The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data
<|reference_start|>The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data: This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition where the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor is constrained to a preset value $Q$ much smaller than the size of the core. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. AL$\ell_0$CORE -- i.e., $allo$cated $\ell_0$-$co$nstrained $core$-- thus enjoys both the computational tractability of 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 full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.<|reference_end|>
@article{hood2024the,
    title={The AL$\ell_0$CORE Tensor Decomposition for Sparse Count Data},
    author={John Hood, Aaron Schein},
    journal={arXiv preprint arXiv:2403.06153},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06153},
    primaryClass={stat.ML cs.LG}
}