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].
On the Concentration of the Minimizers of Empirical Risks
Authors: Paul Escande
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper is to provide concentration inequalities on the distance between the sets of minimizers of the risks for a broad spectrum of estimation problems. In particular, the risks are defined on metric spaces through probability measures that are also supported on metric spaces. A particular attention will therefore be given to include unbounded spaces and non-convex cost functions that might also be unbounded. This work identifies a set of high-level assumptions allowing to describe a regime that seems to govern the concentration in many estimation problems, where the empirical minimizers are stable. This stability can then be leveraged to prove parametric concentration rates in probability and in expectation. The assumptions are verified, and the bounds showcased, on a selection of estimation problems such as barycenters on metric space with positive or negative curvature, subspaces of covariance matrices, regression problems and entropic-Wasserstein barycenters. |
| Researcher Affiliation | Academia | Paul Escande EMAIL Institut de Math ematiques de Toulouse UMR 5219, Universit e de Toulouse, CNRS UPS, F-31062 Toulouse Cedex 9, France |
| Pseudocode | No | No explicit pseudocode or algorithm blocks are provided. The paper focuses on theoretical derivations and proofs. |
| Open Source Code | No | The paper does not provide explicit statements or links for open-source code related to the methodology described. |
| Open Datasets | No | The paper discusses various estimation problems and uses generic terms like 'samples drawn from µ' but does not specify or provide access information for any particular open datasets. |
| Dataset Splits | No | The paper is theoretical and does not present experiments requiring dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup or hardware used for computations. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies or version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any specific experimental setup details, hyperparameters, or training configurations. |