Precise Accuracy / Robustness Tradeoffs in Regression: Case of General Norms
Authors: Elvis Dohmatob, Meyer Scetbon
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our findings are empirically confirmed with simple experiments that represent a variety of settings. This work covers feature covariance matrices and attack norms of any nature, extending previous works in this area. |
| Researcher Affiliation | Collaboration | 1Meta FAIR 2Microsoft Research. Correspondence to: Elvis Dohmatob <dohmatob@meta.com>. |
| Pseudocode | No | No pseudocode or algorithm blocks were explicitly labeled or formatted as such. |
| Open Source Code | Yes | See attached Jupyter (Python) notebook. |
| Open Datasets | Yes | Applying this to the settings considered in Section 5 of (Cui et al., 2022), namely MNIST and Fashion MNIST with kernel K(x, z) = (1 + 10 3x z)5 (the task is to predict the class label via kernel regression), we see from Table 1 of (Cui et al., 2022) that δ = 1+α(2r 1) = 1+1.3(2(0.13) 1) = 0.038 (0, 1) for MNIST and δ = 1+α(2r 1) = 1+1.2(2(0.15) 1) = 0.16 (0, 1) for Fashion MNIST. |
| Dataset Splits | No | The paper does not explicitly mention training, validation, and test splits with specific percentages or sample counts for dataset partitioning. |
| Hardware Specification | No | All experiments in our paper were run on a single modern CPU laptop. No specific CPU model or detailed specifications were provided. |
| Software Dependencies | No | See attached Jupyter (Python) notebook. While this indicates Python, specific version numbers for Python or any libraries used are not provided. |
| Experiment Setup | Yes | For this experiment, we fix the input dimension d = 400, while the covariance matrix Σ and generative model w0 are as in (15) for different values of the sparsity parameter s {10, 20, d = 400}. For different values of sample size n from d to 104, we generate (5 runs) an iid dataset Dn = {(x1, y1), . . . , (xn, yn)} and construct a ordinary least-squares (OLS) estimate bwn for w0. [...] The attack strength r is set as in the second part of Theorem 5.1. |