Robustness of Community Detection to Random Geometric Perturbations
Authors: Sandrine Peche, Vianney Perchet
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The different results provided are theoretical and we proved that two eigenvalues separate from the bulk of the spectrum if the different parameters are big enough and sufficiently far from each other. And if they are too close to each other, it is also quite clear that spectral methods will not work. However, we highlight these statements in Figure 1. It illustrates the effect of perturbation on the spectrum of the stochastic block models for the following specific values: N = 2000, p1 = 2.5%, p2 = 1%, = 0.97 and γ 2 {50, 70, 100, 110}. Notice that for those specific values with get λ1 = 35, λ2 = 15 and µ1 2 {20, 14.3, 10, 9.1}; in particular, two eigenvalues are well separated in the unperturbed stochastic block model. and those theoretical results are validated empirically by some simulations provided in the Appendix. |
| Researcher Affiliation | Collaboration | Sandrine Péché LPSM, University Paris Diderot peche@lpsm.fr Vianney Perchet Crest, ENSAE & Criteo AI Lab vianney.perchet@normalesup.org |
| Pseudocode | No | No pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., repository link, explicit statement of code release, or mention of code in supplementary materials) for the methodology described. |
| Open Datasets | No | The paper does not use an external, publicly available dataset in the traditional sense. It generates data based on a stochastic block model perturbed by a geometric graph where 'Xi are i.i.d., drawn from the 2-dimensional Gaussian distribution N(0, I2)'. |
| Dataset Splits | No | The paper does not describe explicit training, validation, or test dataset splits. The 'experiments' section presents simulation results validating theoretical findings, but not in the context of machine learning model training with distinct data splits. |
| Hardware Specification | No | The paper mentions simulations but does not provide any specific hardware details (e.g., GPU/CPU models, memory, or cloud instance types) used for running the experiments. |
| Software Dependencies | No | The paper mentions simulations but does not provide any specific software dependencies or their version numbers needed to replicate the experiments. |
| Experiment Setup | Yes | The 'Experiments' section details the specific parameter values used for simulations: 'N = 2000, p1 = 2.5%, p2 = 1%, = 0.97 and γ 2 {50, 70, 100, 110}'. |