Efficient Tensor Decomposition
Data Structures and Algorithms
2020-07-31 v1 Machine Learning
Abstract
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.
Cite
@article{arxiv.2007.15589,
title = {Efficient Tensor Decomposition},
author = {Aravindan Vijayaraghavan},
journal= {arXiv preprint arXiv:2007.15589},
year = {2020}
}
Comments
Chapter 19 of the book "Beyond the Worst-Case Analysis of Algorithms", edited by Tim Roughgarden and published by Cambridge University Press (2020). We hope to occasionally update the survey here to include discussions of new results and advances