Uncertainty in Artificial Intelligence
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Iterative Splits of Quadratic Bounds for Scalable Binary Tensor Factorization
Beyza Ermis, Guillaume Bouchard
Binary matrices and tensors are popular data structures that need to be efficiently approxi- mated by low-rank representations. A standard approach is to minimize the logistic loss, well suited for binary data. In many cases, the num- ber m of non-zero elements in the tensor is much smaller than the total number n of possible en- tries in the tensor. This creates a problem for large tensors because the computation of the lo- gistic loss has a linear time complexity with n. In this work, we show that an alternative approach is to minimize the quadratic loss (root mean square error) which leads to algorithms with a training time complexity that is reduced from O(n) to O(m), as proposed earlier in the restricted case of alternating least-square algorithms. In addi- tion, we propose and study a greedy algorithm that partitions the tensor into smaller tensors, each approximated by a quadratic upper bound. This technique provides a time-accuracy trade- off between a fast but approximate algorithm and an accurate but slow algorithm. We show that this technique leads to a considerable speedup in learning of real world tensors.
Pages: 192-199
PS Link:
PDF Link: /papers/14/p192-ermis.pdf
AUTHOR = "Beyza Ermis and Guillaume Bouchard",
TITLE = "Iterative Splits of Quadratic Bounds for Scalable Binary Tensor Factorization",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "192--199"

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