The Effect of the Intrinsic Dimension on the Generalization of Quadratic Classifiers
Authors: Fabian Latorre, Leello Tadesse Dadi, Paul Rolland, Volkan Cevher
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments. We illustrate our theoretical results on synthetic data. We show how the isotropy of the input distribution plays a major role in the generalization properties of quadratic classifiers. As the dimension increases and the sample size remains proportional to it, we observe a constant generalization gap for the nuclear-norm constrained classifier. In contrast, for SVMs, the gap grows at a predicted d rate. In the case of anisotropic distributions, we observe similar performance for both regularization schemes. |
| Researcher Affiliation | Academia | Fabian Latorre, Leello Dadi, Paul Rolland and Volkan Cevher Laboratory for Information and Inference Systems, EPFL, Switzerland. |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. |
| Open Source Code | Yes | Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] |
| Open Datasets | No | The paper describes generating synthetic data ('Generating Isotropic Data', 'Generating Anistropic Data') rather than using an existing public dataset with concrete access information. |
| Dataset Splits | No | The paper mentions 'ntrain samples' and 'ntest samples' but does not specify exact split percentages, absolute sample counts, or reference predefined splits for reproducibility. |
| Hardware Specification | No | Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [No] |
| Software Dependencies | No | The paper mentions software like JAX and scikit-learn but does not provide specific version numbers for reproducibility. |
| Experiment Setup | Yes | We set the radius λ = 1 for both Nuclear and Frobenius norm constrained classifiers. |