references

Hastie, Tibshirani, and Friedman, ESL, §4.2, equations (4.3)–(4.6)

Stanford CS229 Spring 2022 lecture notes, §§2.1–2.2

Used by

Binary logistic and multiclass softmax conditional models Definition
Indicator-response least-squares classification Definition
Common-covariance LDA scores are affine and QDA scores are quadratic Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, 2nd ed., corrected 12th printing (standard reference, not scraped)
Stanford CS229 Spring 2022 lecture notes (standard reference, not scraped)