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：多维阵列的哈达玛-希区柯克分解是一种将其表示为若干张量秩分解的哈达玛乘积的分解方法。此类分解能够编码由完全二分图（一层为观测随机变量，另一层为隐藏随机变量，通常称为受限玻尔兹曼机）相关的统计图形模型导出的概率分布。通过利用重塑Kruskal准则进行张量秩分解，我们建立了哈达玛-希区柯克分解的通用可辨识性。针对张量秩分解，我们引入了一种灵活的算法，该算法利用现有分解算法来计算哈达玛-希区柯克分解。数值实验展示了其计算性能与数值精度。