Minimax Lower Bounds for Estimating Distributions on Low-dimensional Spaces
Authors: Saptarshi Chakraborty
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | 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. |