The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions
Authors: Tim Johnston, Iosif Lytras, Nikolaos Makras, Sotirios Sabanis
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | 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. |