Poisson-Minibatching for Gibbs Sampling with Convergence Rate Guarantees
Authors: Ruqi Zhang, Christopher M. De Sa
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the effectiveness of our method on multiple applications and in comparison with both plain Gibbs and previous minibatched methods. We evaluate Poisson-minibatching Gibbs empirically, and show that its performance can match that of plain Gibbs sampling while using less computation at each iteration. We first test the performance of Poisson-minibatching Gibbs sampling on the Potts model [14] as in De Sa et al. [3]. We compare PGITS, PGDA with: (1) Gibbs sampling with FITS (Gibbs-ITS); (2) Gibbs sampling with Double Chebyshev approximation (Gibbs-DA); (3) Gibbs with rejection sampling (Gibbs-rejection); and (4) Poisson-Gibbs with rejection sampling (PG-rejection). |
| Researcher Affiliation | Academia | Ruqi Zhang Cornell University rz297@cornell.edu Christopher De Sa Cornell University cdesa@cs.cornell.edu |
| Pseudocode | Yes | Algorithm 1 Gibbs Sampling. Algorithm 2 Poisson-Gibbs. Algorithm 3 PGDA: Poisson-Gibbs Double Chebyshev Approximation. |
| Open Source Code | Yes | We release the code at https://github.com/ruqizhang/poisson-gibbs. |
| Open Datasets | No | The paper mentions using specific models and parameters for experiments (e.g., Potts model, continuous spin models, truncated Gaussian mixture), but does not provide concrete access information (link, DOI, specific repository, or formal citation with author/year) for the datasets used in these experiments. It references previous work for model setup, but not for direct dataset access. |
| Dataset Splits | No | The paper does not specify training, validation, or test dataset splits (e.g., percentages or sample counts). It describes the models (e.g., Potts model on an N x N lattice) and how ground truth was obtained for continuous models (running Gibbs-ITS for 10^7 iterations), but not specific dataset splitting methodology. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., CPU, GPU, memory, or cloud instance types) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies. It only mentions the programming language for the released code implicit from the GitHub link, but no libraries or solvers with versions. |
| Experiment Setup | Yes | For Potts models: "We set the model to be fully connected and the interaction Aij is determined by the distance between site i and site j based on a Gaussian kernel [3]. The graph has n = N^2 = 400 variables in total, β = 4.6 and D = 10. On this model, L = 5.09. We set λ = 1 L^2 for all minibatch methods. We tried two values for the second minibatch size in Double MIN-Gibbs λ2 = 1 L^2 and 10^4 L^2." For Continuous Spin Models: "x(i) 2 [0, 1] and β = 1. L = 13.71 and we set λ = L^2. The degree of polynomial is m = 3 for PGITS and the first approximation in PGDA. The degree of polynomial is k = 10 for the second approximation in PGDA. In rejection sampling, we set the proposal distribution to be wg where g is the uniform distribution on [0, 1] and w is a constant tuned for best performance." For Truncated Gaussian Mixture: "y = 2, x1 = 0 and x2 = 1. N = 10^6. L = 1581.14 for this model and we set λ = 500, m = 20 and k = 25. A uniform distribution in [ 6, 6] is used as the proposal distribution in Gibbs with rejection sampling." |