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].
Finite-Time Analysis of Projected Langevin Monte Carlo
Authors: Sebastien Bubeck, Ronen Eldan, Joseph Lehec
NeurIPS 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We ran the volume algorithm with both H&R and LMC on the following set of convex bodies: K = [ 1, 1]n (referred to as the Box ) and K = [ 1, 1]n n 2 Bn (referred to as the Box and Ball ), where n = 10 k, k = 1, . . . , 10. The computed volume (normalized by 2n for the Box and by 0.2 2n for the Box and Ball ) as well as the clock time (in seconds) to terminate are reported in the figure above. From these experiments it seems that LMC and H&R roughly compute similar values for the volume (with H&R being slightly more accurate), and LMC is almost always a bit faster. |
| Researcher Affiliation | Collaboration | S ebastien Bubeck Microsoft Research EMAIL Ronen Eldan Weizmann Institute EMAIL Joseph Lehec Universit e Paris-Dauphine EMAIL |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. The algorithm (1) is presented as a mathematical formula. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | The 'datasets' used are geometric shapes (Box and Box and Ball) defined by mathematical expressions, not publicly available datasets with specific access information. The paper does not provide a link, DOI, or formal citation for accessing these geometric definitions as data. |
| Dataset Splits | No | The paper does not specify training, validation, or test dataset splits. The experiments involve computing the volume of geometric bodies, not training models with data splits. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, or memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'Cousins and Vempala provide a Matlab implementation' but does not specify a version number for Matlab or any other software dependencies with versions. |
| Experiment Setup | Yes | We implemented the same procedure with LMC instead of H&R, and we choose the step-size η = 1/(βn2), where β is the smoothness parameter of the underlying log-concave distribution (in particular here β = 1/σ2 ℓ). |