Positional Encoder Graph Quantile Neural Networks for Geographic Data
Authors: William E. R. de Amorim, Scott A Sisson, Thais Carvalho Valadares Rodrigues, David J Nott, Guilherme S. Rodrigues
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results on benchmark datasets show that the PE-GQNN outperforms existing methods in both predictive accuracy and uncertainty quantification, without incurring additional computational cost. We also identify important special cases arising from our formulation, including the PE-GNN. Section 4 shows experimental results on four real-world datasets. |
| Researcher Affiliation | Academia | William E. R. de Amorim EMAIL Department of Statistics University of Brasília Brazil Scott A. Sisson EMAIL School of Mathematics and Statistics University of New South Wales Australia Thais C. V. Rodrigues EMAIL Department of Statistics University of Brasília Brazil David J. Nott EMAIL Department of Statistics and Data Science National University of Singapore Singapore Guilherme S. Rodrigues EMAIL Department of Statistics University of Brasília Brazil |
| Pseudocode | Yes | Algorithm 1 PE-GQNN training |
| Open Source Code | Yes | The source code is available at: https://github.com/William Rappel98/PE-GQNN. |
| Open Datasets | Yes | Empirical results on benchmark datasets show that the PE-GQNN outperforms existing methods... We conducted comprehensive simulations to explore the prediction performance and other properties of the proposed model. Computation was performed on an Intel i7 (7th Generation) processor. Candidate models: The experiment was designed to compare five primary approaches for addressing spatial regression problems across four diverse real-world datasets (California Housing, Air Temperature, 3D Road, and Australian Census). ... California Housing, recorded during the 1990 U.S. census (Pace & Barry, 1997). ... Air Temperature dataset (Hooker et al. (2018))... 3D Road dataset (Kaul et al. (2013))... The 2021 Australian Census data... publicly available3, and spatial coordinates were obtained from the absmapsdata R package (Mackey, 2025). Footnote 3: https://www.abs.gov.au/census/find-census-data/datapacks?release=2021&product=GCP&geography=SA1&header=S |
| Dataset Splits | Yes | All models were trained and evaluated using 80% of the data for training, 10% for validation, and 10% for testing. In the case of SMACNP, to adhere to the specifications of Bao et al. (2024), a training subsample was extracted to represent 10% of the entire dataset. ... Models were trained with 80% of the data, with 10% for validation and testing each... The data were split into 90% for training, 1% for validation, and 9% for testing. The dataset was split into 80/10/10% training, validation, and test sets. |
| Hardware Specification | Yes | Computation was performed on an Intel i7 (7th Generation) processor. |
| Software Dependencies | No | The paper mentions 'Py Torch (Paszke et al., 2019)' and 'Py Torch Geometric (Fey & Lenssen, 2019)' but does not provide specific version numbers for these software components used in the experiments. |
| Experiment Setup | Yes | All models were trained using the Adam optimizer (Kingma & Ba, 2015), with early stopping employed to prevent overfitting. For GNN-based approaches, we used k = 5 nearest neighbors to construct the graphs. The learning rate was set to 0.001 across all models. A batch size of 1,024 was used for the Air Temperature dataset, while a batch size of 2,048 was used for the remaining three datasets. Table 6: Layer (type & shape) ... Dropout regularization Dropout rate: p = 0.5 |