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..
The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions
Authors: Tim Johnston, Iosif Lytras, Nikolaos Makras, Sotirios Sabanis
TMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Examples and Numerical Experiments: 4.1.1 Sampling: We compare SGULA and MYULA on the task of sampling from a two dimensional mixture of Gaussians with a Laplacian prior, in order to assess their empirical behavior in a non-convex, non-smooth setting. ... Figure 1 compares the empirical densities obtained from pooled samples across all chains with the analytical ground truth densities. ... 4.4.1 Robust Regression: To compliment the theoretical analysis and illustrate the applicability of the Subgradient Unadjusted Langevin Algorithm (SGULA) to a practical optimization problem... Figure 2 displays the MRME boxplots for SCAD, LASSO, and the oracle. |
| Researcher Affiliation | Academia | Tim Johnston EMAIL Ceremade Université Paris Dauphine-PSL, France; Iosif Lytras EMAIL Archimedes Athena Research Center, Greece; Nikolaos Makras EMAIL School of Mathematics University of Edinburgh, United Kingdom; Sotirios Sabanis EMAIL School of Mathematics University of Edinburgh, United Kingdom School of Applied Mathematical and Physical Sciences National Technical University of Athens, Greece Archimedes Athena Research Center, Greece |
| Pseudocode | Yes | 3 Main Results: The Subgradient Unadjusted Langevin Algorithm (θλ n)n 0, is given by the Euler-Maruyama discretisation scheme of (1), in particular (SG-ULA): θλ n+1 = θλ n λh(θλ n) + p 2λβ 1ξn+1, θλ 0 = θ0, n N, (7) |
| Open Source Code | No | The paper does not contain an explicit statement about releasing source code, nor does it provide a link to a code repository. |
| Open Datasets | No | In this experiment we generate 100 datasets according to the following procedure. Let x Rd with Toeplitz covariance Σij = ρ|i j| and ρ = 0.5. For a fixed observations n = 60 and dimension d = 8, we sample X Rn d from the standard Gaussian. The response follows the model Y = XT β + ϵ, where β = (3, 1.5, 0, 0, 2, 0, 0, 0)T and the noise is drawn from a heavy tailed mixture, i.e. ϵ 0.9N(0, 1) + 0.1Cauchy(0, 1). |
| Dataset Splits | Yes | The tuning parameter γ > 0, is chosen independently for both objectives via 5-fold Cross-Validation. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | Both samplers were implemented with a fixed stepsize λ = 10 3 and inverse temperature parameter β = 1, and MYULA employed the same value for its smoothing parameter (γ = λ). For each method, we initialized 12 parallel chains from a broad uniform distribution on [min j µj 2 max j σ2 j , max j µj + 2 max j σ2 j ]2... Each chain was run for 52 103 iterations, discarding the first 12 103 as burn-in and retaining the rest for the assessment. ... The stepsize is fixed at λ = 10 3 and the tuning parameter γ > 0, is chosen independently for both objectives via 5-fold Cross-Validation. Each chain is run for 7.5 103 iterations, while each CV-fold is truncated at 1.25 103 iterations. |