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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Sharp Matrix Empirical Bernstein Inequalities
Authors: Hongjian Wang, Aaditya Ramdas
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We compare the terms, Dmeb1 n of the first matrix empirical Bernstein inequality as in (17), and Dmeb2 n of the second matrix empirical Bernstein inequality as in (28), divided by that of the oracle matrix Bennett-Bernstein inequality Dtb n as in (36). We set α to .05, thus comparing the tightness of one-sided 95%-confidence sets (or equivalently, the spectral diameters of two-sided 90%-confidence sets). The i.i.d. random matrices are generated from 3 fixed orthonormal projections with d = 3, each with an independent Unif[0,1] eigenvalue. The comparison is displayed in Table 1. |
| Researcher Affiliation | Academia | Hongjian Wang Department of Statistics and Data Science Carnegie Mellon University Pittsburgh, PA 15213 EMAIL Aaditya Ramdas Department of Statistics and Data Science Carnegie Mellon University Pittsburgh, PA 15213 EMAIL |
| Pseudocode | No | The paper presents mathematical theorems, lemmas, and proofs, but does not include any explicitly labeled pseudocode or algorithm blocks. The methods are described using mathematical formulations. |
| Open Source Code | Yes | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: Simulation codes are provided as Supplementary Material. |
| Open Datasets | No | The i.i.d. random matrices are generated from 3 fixed orthonormal projections with d = 3, each with an independent Unif[0,1] eigenvalue. |
| Dataset Splits | No | The i.i.d. random matrices are generated from 3 fixed orthonormal projections with d = 3, each with an independent Unif[0,1] eigenvalue. The paper describes the generation of data for simulation but does not mention any training, testing, or validation splits for this generated data. |
| Hardware Specification | No | Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [No] Justification: We do not find it necessary to disclose such information as computation is less of a concern. |
| Software Dependencies | No | Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] Justification: See submitted codes. The paper text does not explicitly list software names with version numbers. |
| Experiment Setup | Yes | We set α to .05, thus comparing the tightness of one-sided 95%-confidence sets (or equivalently, the spectral diameters of two-sided 90%-confidence sets). The i.i.d. random matrices are generated from 3 fixed orthonormal projections with d = 3, each with an independent Unif[0,1] eigenvalue. The comparison is displayed in Table 1. |