Toeplitz Least Squares Problems, Fast Algorithms and Big Data

Autor:	Eshragh, Ali, Di Pietro, Oliver, Saunders, Michael A.
Rok vydání:	2021
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Statistics - Computation 62M10 68T09 62R07
Druh dokumentu:	Working Paper
Popis:	In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two recent algorithms (LSAR and Repeated Halving) have applied randomized numerical linear algebra (RandNLA) techniques to fitting an autoregressive model to big time-series data. We investigate and compare the quality of these two approximation algorithms on large-scale synthetic and real-world data. While both algorithms display comparable results for synthetic datasets, the LSAR algorithm appears to be more robust when applied to real-world time series data. We conclude that RandNLA is effective in the context of big-data time series. Comment: 28 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.12994 Zobrazit plný text záznamu View this record from Arxiv