AlgorithmAlgorithm: AI-adaptedProof: Not applicablePipeline-generated

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.

Full conformal prediction set

Definition

Let $m \geq 0$ observed examples $Z_{1}, \dots, Z_{m}$ and $0 < α < 1$ be given. For each candidate $(x, y)$ , append it to the examples and apply a measurable, permutation-equivariant full score assignment of length $m + 1$ from Conformal scores and rank p-values, obtaining $R_{1} (y), \dots, R_{m + 1} (y)$ . Compute $p (y) = \frac{1}{m + 1} \sum_{i = 1}^{m + 1} 1 {R_{i} (y) \geq R_{m + 1} (y)}$ and return $C (x) = {y \in Y : p (y) > α} .$

An optional exact-randomized version uses one independent $U$ with Lebesgue probability law on $[0, 1]$ , shared across the candidate scan, and returns $C_{U} (x) = {y : p_{U} (y) > α}$ . The full score map must be jointly measurable in the observed examples, $x$ , and $y$ ; the membership event is measurable by Finite order statistics and rank maps are measurable.

Depends on

Used by

Full conformal ranks a candidate in an augmented sample Example
Full conformal marginal coverage Theorem

Dependency tree · two levels

9 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

Jing Lei et al., Distribution-Free Predictive Inference for Regression, JASA 113(523) (2018), §2.1 and Appendix A.1 (standard reference, not scraped)
Glenn Shafer and Vladimir Vovk, A Tutorial on Conformal Prediction, JMLR 9 (2008), §§4.1–4.2 (standard reference, not scraped)
Ryan Tibshirani, Conformal Prediction, Advanced Topics in Statistical Learning, Spring 2024, §3 (standard reference, not scraped)