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..
Fast Conditional Mixing of MCMC Algorithms for Non-log-concave Distributions
Authors: Xiang Cheng, Bohan Wang, Jingzhao Zhang, Yusong Zhu
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct experiments to verify the theoretical results and compare global mixing versus conditional mixing for Gaussian mixture models. We take three Gaussian mixtures: ν1 = 0.9N1( 10, 1) + 0.1N1(10, 1), ν2 = 0.15N1( 5, 1) + 0.15N1( 2.5, 1) + 0.3N1(0, 1) + 0.2N1(2.5, 1) + 0.2N1(5, 1), and ν3 = 0.4N2(( 5, 5), I2) + 0.4N2((5, 5), I2) + 0.1N2(( 5, 5), I2) + 0.1N2((5, 5), I2) as our target distributions. We use Algorithm 1 as our sampling algorithm, and set step size h = 10 2. The initial distributions are both uniform in a large enough range. We plot the sampling distribution after T = 500, 5000, 500 rounds respectively in Figure 1a, 1b, and 1c, and plot the conditional and global KL divergence in Figure 1d, 1e, and 1f. |
| Researcher Affiliation | Academia | Xiang Cheng MIT EMAIL Bohan Wang USTC EMAIL Jingzhao Zhang IIIS, Tsinghua; Shanghai Qizhi Institute EMAIL Yusong Zhu Tsinghua University EMAIL |
| Pseudocode | Yes | Algorithm 1 Langevin Monte Carlo Input: Initial parameter z, potential function V , step size h, number of iteration T 1: Initialization z0 z 2: For t = 0 T: 3: Generate Gaussian random vector ξt N(0, Id) 4: Update z(t+1)h zth h V (zth) + 2hξt 5: End For |
| Open Source Code | No | The paper does not provide an explicit statement or link to open-source code for the described methodology. |
| Open Datasets | No | The paper uses constructed target distributions (mixtures of Gaussians) for its experiments, rather than external publicly available datasets. For instance, in Section 6.1, it states: 'We take three Gaussian mixtures: ν1 = 0.9N1( 10, 1) + 0.1N1(10, 1), ν2 = 0.15N1( 5, 1) + 0.15N1( 2.5, 1) + 0.3N1(0, 1) + 0.2N1(2.5, 1) + 0.2N1(5, 1), and ν3 = 0.4N2(( 5, 5), I2) + 0.4N2((5, 5), I2) + 0.1N2(( 5, 5), I2) + 0.1N2((5, 5), I2) as our target distributions.' |
| Dataset Splits | No | The paper describes experiments involving sampling from target distributions rather than training models on datasets with explicit train/validation/test splits. Therefore, it does not specify dataset splits for validation. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments, such as CPU or GPU models, or memory specifications. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies, libraries, or programming languages used in the experiments. |
| Experiment Setup | Yes | We use Algorithm 1 as our sampling algorithm, and set step size h = 10 2. The initial distributions are both uniform in a large enough range. We plot the sampling distribution after T = 500, 5000, 500 rounds respectively in Figure 1a, 1b, and 1c, and plot the conditional and global KL divergence in Figure 1d, 1e, and 1f. |