Papers › Streaming Coresets for Symmetric Tensor Factorization

Streaming Coresets for Symmetric Tensor Factorization

1 Jun 2020ICML 2020 1arXiv:2006.01225archive 2025-07-28

Rachit Chhaya, Jayesh Choudhari, Anirban Dasgupta, Supratim Shit

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 ℝᵈ, 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 ±ϵ) relative error spectral approximation. We show applications of our algorithms in learning single topic modeling.

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