2023/10/12 by Rainie Bozzai, Thomas Rothvoß, Bozzai, Rainie +1
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · #Computational Geometry (cs.CG) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Mathematical Approximation and Integration #Metal-Organic Frameworks: Synthesis and Applications #MicroRNA in disease regulation
paper · pdf · doi:10.48550/arxiv.2310.08548
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply the discrepancy method and a chaining approach to give improved bounds on the coreset complexity of a wide class of kernel functions. Our results give randomized polynomial time algorithms to produce coresets of size O((√(d))/(ε)√(loglog (1)/(ε))) for the Gaussian and Laplacian kernels in the case that the data set is uniformly bounded, an improvement that was not possible with previous techniques. We also obtain coresets of size O((1)/(ε)√(loglog (1)/(ε))) for the Laplacian kernel for d constant. Finally, we give the best known bounds of O((√(d))/(ε)√log(2max\1,α\)) on the coreset complexity of the exponential, Hellinger, and JS Kernels, where 1/α is the bandwidth parameter of the kernel.