Mirror Langevin Monte Carlo: the Case Under Isoperimetry
Authors: Qijia Jiang
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical Experiments In this section, we test out the induced bias and the benefit of using mirror maps in two experiments. |
| Researcher Affiliation | Academia | Qijia Jiang UT Austin qjiang@austin.utexas.edu Work done while at Stanford University. |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. Equations are presented, and methods are described in text, but not in a structured algorithm format. |
| Open Source Code | No | The paper does not provide any statements about releasing code or links to a code repository. |
| Open Datasets | No | The paper discusses 'uniform sampling from a 2D box' and 'ill-conditioned Gaussian potential' for its experiments, which appear to be synthetic setups or custom problem instances, and does not provide access information (link, DOI, citation) for a publicly available dataset. |
| Dataset Splits | No | The paper conducts numerical experiments but does not provide specific details regarding training, validation, or test dataset splits (e.g., percentages, sample counts, or citations to standard splits). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | For Newton Langevin, we aim to target β / exp( β φ), taking φ(x) = log(1 x2 1) log(0.012 x2 2) as the barrier. We test out the 3 different discretization schemes with β = 10 4 so that β . Stepsize is chosen to be h = 10 5. Projected Langevin is taken to be another option for dealing with constraints, which targets the uniform distribution directly and simply performs ULA followed by projection onto the domain. The plot below shows the samples after 500 iterations, where rφ and the proximal operator are solved with 50 steps of gradient descent steps. Diffusion term φ is solved with 10 inner steps of EM. (...) Stepsize h is picked to be 10 3 in both cases and initialization as N(0, I). |