Hadamard-Hitchcock decompositions: identifiability and computation
Alessandro Oneto and Nick Vannieuwenhoven
多个数组的 Hadamard-Hitchcock 分解是一个分解,表示后者为几个张量级分解的 Hadamard 产品。 这种分解可以编码概率分布,这些分布来自统计图形模型,这些模型与完成双体图形相关,具有一层观察到的随机变量和一层隐藏的变量,通常称为受限玻尔兹曼机器。 我们通过利用重塑的Kruskal标准进行张量等级分解,建立了Hadamard-Hitchcock分解的通用可识别性。 一种利用现有分解算法进行张量等级分解的灵活算法,用于计算哈达马德-希区柯克分解。 数字实验说明了其计算性能和数值精度。
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 decomposit...