Partitioned Tensor Factorizations for Learning Mixed Membership Models

Zilong Tan, Sayan Mukherjee
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3358-3367, 2017.

Abstract

We present an efficient algorithm for learning mixed membership models when the number of variables p is much larger than the number of hidden components k. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O(p^3)$ tensor, to factorizing $O(p/k)$ sub-tensors each of size $O(k^3)$. In addition, we address the issue of negative entries in the empirical method of moments based estimators. We provide sufficient conditions under which our approach has provable guarantees. Our approach obtains competitive empirical results on both simulated and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-tan17a, title = {Partitioned Tensor Factorizations for Learning Mixed Membership Models}, author = {Zilong Tan and Sayan Mukherjee}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3358--3367}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/tan17a/tan17a.pdf}, url = {https://proceedings.mlr.press/v70/tan17a.html}, abstract = {We present an efficient algorithm for learning mixed membership models when the number of variables p is much larger than the number of hidden components k. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O(p^3)$ tensor, to factorizing $O(p/k)$ sub-tensors each of size $O(k^3)$. In addition, we address the issue of negative entries in the empirical method of moments based estimators. We provide sufficient conditions under which our approach has provable guarantees. Our approach obtains competitive empirical results on both simulated and real data.} }
Endnote
%0 Conference Paper %T Partitioned Tensor Factorizations for Learning Mixed Membership Models %A Zilong Tan %A Sayan Mukherjee %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-tan17a %I PMLR %P 3358--3367 %U https://proceedings.mlr.press/v70/tan17a.html %V 70 %X We present an efficient algorithm for learning mixed membership models when the number of variables p is much larger than the number of hidden components k. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O(p^3)$ tensor, to factorizing $O(p/k)$ sub-tensors each of size $O(k^3)$. In addition, we address the issue of negative entries in the empirical method of moments based estimators. We provide sufficient conditions under which our approach has provable guarantees. Our approach obtains competitive empirical results on both simulated and real data.
APA
Tan, Z. & Mukherjee, S.. (2017). Partitioned Tensor Factorizations for Learning Mixed Membership Models. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3358-3367 Available from https://proceedings.mlr.press/v70/tan17a.html.

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