A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statistical graphical models associated to complete bipartite graphs with one layer of observed random variables and one layer of hidden ones, usually called restricted Boltzmann machines. We establish generic identifiability of Hadamard-Hitchcock decompositions by exploiting the reshaped Kruskal criterion for tensor rank decompositions. A flexible algorithm leveraging existing decomposition algorithms for tensor rank decomposition is introduced for computing a Hadamard-Hitchcock decomposition. Numerical experiments illustrate its computational performance and numerical accuracy.

翻译：多维数组的Hadamard-Hitchcock分解是一种将数组表示为若干张量秩分解的Hadamard积的分解形式。此类分解能够编码源于统计图模型的概率分布，这些模型与具有一层观测随机变量和一层隐藏变量的完全二分图相关联，通常称为受限玻尔兹曼机。通过利用张量秩分解的重塑Kruskal准则，我们建立了Hadamard-Hitchcock分解的通用可识别性。本文引入了一种灵活算法，该算法利用现有张量秩分解算法来计算Hadamard-Hitchcock分解。数值实验展示了其计算性能和数值精度。