Efficient Nonparametric Tensor Decomposition for Binary and Count Data
Zerui Tao Toshihisa Tanaka Qibin Zhao
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.