Synthesis of MCMC and Belief Propagation
Authors: Sung-Soo Ahn, Michael Chertkov, Jinwoo Shin
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we report experimental results for computing partition function of the Ising model and the hard-core model. We compare Algorithm 2 in Section 3 (coined MCMC-BP-2reg) and Algorithm 3 in Section 4.2 (coined MCMC-BP-whole), with the bare Bethe approximation (coined BP) and the popular Gibbs-sampler (coined MCMC-Gibbs). To make the comparison fair, we use the same annealing scheme for all MCMC schemes, thus making their running times comparable. More specifically, we generate each sample after running T1 = 1, 000 iterations of an MC and take s1 = 100 samples to compute each estimation (e.g., Hi) at intermediate steps. For performance measure, we use the log-partition function approximation error defined as | log Z log Zapprox|/| log Z|, where Zapprox is the output of the respective algorithm. We conducted 3 experiments on the 4 4 grid graph. As seen clearly in Figure 1, BP and MCMC-Gibbs are outperformed by MCMC-BP-2reg or MCMC-BP-whole at most tested regimes in the first experiment with no external field, where in this case, the 2-regular loop series (LS) is equal to the full one. |
| Researcher Affiliation | Academia | School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea 1 Theoretical Division, T-4 & Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, 2Skolkovo Institute of Science and Technology, 143026 Moscow, Russia |
| Pseudocode | Yes | Algorithm 1 Sampling 2-regular loops; Algorithm 2 Approximation for Z2-Loop; Algorithm 3 Approximation for ZLoop |
| Open Source Code | No | The paper does not provide an explicit statement about the availability of its source code, nor does it include a link to a repository. |
| Open Datasets | No | The paper describes generating instances of the Ising model and hard-core model on a 4x4 grid graph for experiments, but does not provide access information (link, DOI, specific citation) for these generated datasets or a general public source for the specific data used in their experiments. |
| Dataset Splits | No | The paper discusses the number of samples and iterations for its MCMC algorithms but does not provide specific training, validation, or test dataset splits. |
| Hardware Specification | No | The paper describes experiments conducted on a 4x4 grid graph but does not specify any hardware details such as CPU, GPU, or memory used for these experiments. |
| Software Dependencies | No | The paper describes algorithms and methods but does not list any specific software dependencies or their version numbers (e.g., programming languages, libraries, frameworks). |
| Experiment Setup | Yes | To make the comparison fair, we use the same annealing scheme for all MCMC schemes, thus making their running times comparable. More specifically, we generate each sample after running T1 = 1, 000 iterations of an MC and take s1 = 100 samples to compute each estimation (e.g., Hi) at intermediate steps. |