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