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].
Unbiased Multilevel Monte Carlo Methods for Intractable Distributions: MLMC Meets MCMC
Authors: Tianze Wang, Guanyang Wang
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments confirm our theoretical findings and demonstrate the benefits of unbiased estimators in the massively parallel regime. Keywords: unbiased estimator, function of expectation, parallel computation, nested expectation, coupling |
| Researcher Affiliation | Academia | Tianze Wang EMAIL Department of Statistics Rutgers University, Piscataway, NJ 08854 Guanyang Wang EMAIL Department of Statistics Rutgers University, Piscataway, NJ 08854 |
| Pseudocode | Yes | Algorithm 1: Unbiased Multilevel Monte-Carlo estimator. Algorithm 2: Unbiased Multilevel Monte-Carlo estimator for nested expectation |
| Open Source Code | No | The paper mentions using a third-party R package 'unbiasedmcmc' (Jacob et al., 2020) for parts of its implementation but does not state that the authors are releasing their own code or provide a specific link to their implementation. For example: 'Setting K = 8, and using the R package unbiasedmcmc in Jacob et al. (2020) for estimating E[Xi] 2...' and 'The JOA estimators can be obtained via coupling two Gibbs samplers using the package unbiasedmcmc in Jacob et al. (2020).' |
| Open Datasets | Yes | In our case, we consider the real-data example used in (Plummer, 2015; Jacob et al., 2020) from epidemiology, which is motivated by a study of the international correlation between human papilloma virus (HPV) prevalence and cervical cancer incidence (Maucort Boulch et al., 2008). |
| Dataset Splits | No | The paper describes the real-data example by referencing previous works (Plummer, 2015; Jacob et al., 2020; Maucort Boulch et al., 2008) and outlines the data structure for HPV prevalence and cervical cancer incidence. However, it does not provide explicit training, validation, or test dataset splits; the data is used in a simulation context rather than a typical machine learning task requiring such splits. |
| Hardware Specification | No | The paper states: 'We implement our method using n = 12, p = 0.7, k = 4 103, m = 2k, θ1 {0.02, 0.03, . . . , 0.18} and θ2 {0.02, 0.10} on a CPU-based computer cluster.' This description is too general as it only mentions 'CPU-based computer cluster' without any specific details such as CPU model, number of cores, or memory. |
| Software Dependencies | No | The paper mentions using 'R package unbiasedmcmc' in its numerical examples, but it does not specify the version number for either R or the 'unbiasedmcmc' package. For example: 'Setting K = 8, and using the R package unbiasedmcmc in Jacob et al. (2020)...' |
| Experiment Setup | Yes | Setting K = 8, and using the R package unbiasedmcmc in Jacob et al. (2020) for estimating E[Xi] 2, we generate 5 104 unbiased estimates of g K ( ) using Algorithm 1 with parameter p ranging from 0.6 to 0.8, k = 4 104 and m = 4k... We implement our method using n = 12, p = 0.7, k = 4 103, m = 2k, θ1 {0.02, 0.03, . . . , 0.18} and θ2 {0.02, 0.10} on a CPU-based computer cluster... We implement Algorithm 2 with parameter p = 0.7 to get unbiased estimators of U. In each run, we first sample one θ1 from the product beta posterior, then use the JOA estimator with k = 2 103, m = 3 103 by the R package unbiased MCMC to generate unbiased estimators of Eθ2|θ1[λd]. |