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

John Hood · Aaron Schein

MR1 & MR2 - Number 177
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Sat 4 May 6 a.m. PDT — 8:30 a.m. PDT

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.

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