The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data

John Hood, Aaron J. Schein
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4654-4662, 2024.

Abstract

This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition that constrains the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor to be at most $Q$. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables allocated across the core tensor during inference. AL$\ell_0$CORE—i.e., allocated $\ell_0$-constrained core—thus enjoys both the computational tractability of canonical polyadic (CP) decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\ell_0$CORE typically requires only tiny fractions (e.g., 1%) of the core to achieve the same results as Tucker at a correspondingly small fraction of the cost.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-hood24a, title = {The {AL$\ell_0$CORE} Tensor Decomposition for Sparse Count Data}, author = {Hood, John and Schein, Aaron J.}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {4654--4662}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/hood24a/hood24a.pdf}, url = {https://proceedings.mlr.press/v238/hood24a.html}, abstract = {This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition that constrains the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor to be at most $Q$. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables allocated across the core tensor during inference. AL$\ell_0$CORE—i.e., allocated $\ell_0$-constrained core—thus enjoys both the computational tractability of canonical polyadic (CP) decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\ell_0$CORE typically requires only tiny fractions (e.g., 1%) of the core to achieve the same results as Tucker at a correspondingly small fraction of the cost.} }
Endnote
%0 Conference Paper %T The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data %A John Hood %A Aaron J. Schein %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-hood24a %I PMLR %P 4654--4662 %U https://proceedings.mlr.press/v238/hood24a.html %V 238 %X This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition that constrains the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor to be at most $Q$. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables allocated across the core tensor during inference. AL$\ell_0$CORE—i.e., allocated $\ell_0$-constrained core—thus enjoys both the computational tractability of canonical polyadic (CP) decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\ell_0$CORE typically requires only tiny fractions (e.g., 1%) of the core to achieve the same results as Tucker at a correspondingly small fraction of the cost.
APA
Hood, J. & Schein, A.J.. (2024). The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:4654-4662 Available from https://proceedings.mlr.press/v238/hood24a.html.

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