Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing
Authors: Youwei Shu, Xi Xiao, Derui Wang, Yuxin Cao, Siji Chen, Jason Xue, Linyi Li, Bo Li
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experiments on real-world datasets confirm our theoretical analysis of the ESG distributions, that they provide almost the same certification under different exponents η for both RS and DSRS. |
| Researcher Affiliation | Collaboration | Youwei Shu 1 Xi Xiao 1 Derui Wang 2 Yuxin Cao 1 Siji Chen 1 Minhui Xue 2 Linyi Li 3 4 Bo Li 3 5 Shenzhen International Graduate School, Tsinghua University 2CSIRO s Data61 3University of Illinois Urbana-Champaign 4Simon Fraser University 5University of Chicago. |
| Pseudocode | Yes | Algorithm 1: Algorithm for finding tight µ for the Ω( d) lower bound |
| Open Source Code | Yes | Our code is available at https://gi thub.com/tdano1/eg-on-smoothing. |
| Open Datasets | Yes | All base classifiers used in this work are trained by CIFAR-10 (Krizhevsky et al., 2009) or Image Net (Russakovsky et al., 2015), taking EGG with η = 2 as the noise distribution. |
| Dataset Splits | No | The paper mentions using a "test dataset" but does not provide explicit details on train/validation/test splits by percentages or sample counts for reproducibility. It primarily details sampling numbers for noise distributions for certification, rather than data partitioning for training. |
| Hardware Specification | Yes | All of our experiments on real-world datasets are composed of sampling and certification, which are finished with 4 NVIDIA RTX 3080 GPUs and CPUs. |
| Software Dependencies | No | The scipy package loses precision when calculating integrals for the Γ(a, 1) distribution with large parameters (say, a > 500 ) on infinite intervals. To solve this problem, we implement a Linear Numerical Integration (LNI) method to compute the expectations fast and accurately based on Lemma 5.6. |
| Experiment Setup | Yes | The sampling number N is set to 100000, with the significance level α = 0.001. In the double-sampling process, we set k = 1530 and k = 75260 for CIFAR-10 and Image Net, respectively, in consistent with base classifiers. The sampling numbers N1, N2 are 50000, and the significance levels α1, α2 are 0.0005 for Monte Carlo sampling, equal for P and Q. The error bound e for certified radius is set at 1 10 6. For all the ESG experiments, we set the number of segments to 256, and ι = 10 4. |