Factorizing tensors has recently become an important optimization module in a number of machine learning pipelines, especially in latent variable models. We show how to do this efficiently in the streaming setting. Given a set of $n$ vectors, each in $\mathbb{R}^d$, we present algorithms to select a sublinear number of these vectors as coreset, while guaranteeing that the CP decomposition of the $p$-moment tensor of the coreset approximates the corresponding decomposition of the $p$-moment tensor computed from the full data. We introduce two novel algorithmic techniques: online filtering and kernelization. Using these two, we present four algorithms that achieve different tradeoffs of coreset size, update time and working space, beating or matching various state of the art algorithms. In case of matrices (2-ordered tensor) our online row sampling algorithm guarantees $(1 \pm \epsilon)$ relative error spectral approximation. We show applications of our algorithms in learning single topic modeling.

本研究重要的优化模块是张量分解，特别是在潜变量模型中。作者介绍了两种新的算法技术：在线过滤和核化，并提供了六种算法来实现不同的核心集大小、更新时间和工作空间的折衷方案，以击败或匹配各种现有算法。在矩阵的情况下，作者的在线行采样算法保证了（1 + ε）的相对误差谱逼近。本研究还展示了张量分解在学习单主题建模中的应用。

对称张量分解的流式核心集