# Nystr"om Regularization for Time Series Forecasting

arXiv: https://arxiv.org/abs/2111.07109 · HTML: https://mlsanity.com/paper/2111.07109/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 67 references that are in the map.
- First posted on arXiv 13 Nov 2021.

## Builds on (most cited first, 13 of 13)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Revisiting the Nystrom Method for Improved Large-Scale Machine Learning](https://mlsanity.com/paper/1303.1849/) (2013)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Randomized sketches for kernels: Fast and optimal non-parametric regression](https://mlsanity.com/paper/1501.06195/) (2015)
- [Distributed Kernel Ridge Regression with Communications](https://mlsanity.com/paper/2003.12210/) (2020)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [Analysis of regularized Nystr"om subsampling for regression functions of low smoothness](https://mlsanity.com/paper/1806.00826/) (2018)
- [Spatial Decompositions for Large Scale SVMs](https://mlsanity.com/paper/1612.00374/) (2016)
- [Distributed Learning with Dependent Samples](https://mlsanity.com/paper/2002.03757/) (2020)
- [Non-parametric Sparse Additive Auto-regressive Network Models](https://mlsanity.com/paper/1801.07644/) (2018)

## Built on by (most cited first, 3 of 3)

- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)
- [Sketching with Spherical Designs for Noisy Data Fitting on Spheres](https://mlsanity.com/paper/2303.04550/) (2023)
- [Theta-regularized Kriging: Modelling and Algorithms](https://mlsanity.com/paper/2604.14975/) (2026)

## Abstract (arXiv)

This paper focuses on learning rate analysis of Nystr"om regularization with sequential sub-sampling for τ-mixing time series. Using a recently developed Banach-valued Bernstein inequality for τ-mixing sequences and an integral operator approach based on second-order decomposition, we succeed in deriving almost optimal learning rates of Nystr"om regularization with sequential sub-sampling for τ-mixing time series. A series of numerical experiments are carried out to verify our theoretical results, showing the excellent learning performance of Nystr"om regularization with sequential sub-sampling in learning massive time series data. All these results extend the applicable range of Nystr"om regularization from i.i.d. samples to non-i.i.d. sequences.