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Streaming Coresets for Symmetric Tensor Factorization
Supratim Shit · Rachit Chhaya · Jayesh Choudhari · Anirban Dasgupta

Tue Jul 14 09:00 AM -- 09:45 AM & Tue Jul 14 10:00 PM -- 10:45 PM (PDT) @ Virtual #None
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 $\~R^d$, 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 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.

Author Information

Supratim Shit (IIT Gandhinagar)
Rachit Chhaya (IIT Gandhinagar)
Jayesh Choudhari (IIT Gandhinagar)
Anirban Dasgupta (IIT Gandhinagar)

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