Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition
CoRR(2023)
摘要
We present a data structure to randomly sample rows from the Khatri-Rao
product of several matrices according to the exact distribution of its leverage
scores. Our proposed sampler draws each row in time logarithmic in the height
of the Khatri-Rao product and quadratic in its column count, with persistent
space overhead at most the size of the input matrices. As a result, it
tractably draws samples even when the matrices forming the Khatri-Rao product
have tens of millions of rows each. When used to sketch the linear least
squares problems arising in CANDECOMP / PARAFAC tensor decomposition, our
method achieves lower asymptotic complexity per solve than recent
state-of-the-art methods. Experiments on billion-scale sparse tensors validate
our claims, with our algorithm achieving higher accuracy than competing methods
as the decomposition rank grows.
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关键词
tensor decomposition,leverage,khatri-rao
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