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 [1].
Langevin Monte Carlo: random coordinate descent and variance reduction
Authors: Zhiyan Ding, Qin Li
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we test the efficiency of variance reduction enhanced RCD methods using the following three examples. We should mention that it is numerically challenging to compute the Wasserstein distance on a high dimensional space, so we present the convergence of error only in the weak sense, by testing it on a test function. ... In all the numerical examples above, we observe, in the O-LMC framework, the classical O-LMC gives the error saturating at h while the variance reduced algorithms roughly gives saturation error h2. In the U-LMC framework, the dependence of such error on h increases from 1 to 2.5 when variance reduction techniques are incorporated. |
| Researcher Affiliation | Academia | Zhiyan Ding EMAIL Mathematics Department University of Wisconsin-Madison Madison, WI 53705 USA. Qin Li EMAIL Mathematics Department and Wisconsin Institutes for Discovery University of Wisconsin-Madison Madison, WI 53705 USA. |
| Pseudocode | Yes | Algorithm 1 Overdamped/Underdamped Langevin Monte Carlo (O/U-LMC) ... Algorithm 2 RCD-O/U-LMC ... Algorithm 3 SVRG-O(U)-LMC ... Algorithm 4 RCAD-O(U)-LMC |
| Open Source Code | No | The paper does not provide explicit access to source code for the methodology described. It only provides license information for the paper itself, not for code. |
| Open Datasets | No | The paper uses synthetic data for examples 1 and 2 (Gaussian distributions) and generates its own data for example 3 (Generalized linear regression) without providing public access or linking to an external dataset. For example 3: 'We choose d = 100, x = 1 and generate I = 100 data pairs. We further set the prior to be N(0, Id), and we evaluate the algorithms with two different choices of pnos.' |
| Dataset Splits | No | The paper uses synthetic data and generated data for its examples. For Example 3 (Generalized linear regression), it states 'We choose d = 100, x = 1 and generate I = 100 data pairs.' No information about dataset splits for training, validation, or testing is provided, as the problems are set up as sampling tasks rather than supervised learning with fixed datasets. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., CPU, GPU models, or memory specifications) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers used for the implementation or experiments. |
| Experiment Setup | Yes | We run RCD-O/U-LMC, RCAD-O/U-LMC and SVRG-O/U-LMC with N = 5 10^5 particles with different stepsizes h, and test expectation estimation error by calculating ... In this example, our target distribution is the summation of two Gaussians... We choose d = 1000 and N = 10^6 particles. ... In the test, we choose d = 100, x = 1 and generate I = 100 data pairs. ... All six algorithms, RCD-O/U-LMC, RCAD-O/U-LMC, SVRG-O/U-LMC are run with N = 10^6. |