• Corpus ID: 208310367

# LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data

@article{Eshragh2019LSAREL,
title={LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data},
author={Ali Eshragh and Fred Roosta and Asef Nazari and Michael W. Mahoney},
journal={arXiv: Methodology},
year={2019}
}
• A. Eshragh, +1 author M. Mahoney
• Published 27 November 2019
• Computer Science, Mathematics
• arXiv: Methodology
We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive (AR) model in big data regimes. We show that the accuracy of approximations lies within $(1+\mathcal{O}(\varepsilon))$ of the true leverage scores with high probability. These theoretical results are subsequently exploited to develop an efficient algorithm…

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## References

SHOWING 1-10 OF 40 REFERENCES
Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting
• Computer Science
International Journal of Forecasting
• 2019
This paper proposes a time-adaptive lasso estimator and an efficient coordinate descent algorithm for updating the VAR model parameters recursively online and shows good abilities to track changes in the multivariate time series dynamics on simulated data.
Information-Based Optimal Subdata Selection for Big Data Linear Regression
• Mathematics, Computer Science
Journal of the American Statistical Association
• 2018
Theoretical results and extensive simulations demonstrate that the IBOSS approach is superior to subsampling-based methods, sometimes by orders of magnitude, and the advantages of the new approach are also illustrated through analysis of real data.
A statistical perspective on algorithmic leveraging
• Computer Science, Mathematics
J. Mach. Learn. Res.
• 2015
This work provides an effective framework to evaluate the statistical properties of algorithmic leveraging in the context of estimating parameters in a linear regression model and shows that from the statistical perspective of bias and variance, neither leverage-based sampling nor uniform sampling dominates the other.
Fast approximation of matrix coherence and statistical leverage
• Computer Science, Mathematics
ICML
• 2012
A randomized algorithm is proposed that takes as input an arbitrary n × d matrix A, with n ≫ d, and returns, as output, relative-error approximations to all n of the statistical leverage scores.
The Importance of Environmental Factors in Forecasting Australian Power Demand
• Mathematics
Environmental Modeling & Assessment
• 2021
We develop a time series model to forecast weekly peak power demand for three main states of Australia for a yearly timescale, and show the crucial role of environmental factors in improving the
Randomized Algorithms for Matrices and Data
This monograph will provide a detailed overview of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis.
Low-Rank Approximation and Regression in Input Sparsity Time
• Mathematics, Computer Science
ArXiv
• 2012
We design a new distribution over m × n matrices S so that, for any fixed n × d matrix A of rank r, with probability at least 9/10, ∥SAx∥2 = (1 ± ε)∥Ax∥2 simultaneously for all x ∈ Rd. Here, m is
Assessing stochastic algorithms for large scale nonlinear least squares problems using extremal probabilities of linear combinations of gamma random variables
• Mathematics, Computer Science
SIAM/ASA J. Uncertain. Quantification
• 2015
This paper proposes eight variants of a practical randomized algorithm where the uncertainties in the major stochastic steps are quantified, and proves tight necessary and sufficient conditions on the sample size to satisfy the prescribed probabilistic accuracy.
A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle
This paper models occasional, discrete shifts in the growth rate of a nonstationary series. Algorithms for inferring these unobserved shifts are presented, a byproduct of which permits estimation of
Demand forecasting in the presence of systematic events: Cases in capturing sales promotions
• Mathematics, Computer Science
• 2019
This paper develops and test a novel regime-switching approach to quantify systematic information/events and objectively incorporate them into the baseline statistical model and indicates that the proposed model can successfully improve the forecast accuracy when compared to the current industry practice which heavily relies on human judgment to factor in all types of information/ Events.