Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimation
Authors: Ulrike Schneider, Patrick Tardivel
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We provide a necessary and sufficient condition for the uniqueness of penalized least-squares estimators whose penalty term is given by a norm with a polytope unit ball, covering a wide range of methods including SLOPE, PACS, fused, clustered and classical LASSO as well as the related method of basis pursuit. We consider a strong type of uniqueness that is relevant for statistical problems. The uniqueness condition is geometric and involves how the row span of the design matrix intersects the faces of the dual norm unit ball, which for SLOPE is given by the signed permutahedron. Further considerations based this condition also allow to derive results on sparsity and clustering features. In particular, we define the notion of a SLOPE pattern to describe both sparsity and clustering properties of this method and also provide a geometric characterization of accessible SLOPE patterns. |
| Researcher Affiliation | Academia | Ulrike Schneider EMAIL Insitute of Statistics and Mathematical Methods in Economics TU Wien Vienna, Austria Patrick Tardivel EMAIL Institute of Mathematics University of Wroc law and University of Burgundy Wroc law, Poland and Dijon, France |
| Pseudocode | No | The paper focuses on mathematical proofs and theoretical derivations, not on presenting algorithms in a structured pseudocode format. |
| Open Source Code | No | The paper does not contain any explicit statements about the release of source code, nor does it provide links to a code repository. |
| Open Datasets | No | The paper primarily focuses on theoretical analysis and does not report on experiments conducted using specific datasets. References to data like 'gisette' are in the context of discussing prior work, not for experiments performed in this paper. |
| Dataset Splits | No | The paper does not conduct experiments on datasets, therefore, no dataset splits are provided. |
| Hardware Specification | No | The paper presents theoretical work and does not describe any experimental setup or the hardware used for computations. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies with version numbers for implementation or experimentation. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup, hyperparameters, or training configurations. |