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.

Gaussian LDA and QDA model contracts

Definition

Assume the Axiom of Choice. Let $d \geq 1$ and $K \geq 2$ be finite integers, let the class label be $Y \in {1, \dots, K}$ , and let $X \in R^{d}$ . Choose class priors $π_{k} > 0$ with $\sum_{k = 1}^{K} π_{k} = 1$ , means $μ_{k} \in R^{d}$ , and real symmetric positive-definite covariance matrices $Σ_{k} \in R^{d \times d}$ . The Gaussian generative model has $\Pr (Y = k) = π_{k}$ and conditional laws $X ∣ Y = k \sim N_{d} (μ_{k}, Σ_{k})$ . The LDA subfamily imposes one common covariance matrix, $Σ_{k} = Σ$ for every $k$ ; the QDA subfamily permits the covariance matrices to differ by class.

Definition references

Multivariate normal law, including singular covariance

The Axiom of Choice

Hastie, Tibshirani, and Friedman, ESL, §4.3, equations (4.7)–(4.12)

Stanford CS229 Spring 2022 lecture notes, §4.1

Depends on

Used by

Common-covariance LDA scores are affine and QDA scores are quadratic Theorem

Dependency tree · two levels

14 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

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)