Log-concave sampling: Metropolis-Hastings algorithms are fast
Authors: Raaz Dwivedi, Yuansi Chen, Martin J. Wainwright, Bin Yu
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We study the problem of sampling from a strongly log-concave density supported on Rd, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA)... We provide numerical examples that support our theoretical findings, and demonstrate the benefits of Metropolis-Hastings adjustment for Langevin-type sampling algorithms. |
| Researcher Affiliation | Academia | Raaz Dwivedi , EMAIL Yuansi Chen , EMAIL Martin J. Wainwright , , EMAIL Bin Yu , EMAIL Department of Statistics Department of Electrical Engineering and Computer Sciences University of California, Berkeley Voleon Group , Berkeley |
| Pseudocode | Yes | Algorithm 1: Metropolis adjusted Langevin algorithm (MALA) |
| Open Source Code | No | The paper does not contain any explicit statements about releasing code or links to source code repositories. |
| Open Datasets | No | The paper uses simulated data or describes methods for generating data based on theoretical models (e.g., "sampling a multivariate Gaussian", "sampling a Gaussian mixture", "Bayesian logistic regression" where data is "randomly draw[n] i.i.d. samples"). It does not provide concrete access information to any publicly available or open datasets. |
| Dataset Splits | No | The experiments involve simulating Markov chains for a number of samples or generating i.i.d. data points for logistic regression. No training/test/validation splits are mentioned for pre-existing datasets, as the datasets are either custom-generated or theoretical distributions. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software components or libraries used. |
| Experiment Setup | Yes | The step-sizes are chosen according to Table 3. For ULA, the error-tolerance δ is chosen to be 0.2. The step-size is error-dependent, precisely chosen to be 10 times of δ. For weakly log-concave density, m is chosen to be δ/(d L). The initial distribution is chosen as µ = N(0, L-1Id) and the step-sizes are chosen according to Table 1, where for ULA, we set three different choices of δ = 0.2 (ULA), δ = 0.1 (small-step ULA) and δ = 1.0 (large-step ULA). |