2012/06/27 by Dongryeol Lee, Lee, Dongryeol, Alexander Gray +1
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning and Data Classification #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1206.6857
openalex publication_date 2012/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).