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].