Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams
Authors: Vasileios Maroulas, Joshua L Mike, Christopher Oballe
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, examples of kernel density estimation are presented for typical underlying datasets as well as for virtual electroencephalographic data related to cognition. Applications of the kernel density estimator to analyze data data arising from a neuroscience problem related to cognition. In this example, we consider the widely used autoregressive EEG model introduced in (Franaszczuk and Bilnowaska, 1985), and we employ the KDE established in Proposition 25 to statistically analyze EEG. |
| Researcher Affiliation | Academia | Vasileios Maroulas EMAIL Department of Mathematics University of Tennessee Knoxville, TN 37996, USA. Joshua L Mike EMAIL Computational Mathematics, Science, and Engineering Department Michigan State University East Lansing, MI 48823, USA. Christopher Oballe EMAIL Department of Mathematics University of Tennessee Knoxville, TN 37996, USA. |
| Pseudocode | No | The paper describes methods using mathematical notation, propositions, theorems, and proofs, but does not include any clearly labeled pseudocode or algorithm blocks with structured steps. |
| Open Source Code | No | The text mentions third-party software like Ripser and Dionysus but does not provide a direct link or explicit statement from the authors about the availability of source code for their own methodology. |
| Open Datasets | No | Example 3: '...datasets which each consist of 10 points sampled uniformly from the unit circle with additive Gaussian noise...' Example 4: '...we simulate 200 EEG signals in the alpha range by first generating 200 white noise vectors of length L = 1, 024...' Example 6: '...100 points sampled from a two-lobed polar curve, which are then perturbed by Gaussian noise...' The datasets used are generated by the authors for their experiments and no public access information (link, DOI, or repository) is provided for these specific generated datasets. |
| Dataset Splits | No | The paper describes the generation and categorization of synthetic data for experimental analysis (e.g., 100 EEG signals with SNR1 and 100 with SNR5), but it does not specify explicit training, validation, or test dataset splits in percentages or sample counts for model evaluation or reproduction. |
| Hardware Specification | No | The paper does not contain any specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions software packages like Dionysus and Ripser, but it does not provide specific version numbers for these or any other ancillary software components, which is necessary for reproducible dependency information. |
| Experiment Setup | Yes | Example 3: '...each consist of 10 points sampled uniformly from the unit circle with additive Gaussian noise, N((0, 0), 1/50 2 I2).' Example 4: '...p = 1, β1 = 3.7, and ω1 = 10.5. We corrupt 100 signals by additive noise N(0, 10-1/20), while the rest are corrupted by N(0, 10-5/20)...delay parameter was determined by the sampling rate (100 Hz) along with the dominant underlying frequency of the signals (10 Hz)...' Table 1: 'Choices of sample size n (number of persistence diagrams) and bandwidth σ for each kernel density estimate fˆn,σ(Z) shown in Fig. 9. n 100 300 1000 5000 σ 0.03 0.025 0.020 0.015'. |