We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most exporter--importer--product--year cells are zero while positive values are continuous and highly variable. To model these data, we propose a Bayesian hierarchical tensor factorization model that places a low-rank CP structure on a latent Poisson rate tensor and couples it with a conditional Gamma model for positive outcomes, with rate parameters that can vary across slices within a mode. The model therefore separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions through a shared low-rank latent structure. To scale posterior inference to large arrays, we develop a hybrid variational--Monte Carlo algorithm that combines efficient coordinate ascent updates with a partially collapsed augmented-data sampler. Applied to approximately 60 million trade flows, the method surfaces multiway dependence across exporters, importers, products, and years that is difficult to recover from gravity-type or pairwise network analyses, which do not jointly model the product and temporal dimensions.

翻译：我们研究了具有过度零值、重右尾及切片特异性离散特性的稀疏半连续张量数据。这类特征在货币计量的多维数据（如国际贸易）中自然出现，其中大多数出口国-进口国-产品-年份单元格取值为零，而正值则呈现连续且高度异质性。为建模此类数据，我们提出一种贝叶斯层次张量分解模型，该模型在潜在泊松率张量上施加低秩CP结构，并将其与基于伽马分布的条件模型耦合以建模正值，其中率参数可随模态内切片变化。该模型因此实现了正观测值的发生与量值分离，同时通过共享低秩潜在结构跨所有张量维度借用统计强度。为将后验推断扩展到大型数组，我们开发了一种混合变分-蒙特卡洛算法，该算法结合了高效坐标上升更新与部分折叠增广数据采样器。应用于约6000万条贸易流数据时，该方法揭示了跨越出口国、进口国、产品和年份的多维依赖关系，这种关系难以通过未联合建模产品与时序维度的引力型或成对网络分析恢复。