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Efficient Tensor Decomposition

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arxiv 2007.15589 v1 pith:WPOR7TSU submitted 2020-07-30 cs.DS cs.LG

Aravindan Vijayaraghavan This is my paper · ORCID
classification cs.DScs.LG
keywords tensoralgorithmsanalysisefficientworst-caseassumptionsbeyondchapter
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This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will see how to design efficient algorithms with provable guarantees under mild assumptions, and using beyond worst-case frameworks like smoothed analysis.

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  1. Improving the Threshold for Finding Rank-1 Matrices in a Subspace

    cs.DS 2025-04 accept novelty 7.0 of 10

    For generic planted rank-one matrices in an R-dimensional subspace of m by n matrices, the JLV algorithm is proven to recover them when R is about half of mn, and proven to fail above about 0.71 times mn.

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