Accurate Quantization of Measures via Interacting Particle-based Optimization
Authors: Lantian Xu, Anna Korba, Dejan Slepcev
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical results are to be found in Section 6. In this section, we investigate numerically the quantization properties of the sampling algorithms discussed above, namely SVGD (Liu & Wang, 2016), Normalized SVGD presented in Section 4, MMD descent (Arbel et al., 2019), and KSD Descent (Korba et al., 2021), as well as greedy algorithms such as Kernel Herding (KH) (Chen et al., 2012) and Stein points (SP) (Chen et al., 2018). |
| Researcher Affiliation | Academia | 1Carnegie Mellon University 2CREST, ENSAE, IP Paris. |
| Pseudocode | Yes | Algorithm 1 Normalized SVGD (NSVGD) |
| Open Source Code | Yes | The code to reproduce the experiments are available at https://github.com/xulant/accurate-quantization-and-nsvgd. |
| Open Datasets | No | We chose a Gaussian kernel for the MMD, since MMD between a discrete distribution and a Gaussian (continuous) target can be computed in closed form... when the target is a Gaussian distribution, for d = 2, 3, 4. In Appendix E.3, 'when the target distribution is a 2-dimensional bimodal Gaussian mixture.' The paper defines synthetic target distributions, but does not provide specific access information (URL, DOI, citation to a specific dataset instance) for pre-existing datasets. |
| Dataset Splits | No | Each point is the result of averaging 10 runs of each algorithm run for 1e4 iterations, where the initial particles are i.i.d. samples of π (this does not apply to greedy algorithms). Results are averaged over 50 independent experiments, with 50 p p matrices (i.e., the number of particles in this experiment). This describes experimental runs and averaging, but not traditional train/validation/test splits of a fixed dataset. |
| Hardware Specification | No | The paper does not contain any explicit details regarding the hardware specifications (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions optimizers like L-BFGS (Liu & Nocedal, 1989) and Ada Grad (Duchi et al., 2011), but does not provide specific version numbers for any software dependencies, programming languages, or libraries used in the implementation. |
| Experiment Setup | Yes | In our experiments... SVGD with Gaussian and Laplace kernel, γ=0.5, after 1000 iterations; NSVGD with Laplace kernel and γ=0.1, after 30 iterations. Figure 3 caption states 'The kernel bandwidth for all algorithm is set to 1.' Section 6.2 mentions 'Each point is the result of averaging 10 runs of each algorithm run for 1e4 iterations'. NSVGD uses 'a self-tuning kernel bandwidth h = (1/n2 P i,j xi xj 2)1/2n 1/d+4 inspired from Scott s rule (Scott, 1979)'. |