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..
Minimax Lower Bounds for Estimating Distributions on Low-dimensional Spaces
Authors: Saptarshi Chakraborty
TMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper demonstrates that the minimax rate for estimating unknown distributions in the β-Hölder IPM on M scales as Ω n β d M δ n 1/2, where d M is the lower Minkowski dimension of M. Thus if the low-dimensional structure M is regular in the Minkowski sense, i.e. d M = d M, GANs are roughly minimax optimal in estimating distributions on M. Further, the paper shows that the minimax estimation rate in the p-Wasserstein metric scales as Ω n 1 d M δ n 1/(2p) . |
| Researcher Affiliation | Academia | Saptarshi Chakraborty EMAIL Department of Statistics University of California, Berkeley |
| Pseudocode | No | The paper focuses on theoretical analysis and mathematical proofs, such as "3 Proof of the Main Result (Theorem 7)", without including any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about releasing source code, nor does it provide links to code repositories or supplementary materials with code. |
| Open Datasets | No | The paper is a theoretical work focusing on minimax lower bounds for estimating distributions, and thus does not utilize or provide access information for any specific open datasets for experimental validation. |
| Dataset Splits | No | The paper does not describe any experimental setup involving datasets or their splits, as it focuses on theoretical analysis. |
| Hardware Specification | No | The paper is a theoretical work and does not describe any experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper is a theoretical work and does not mention any specific software dependencies or versions required for replication. |
| Experiment Setup | No | The paper is a theoretical analysis of minimax lower bounds and does not provide details on experimental setup, hyperparameters, or training configurations. |