# Optimal Sampling Designs for Multi-dimensional Streaming Time Series with Application to Power Grid Sensor Data

arXiv: https://arxiv.org/abs/2303.08242 · HTML: https://mlsanity.com/paper/2303.08242/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 17 of 17)

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Revisiting the Nystrom Method for Improved Large-Scale Machine Learning](https://mlsanity.com/paper/1303.1849/) (2013)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data](https://mlsanity.com/paper/2005.10435/) (2020)
- [Information-Based Optimal Subdata Selection for Big Data Linear Regression](https://mlsanity.com/paper/1710.10382/) (2017)
- [Joint Status Sampling and Updating for Minimizing Age of Information in the Internet of Things](https://mlsanity.com/paper/1807.04356/) (2018)
- [Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithms](https://mlsanity.com/paper/2002.10526/) (2020)
- [LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data](https://mlsanity.com/paper/1911.12321/) (2019)
- [Orthogonal Subsampling for Big Data Linear Regression](https://mlsanity.com/paper/2105.14647/) (2021)
- [LowCon: A design-based subsampling approach in a misspecified linear modeL](https://mlsanity.com/paper/2010.12178/) (2020)
- [On statistics, computation and scalability](https://mlsanity.com/paper/1309.7804/) (2013)
- [Sequential online subsampling for thinning experimental designs](https://mlsanity.com/paper/2004.00792/) (2020)
- [Online Censoring for Large-Scale Regressions with Application to Streaming Big Data](https://mlsanity.com/paper/1507.07536/) (2015)
- [Database of Power Grid Frequency Measurements](https://mlsanity.com/paper/2006.01771/) (2020)
- [Sampling Strategies for Static Powergrid Models](https://mlsanity.com/paper/2204.09053/) (2022)

## Built on by (most cited first, 1 of 1)

- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)

## Abstract (arXiv)

The Internet of Things (IoT) system generates massive high-speed temporally correlated streaming data and is often connected with online inference tasks under computational or energy constraints. Online analysis of these streaming time series data often faces a trade-off between statistical efficiency and computational cost. One important approach to balance this trade-off is sampling, where only a small portion of the sample is selected for the model fitting and update. Motivated by the demands of dynamic relationship analysis of IoT system, we study the data-dependent sample selection and online inference problem for a multi-dimensional streaming time series, aiming to provide low-cost real-time analysis of high-speed power grid electricity consumption data. Inspired by D-optimality criterion in design of experiments, we propose a class of online data reduction methods that achieve an optimal sampling criterion and improve the computational efficiency of the online analysis. We show that the optimal solution amounts to a strategy that is a mixture of Bernoulli sampling and leverage score sampling. The leverage score sampling involves auxiliary estimations that have a computational advantage over recursive least squares updates. Theoretical properties of the auxiliary estimations involved are also discussed. When applied to European power grid consumption data, the proposed leverage score based sampling methods outperform the benchmark sampling method in online estimation and prediction. The general applicability of the sampling-assisted online estimation method is assessed via simulation studies.