Streaming Coresets for Symmetric Tensor Factorization

Autor:	Chhaya, Rachit, Choudhari, Jayesh, Dasgupta, Anirban, Shit, Supratim
Rok vydání:	2020
Předmět:	Computer Science - Machine Learning Computer Science - Data Structures and Algorithms Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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 six algorithms that achieve different tradeoffs of coreset size, update time and working space, beating or matching various state of the art algorithms. In the 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. Comment: Accepted at ICML 2020. Included algorithm with improved update time and fixed minor bugs
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.01225 Zobrazit plný text záznamu View this record from Arxiv