# Stochastic Approximation for Online Tensorial Independent Component Analysis

arXiv: https://arxiv.org/abs/2012.14415 · HTML: https://mlsanity.com/paper/2012.14415/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2020.

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

- [Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs](https://mlsanity.com/paper/2406.02157/) (2024)
- [Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems](https://mlsanity.com/paper/2112.14738/) (2021)
- [A 1/R Law for Kurtosis Contrast in Balanced Mixtures](https://mlsanity.com/paper/2602.22334/) (2026)

## Abstract (arXiv)

Independent component analysis (ICA) has been a popular dimension reduction tool in statistical machine learning and signal processing. In this paper, we present a convergence analysis for an online tensorial ICA algorithm, by viewing the problem as a nonconvex stochastic approximation problem. For estimating one component, we provide a dynamics-based analysis to prove that our online tensorial ICA algorithm with a specific choice of stepsize achieves a sharp finite-sample error bound. In particular, under a mild assumption on the data-generating distribution and a scaling condition such that d4/T is sufficiently small up to a polylogarithmic factor of data dimension d and sample size T, a sharp finite-sample error bound of tildeO(√d/T) can be obtained.