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 $d^4/T$ is sufficiently small up to a polylogarithmic factor of data dimension $d$ and sample size $T$, a sharp finite-sample error bound of $\tilde{O}(\sqrt{d/T})$ can be obtained.

翻译：独立组件分析(ICA)一直是统计机学习和信号处理中流行的减少维度工具。 在本文中,我们通过将这一问题视为非convex 随机近似问题,为在线强制ICA算法提供了趋同分析。为了估算一个组件,我们提供了动态分析,以证明我们具有特定步骤选择的在线强制ICA算法实现了一个严格的有限抽样错误。特别是,根据对数据生成分布的微小假设和规模化条件,即$4/T$足够小到数据维度的多元系数$和样本大小$T$,可以获得一个包含$\tilde{O}(sqrt{d/T}$的急性有限抽样错误。