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The ALℓ0CORE Tensor Decomposition for Sparse Count Data
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4654-4662, 2024.
Abstract
This paper introduces ALℓ0CORE, a new form of probabilistic non-negative tensor decomposition. ALℓ0CORE is a Tucker decomposition that constrains the number of non-zero elements (i.e., the ℓ0-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. ALℓ0CORE—i.e., allocated ℓ0-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 ALℓ0CORE 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.