Relating Leverage Scores and Density using Regularized Christoffel Functions
Authors: Edouard Pauwels, Francis Bach, Jean-Philippe Vert
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our main result quantitatively describes a decreasing relation between leverage score and population density for a broad class of kernels on Euclidean spaces. Numerical simulations support our findings. [...] We illustrate our results numerically in Section 4. |
| Researcher Affiliation | Collaboration | Edouard Pauwels IRIT-AOC Université Toulouse 3 Paul Sabatier Toulouse, France Francis Bach INRIA Ecole Normale Supérieure PSL Research University Paris, France Jean-Philippe Vert Google Brain CBIO Mines Paris Tech PSL Research University Paris, France |
| Pseudocode | No | The paper describes mathematical formulations and theoretical results, but does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing source code or a link to a code repository. |
| Open Datasets | No | The paper describes numerical illustrations using a "compactly supported sinusoidal density in dimension 1" for which it uses Riemann sums and i.i.d. samples, rather than a named, publicly available dataset with concrete access information. No specific dataset source or link is provided. |
| Dataset Splits | No | The paper does not specify training, validation, and test dataset splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the numerical simulations or experiments. |
| Software Dependencies | No | The paper does not list any specific software dependencies or their version numbers. |
| Experiment Setup | Yes | We use the Riemann sum plug-in approximation described in (2) with n = 2000. [...] We perform extensive investigations with compactly supported sinusoidal density in dimension 1. |