Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
Authors: Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach, Alessandro Rudi
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 3: (Left) Comparison between our kernelized Laplacian method ... and graph-based Laplacian... We report classification error as a function of the number of samples n. The error is averaged over 50 trials... Our method discovers the structure of the data much faster than graph-based Laplacian... |
| Researcher Affiliation | Academia | Vivien Cabannes ENS INRIA PSL Paris, France ... Loucas Pillaud-Vivien EPFL Lausanne, Switzerland ... Francis Bach ENS INRIA PSL Paris, France ... Alessandro Rudi ENS INRIA PSL Paris, France |
| Pseudocode | Yes | Algorithm 1: Empirical estimates based on spectral filtering. |
| Open Source Code | Yes | Our code is available online at https://github.com/Vivien Cabannes/partial_labelling. |
| Open Datasets | No | We fixed the ratio nℓ/n to one tenth, and generated the data according to two Gaussians in dimension d = 10 with unit variance and whose centers are at distance δ = 3 of each other. Explanation: The paper describes how data was generated but does not provide concrete access information (link, citation, repository) for a publicly available dataset, nor does it specify that this generated data is made publicly available. |
| Dataset Splits | No | We report classification error as a function of the number of samples n. The error is averaged over 50 trials, with errorbars representing standard deviations. Explanation: The paper does not specify percentages or counts for training, validation, or test sets. It only mentions the total number of samples and the ratio of labeled to unlabeled points. |
| Hardware Specification | Yes | When dealing with 1000 points, our algorithm, as well as graph-based Laplacian, can be computed in about one tenth of a second on a 2 GHz processor, while the naive kernel implementation requires 10 seconds. |
| Software Dependencies | No | The paper mentions 'Implemented with Lapack' but does not provide any specific version numbers for software dependencies. |
| Experiment Setup | Yes | Figure 3: (Left) Comparison between our kernelized Laplacian method (Tikhonov regularization version with λ = 1, µn = n 1, p = 50) and graph-based Laplacian based on the same Gaussian kernel with bandwidth σn = n 1 d+4 log(n) as suggested by graph-based theoretical results [24]. |