Randomized Least Squares Optimization and its Incredible Utility for Large-Scale Tensor Decomp...
summary
Randomized approximate leverage-score sampling uses the Khatri–Rao structure of tensor ALS least-squares to avoid forming the giant design matrix, sampling about 2^17 rows per solve and cutting a Reddit run from 96 → 8 hours (4.7 billion nonzeros, 106 GB store) for a rank-25 fit. Theory gives sample counts ~r^2/ε when using product-approximate scores (β≈1/r). Practical fixes — deduplicate repeated rows and forcibly include heavy hitters — yield up to 20× savings and far more stable convergence.
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chapters (8)
- 0:00Introduction
- 1:04Randomized least squares overview
- 7:35Tensor factorization applications
- 15:29Large-scale tensor decomposition
- 23:21Sampling techniques for tensors
- 28:48Numerical results
- 30:17Future directions
- 32:01Q&A
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