Subgroup-based Rank-1 Lattice Quasi-Monte Carlo
Authors: Yueming LYU, Yuan Yuan, Ivor Tsang
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirically, our methods can generate a near-optimal rank-1 lattice compared with the Korobov exhaustive search regarding the l1-norm and l2-norm minimum distance. Moreover, experimental results show that our method achieves superior approximation performance on benchmark integration test problems and kernel approximation problems. In this section, we first evaluate the minimum distance generated by our subgroup rank-1 lattice in section 5.1. We then evaluate the subgroup rank-1 lattice on integral approximation tasks and kernel approximation task in section 5.2 and 5.3, respectively. |
| Researcher Affiliation | Academia | Yueming Lyu Australian Artificial Intelligence Institute University of Technology Sydney yueminglyu@gmail.com Yuan Yuan CSAIL Massachusetts Institute of Technology miayuan@mit.edu Ivor W. Tsang Australian Artificial Intelligence Institute University of Technology Sydney Ivor.Tsang@uts.edu.au |
| Pseudocode | No | The paper describes methods in prose and mathematical formulations but does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper states "A side product is a closed-form method to generate QMC points set on sphere Sd 1 with bounded mutual coherence, which is presented in Appendix." but does not provide an explicit statement or link confirming the release of source code for the described methodology. |
| Open Datasets | Yes | We evaluate the methods on the DNA [28] and the SIFT1M [14] dataset over 50 independent runs. |
| Dataset Splits | No | The paper mentions running experiments over "50 independent runs" and using "2000 random samples to construct the Gram matrix" but does not specify explicit train/validation/test dataset splits, percentages, or pre-defined split references. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., GPU/CPU models, memory, or cluster configurations) used for running its experiments. |
| Software Dependencies | No | The paper mentions using "MATLAB" and specific functions ("slicesample", "hmc Sampler") but does not provide specific version numbers for MATLAB or any other software dependencies. |
| Experiment Setup | Yes | We set the dimension d as in {50, 100, 200, 500}. For each dimension d, we set the number of points n as the first ten prime numbers such that 2d divides n 1, i.e., 2d (n 1). ... We fix b = 2 and c = 1 in all the experiments. ... For both Halton sequence and Sobol sequence, we use the scrambling technique suggested in [8]. For all the QMC methods, we use the random shift technique as in Eq.(4). ... Each run contains 2000 random samples to construct the Gram matrix. The bandwidth parameter of Gaussian kernel is set to 15 in all the experiments. |