论文标题
随机近似用于在线张力独立组件分析
Stochastic Approximation for Online Tensorial Independent Component Analysis
论文作者
论文摘要
独立的组件分析（ICA）一直是统计机器学习和信号处理中的流行维度缩小工具。在本文中，我们通过将问题视为非convex随机近似问题，为在线张力ICA算法提供了收敛分析。为了估算一个组件，我们提供了基于动态的分析，以证明具有特定步骤尺寸选择的在线紧张ICA算法可以实现急剧的有限样本误差。特别是，在对数据生成分布和缩放条件的温和假设下，$ d^4/t $的数据尺寸$ d $和样本尺寸$ t $的多核因子是足够小的，这是$ \ tilde {o}（O}（O}（O}（\ sqrt {\ sqrt {d/t}），
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.
