Sample Complexity of Probability Divergences under Group Symmetry

Authors: Ziyu Chen, Markos Katsoulakis, Luc Rey-Bellet, Wei Zhu

ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Numerical simulations verify our theories.
Researcher Affiliation Academia 1Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA.
Pseudocode No No. The paper contains mathematical formulations and theorems but no structured pseudocode or algorithm blocks.
Open Source Code No No. The paper does not contain any statement about open-sourcing the code for the described methodology or a link to a code repository.
Open Datasets No No. The numerical simulations in the paper (Examples 4.6, 4.7, 4.13) use synthetic data constructed by the authors based on defined distributions and sampling methods, not by drawing from an external publicly available dataset with concrete access information. While the LYSTO dataset (Ciompi et al., 2019) is mentioned as an example in Figure 1, it is not the dataset used for the main empirical results.
Dataset Splits No No. The paper focuses on statistical estimation from i.i.d. samples drawn from probability measures, and does not involve typical machine learning model training or evaluation that would require explicit training, validation, or testing dataset splits.
Hardware Specification No No. The paper does not provide any specific details about the hardware (e.g., GPU/CPU models, memory, or specific computing environments) used to run the numerical simulations.
Software Dependencies No No. The paper does not specify any software dependencies with version numbers (e.g., programming languages, libraries, or solvers).
Experiment Setup Yes Yes. The paper provides details for setting up its numerical simulations, such as the definition of the distributions from which samples are drawn (e.g., 'mixture of 8 Gaussians centered at cos( 2πr 8 ), sin( 2πr 8 ) , r = 0, 1, . . . , 7, with the same covariance' in Example 4.7, and 'samples xi P = Q PΣ(X) in the following way: xi = r 1ξ1/3 i + ηi' in Example 4.6) and specific kernel parameters like bandwidth s (Example 4.13).