In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an \underline{E}fficient \underline{N}onparametric \underline{TE}nsor \underline{D}ecomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the \pg augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.

提出了一种基于非参数高斯过程的EFFICIENT NONPARAMETRIC TENSOR DECOMPOSITION（ENTED）方法，通过使用非参数高斯过程取代传统的多线性结构，并利用PG增强模型，建立了适用于二进制和计数分布的共轭模型，通过引入稀疏正交变分推理来提高计算效率。在多个真实世界的张量完整任务中对该模型进行评估，结果表明该模型在性能和计算优势方面取得了更好的表现。

二进制和计数数据的高效非参数张量分解