Approximating Metric Magnitude of Point Sets
Authors: Rayna Andreeva, James Ward, Primoz Skraba, Jie Gao, Rik Sarkar
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments in Section 5 show that the approximation methods are fast and accurate. Iterative Normalization outperforms inversion for larger dataset sizes and converges fast; for the subset selection algorithms, Discrete centers approximates the Greedy Maximization approach empirically at a fraction of the computational cost. |
| Researcher Affiliation | Academia | Rayna Andreeva1, James Ward1, Primoz Skraba2, Jie Gao3, Rik Sarkar1 1School of Informatics, University of Edinburgh 2Queen Mary University of London 3Rutgers University EMAIL, EMAIL |
| Pseudocode | Yes | Algorithm 1: Iterative normalization algorithm for the approximation of magnitude; Algorithm 2: Greedy algorithm for the computation of original magnitude; Algorithm 3: Discrete Center Hierarchy construction; Algorithm 4: Magnitude Clusterer |
| Open Source Code | Yes | Code https://github.com/rorondre/approx_magnitude |
| Open Datasets | Yes | Figure 3 shows the performance of the subset selection algorithms for a number of scikit-learn datasets (Iris, Breast Cancer, Wine) and for subsamples of MNIST, CIFAR10 (Krizhevsky, Nair, and Hinton 2014) and CIFAR100 (Krizhevsky 2009). |
| Dataset Splits | No | The paper mentions 'a randomly generated dataset with 10^4 points sampled from N(0, 1) in R^2' and 'subsamples of size 500 for popular image datasets'. It uses 'MNIST dataset for 2000 epochs' and 'CIFAR10', but does not explicitly provide specific percentages, sample counts, or citations for train/test/validation splits within the main text for these experiments. |
| Hardware Specification | Yes | Experiments ran on a NVIDIA 2080Ti GPU with 11GB RAM and Intel Xeon Silver 4114 CPU. |
| Software Dependencies | No | The paper states 'We use PyTorch's GPU implementation for matrix inversion.' However, it does not provide specific version numbers for PyTorch or any other software dependencies. |
| Experiment Setup | Yes | The Gradient descent experiments used a learning rate of 0.005 and momentum of 0.9. We train five neural networks each with two fully connected hidden layers on the MNIST dataset for 2000 epochs, using cross entropy loss on MNIST. For generalization experiments, ADAM optimizer was used, with a grid of 6 different learning rates in the range [10^-5, 10^-3] and 6 batch sizes between [8, 256]. |