Alphabeta MathDefinitionDefinition: 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.
Soft-thresholding map
Definition
For and , define the soft-thresholding map
Used by
- Nonunique Lasso coefficients with a unique fitted value Example
- The orthogonal-design Lasso is coordinatewise soft thresholding Example
- Exact Lasso coordinate update, including a zero column Lemma
- The one-coordinate absolute-value quadratic minimizer Lemma
- The proximal map of the l1 norm is soft thresholding Lemma
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Philippe Rigollet, 18.S997 High-Dimensional Statistics, Chapter 2, Section 2.4 (standard reference, not scraped)
- Philippe Rigollet and Jan-Christian Hütter, High-Dimensional Statistics: Lecture Notes, Chapter 2, Section 2.4 (standard reference, not scraped)