2020/07/31 by Zhishen Huang, Stephen Becker · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Autocorrelation #Combinatorics #Computer science #Dimension (graph theory) #Dimensionality reduction #Gaussian Processes and Bayesian Inference #Graph #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Regression #Spectral density #Spectral density estimation #Statistics #Stochastic Gradient Optimization Techniques #Theoretical computer science #cs.LG #eess.SP #msc:65Z05 #physics.comp-ph #stat.ML
paper · pdf · doi:10.1016/j.jcp.2021.110686
published in Journal of Computational Physics 447, 110686 (Elsevier BV) · 17 pages
openalex publication_date 2021/09/09 · arxiv created 2021/09/16 · arxiv updated 2021/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can be used to compress simulation data and still accurately estimate time autocorrelation and power spectral density. For a given compression ratio, the accuracy is much higher than using previously known methods. In addition to providing theoretical guarantees, we apply sketching to a molecular dynamics simulation of methanol and find that the estimate of spectral density is 90% accurate using only 10% of the data.