Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Robust Topological Inference: Distance To a Measure and Kernel Distance
Authors: Frédéric Chazal, Brittany Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, Larry Wasserman
JMLR 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1 shows three complex point clouds, based on a model used for simulating cosmology data. Visually, the three samples look very similar. Below the data plots are the persistence diagrams, which are summaries of topological features defined in Section 2. The persistence diagrams make it clearer that the third data set is from a different data generating process than the first two. [...] The DTM captures the difference between the two players: the defender leaves one big portion of the filed uncovered (1 significant loop in the persistence diagram), while the midfielder does not cover the 4 corners (4 significant loops). |
| Researcher Affiliation | Academia | Frédéric Chazal EMAIL Inria Saclay Ile-de-France [...] Brittany Fasy EMAIL Computer Science Department Montana State University [...] Bertrand Michel EMAIL Ecole Centrale de Nantes [...] Alessandro Rinaldo EMAIL Department of Statistics Carnegie Mellon University [...] Larry Wasserman EMAIL Department of Statistics Carnegie Mellon University [...] All listed affiliations are academic institutions or public research organizations (Inria). |
| Pseudocode | No | The paper describes mathematical proofs, theorems, and algorithms in natural language and mathematical notation but does not contain any clearly labeled pseudocode blocks or algorithm listings. |
| Open Source Code | Yes | The computing for the examples in this paper were done using the R package TDA. See Fasy et al. (2014a). The package can be downloaded from http://cran.r-project.org/web/packages/TDA/index.html. |
| Open Datasets | No | The paper uses data from 'simulating cosmology data', 'Voronoi Models', 'Cassini curve', '2D grid', and 'soccer players' (referencing Pettersen et al. (2014)). However, it does not provide direct links, DOIs, or specific repositories for accessing these datasets or the generated data. |
| Dataset Splits | No | The paper analyzes various datasets and models but does not describe any specific training, validation, or test dataset splits required for reproduction. The methods are applied to entire datasets or simulated data points. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments, such as CPU or GPU models, or cloud computing specifications. |
| Software Dependencies | No | The paper mentions using 'the R package TDA' but does not specify the version number of the R language or the TDA package. The problem statement requires specific version numbers. |
| Experiment Setup | Yes | We propose a method for choosing the tuning parameter m for DTM and the bandwidth h for the kernel distance. (Section 7.1). [...] We chose the smoothing parameters by maximizing the quantity S( ), defined in Section 7.1. [...] The data in Figure 12 are 10,000 data points on a 2D grid. We add Gaussian noise plus 1,000 outliers and compute the persistence diagrams of Kernel Density Estimator, Kernel distance, and Distance to Measure. [...] DTM m=0.005 [...], KDE h=0.05 [...]. |