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..
Bregman Proximal Langevin Monte Carlo via Bregman-Moreau Envelopes
Authors: Tim Tsz-Kit Lau, Han Liu
ICML 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We perform numerical experiments of sampling anisotropic Laplace distributions which have nonsmooth potentials. Other additional numerical experiments are given in Appendix D. In this section, we use bold lower case letters θ = (θi) 1 i d Rd to denote vectors. All numerical implementations can be found at https://github.com/ timlautk/bregman_prox_langevin_mc. ... The marginal empirical densities are given in Figure 1 (Figure D.4 for BMMMLA in Appendix B). |
| Researcher Affiliation | Academia | 1Department of Statistics and Data Science, Northwestern University, Evanston, IL, USA 2Department of Computer Science, Northwestern University, Evanston, IL, USA. |
| Pseudocode | Yes | Algorithm 1 The Bregman Moreau Mirrorless Mirror-Langevin Algorithm (BMMMLA) |
| Open Source Code | Yes | All numerical implementations can be found at https://github.com/ timlautk/bregman_prox_langevin_mc. |
| Open Datasets | Yes | For such a nonsmooth sampling task, inspired by Vorstrup Goldman et al. (2021); Bouchard-Cˆot e et al. (2018), we consider the case where f = 0 and g(θ) = α θ 1 = Pd i=1 αi|θi| with α = (1, 2, . . . , d) . ... We take d = 100, N = 1000 and θ = (0 10, 0.1 1 10, 0.2 1 10, . . . , 0.9 1 10) R100 as the ground truth. Then, each xn,i is generated from a standard Gaussian distribution and each yn is sampled following (D.5) with θ = θ . |
| Dataset Splits | No | The paper focuses on sampling algorithms and does not describe experiments with traditional training, validation, and test splits of a fixed dataset. Instead, it generates samples and evaluates their properties against a known distribution or estimated posteriors. |
| Hardware Specification | No | The paper does not specify any hardware details like CPU or GPU models used for the experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies used. |
| Experiment Setup | Yes | We consider d = 100, draw K = 105 samples, with a tight Bregman Moreau envelope using a small smoothing parameter λ = 10 5 and a small step size γ = λ/2. The parameter of the hyperbolic entropy is β = (2 d i + 1) 1 i d. ... In the experiment, we consider the case where ai = i and bi = i for all i Jd K. We use γ = 0.01, λ = 1 and β = (2 d i + 1) 1 i d. ... In addition, we choose α1 = (10 1 10, 9 1 10, . . . , 1 1 10) and α2 = 0.1. Again, we use the hypentropy functions ϕβ (for the mirror map) and ψσ (for the Bregman Moreau envelope), with β = (2i 1/4 1 10) 1 i 10 and σ = (α2 1,i) 1 i d. We also use a step size γ = 5 10 4 and a smoothing parameter λ = 0.01. |