Exponential ergodicity of mirror-Langevin diffusions
Authors: Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet, Austin Stromme
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical experiments In this section, we examine the numerical performance of the Newton-Langevin Algorithm (NLA)... Figure 4 compares the performance of NLA to that of the Unadjusted Langevin Algorithm (ULA) [DM+19] and of the Tamed Unadjusted Langevin Algorithm (TULA) [Bro+19]. |
| Researcher Affiliation | Academia | Sinho Chewi MIT schewi@mit.edu Thibaut Le Gouic MIT tlegouic@mit.edu Chen Lu MIT chenl819@mit.edu Tyler Maunu MIT maunut@mit.edu Philippe Rigollet MIT rigollet@mit.edu Austin Stromme MIT astromme@mit.edu |
| Pseudocode | Yes | In this section, we examine the numerical performance of the Newton-Langevin Algorithm (NLA), which is given by the following Euler discretization of NLD: V (Xk+1) = (1 h) V (Xk) + 2h [ 2V (Xk)] 1/2ξk, (NLA) |
| Open Source Code | No | The paper does not provide any statement or link regarding the public availability of its source code. |
| Open Datasets | No | The paper mentions 'sampling from an ill-conditioned generalized Gaussian distribution on R100' and 'sampling from the uniform distribution on a convex body C', but does not provide concrete access information (link, DOI, repository, or citation) for a specific public dataset used in experiments. |
| Dataset Splits | No | The paper does not provide specific details on train, validation, or test dataset splits (e.g., percentages, sample counts, or predefined split references). |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU/GPU models, processor types, or memory used for running the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., programming languages, libraries, or frameworks with their respective versions) used for implementation or experiments. |
| Experiment Setup | Yes | Figure 4 compares the performance of NLA to that of the Unadjusted Langevin Algorithm (ULA) [DM+19] and of the Tamed Unadjusted Langevin Algorithm (TULA) [Bro+19]. We run the algorithms 50 times and compute running estimates for the mean and scatter matrix of the family following [ZWG13]. and NLA, h = 0.2 ULA, h = 0.2 TULA, h = 0.2 NLA, h = 0.05 ULA, h = 0.05 TULA, h = 0.05 (from Figure 4 legend) and in Section 4.2 For NLA, we take e V (x) = log(1 x2 1) log(a2 x2 2) and β = 10 4. |