Improved algorithm and bounds for successive projection

Authors: Jiashun Jin, Tracy Ke, Gabriel Moryoussef, Jiajun Tang, Jingming Wang

ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental 5 NUMERICAL STUDY We compare SPA, pp-SPA, and two simplified versions P-SPA and D-SPA (for illustration). ... We evaluate the vertex hunting error maxk{ ˆvk vk } (subject to a permutation of ˆv1, . . . , ˆv K). For each set of parameters, we report the average error over 20 repetitions. The results are in Figure 3.
Researcher Affiliation Academia Jiashun Jin & Gabriel Moryoussef Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213, USA {jiashun, gmoryous}@andrew.cmu.edu Zheng Tracy Ke & Jiajun Tang & Jingming Wang Department of Statistics Harvard University Cambridge, MA 02138, USA {zke,jiajuntang,jingmingwang}@fas.harvard.edu
Pseudocode Yes Algorithm 1 The (orthodox) Successive Projection Algorithm (SPA) ... Algorithm 2 Pseudo-Point Successive Projection Algorithm (pp-SPA)
Open Source Code Yes The code to reproduce these experiments is available at https://github.com/Gabriel78110/Vertex Hunting.
Open Datasets No The paper describes generating its own synthetic data for the experiments: 'Given (n, d, σ), we first draw (n 30) points uniformly from the 2-dimensional simplex whose vertices are y1, y2, y3, and then put 10 points on each vertex of this simplex. ... Finally, we generate X1, X2, . . . , Xn from model (1).' No concrete access information (link, DOI, citation) is provided for a publicly available dataset.
Dataset Splits No The paper describes generating data for its experiments but does not provide details on specific training, validation, or testing splits (e.g., percentages, sample counts, or methods like cross-validation).
Hardware Specification No The paper does not provide any specific hardware details such as exact GPU/CPU models, processor types, or memory amounts used for running its experiments.
Software Dependencies No The paper does not provide specific ancillary software details with version numbers (e.g., library or solver names with version numbers like Python 3.8, PyTorch 1.9) needed to replicate the experiment.
Experiment Setup Yes For pp-SPA and D-SPA, we need to specify tuning parameters (N, ). We use the heuristic choice in Remark 2. ... For N, we typically take N = log(n) in theory and N = 3 in practice. Concerning , we use a heuristic choice = maxi Yi Y /5, where Y = 1n Pn i=1 Yi.