# Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization

arXiv: https://arxiv.org/abs/1803.02312 · HTML: https://mlsanity.com/paper/1803.02312/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2018.

## Built on by (most cited first, 5 of 5)

- [Streaming PCA for Markovian Data](https://mlsanity.com/paper/2305.02456/) (2023)
- [Oja's Algorithm for Streaming Sparse PCA](https://mlsanity.com/paper/2402.07240/) (2024)
- [Beyond Sin-Squared Error: Linear-Time Entrywise Uncertainty Quantification for Streaming PCA](https://mlsanity.com/paper/2506.12655/) (2025)
- [Low-Precision Streaming PCA](https://mlsanity.com/paper/2510.22440/) (2025)
- [High-dimensional Adaptive MCMC with Reduced Computational Complexity](https://mlsanity.com/paper/2604.09286/) (2026)

## Abstract (arXiv)

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies this fundamental challenge through a streaming PCA problem for stationary time series data. Specifically, our goal is to estimate the principle component of time series data with respect to the covariance matrix of the stationary distribution. Computationally, we propose a variant of Oja's algorithm combined with downsampling to control the bias of the stochastic gradient caused by the data dependency. Theoretically, we quantify the uncertainty of our proposed stochastic algorithm based on diffusion approximations. This allows us to prove the asymptotic rate of convergence and further implies near optimal asymptotic sample complexity. Numerical experiments are provided to support our analysis.