Estimating Convergence of Markov chains with L-Lag Couplings
Authors: Niloy Biswas, Pierre E. Jacob, Paul Vanetti
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate numerically that the bounds provide a practical assessment of convergence for various popular MCMC algorithms, on either discrete or continuous and possibly high-dimensional spaces. In Section 3 we consider applications including Gibbs samplers on the Ising model and gradient-based MCMC algorithms on log-concave targets. |
| Researcher Affiliation | Academia | Niloy Biswas Harvard University niloy_biswas@g.harvard.edu; Pierre E. Jacob Harvard University pjacob@fas.harvard.edu; Paul Vanetti University of Oxford paul.vanetti@spc.ox.ac.uk |
| Pseudocode | Yes | Algorithm 1: Sampling L-lag meeting times; Algorithm 2: A maximal coupling of p and q |
| Open Source Code | Yes | All scripts in R are available at https://github.com/niloyb/Llag Couplings. |
| Open Datasets | Yes | Consider the German Credit data from [34]. There are n = 1000 binary responses (Yi)n i=1 { 1, 1}n indicating whether individuals are creditworthy or not creditworthy, and d = 49 covariates xi Rd for each individual i. [34] Moshe Lichman. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ml. |
| Dataset Splits | No | The paper describes experiments comparing different MCMC algorithms and validating the proposed bounds against exact distances or theoretical work. However, it does not specify explicit training/validation/test dataset splits as these are not typically defined for MCMC convergence studies. |
| Hardware Specification | No | The paper does not specify any particular hardware (e.g., GPU models, CPU types, or memory) used for running the experiments. |
| Software Dependencies | Yes | All scripts in R are available at https://github.com/niloyb/Llag Couplings. The figures were created with packages [58, 57] in R Core Team [45]. [58] Claus O. Wilke. ggridges: Ridgeline plots in ggplot2 . R package version 0.4, 1, 2017. |
| Experiment Setup | Yes | We set the initial distribution π0 to be a point mass at 10. We use L = 1 and L = 150. For each L, N = 10000 independent runs of Algorithm 1 were performed to estimate the bounds in Theorem 2.5 by empirical averages. (from Section 2.2.1) For β = 0.46, we obtain TV bounds for SSG using a lag L = 106, and N = 500 independent repeats. For PT we use 12 chains, each targeting πβ with β in an equispaced grid ranging from 0.3 to 0.46, a frequency of swap moves of 0.02, and a lag L = 2 104. (from Section 3.1) |