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In numerous applications, binary reactions or event counts are observed andstored within high-order tensors. Tensor decompositions (TDs) serve as apowerful tool to handle such high-dimensional and sparse data. However, manytraditional TDs are explicitly or implicitly designed based on the Gaussiandistribution, which is unsuitable for discrete data. Moreover, most TDs rely onpredefined multi-linear structures, such as CP and Tucker formats. Therefore,they may not be effective enough to handle complex real-world datasets. Toaddress these issues, we propose ENTED, an \underline{E}fficient\underline{N}onparametric \underline{TE}nsor \underline{D}ecomposition forbinary and count tensors. Specifically, we first employ a nonparametricGaussian process (GP) to replace traditional multi-linear structures. Next, weutilize the \pg augmentation which provides a unified framework to establishconjugate models for binary and count distributions. Finally, to address thecomputational issue of GPs, we enhance the model by incorporating sparseorthogonal variational inference of inducing points, which offers a moreeffective covariance approximation within GPs and stochastic natural gradientupdates for nonparametric models. We evaluate our model on several real-worldtensor completion tasks, considering binary and count datasets. The resultsmanifest both better performance and computational advantages of the proposedmodel.

Efficient Nonparametric Tensor Decomposition for Binary and Count Data