Regularization and the small-ball method II: complexity dependent error rates
Authors: Guillaume Lecué, Shahar Mendelson
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study estimation properties of regularized procedures... We obtain bounds on the L2 estimation error rate that depend on the complexity of the true model... As a proof of concept, we apply our general estimation bound to various choices of Ψ, for example, the ℓp and Sp-norms (for p 1), weak-ℓp, atomic norms, max-norm and SLOPE. In many cases, the estimation rate almost coincides with the minimax rate in the class F. |
| Researcher Affiliation | Academia | Guillaume Lecu e EMAIL ENSAE 5 avenue Henry Le Chatelier 91120 Palaiseau, France. Shahar Mendelson EMAIL Department of Mathematics Technion, Haifa, Israel |
| Pseudocode | No | The paper presents mathematical definitions, theorems, lemmas, and proofs related to regularization and error rates. It does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about the availability of open-source code, nor does it provide links to any code repositories or supplementary materials containing code. |
| Open Datasets | No | The paper focuses on theoretical derivations and does not present any empirical results based on specific datasets. Consequently, it does not provide concrete access information for any publicly available or open datasets. |
| Dataset Splits | No | As the paper is theoretical and does not report on empirical experiments using specific datasets, there is no information provided regarding training, test, or validation dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments, thus it does not provide specifications for the hardware used. |
| Software Dependencies | No | The paper is theoretical and does not describe any computational experiments or implementations, therefore no specific software dependencies with version numbers are mentioned. |
| Experiment Setup | No | The paper focuses on theoretical analysis and does not present details of any experimental setup, including hyperparameters or system-level training settings. |