Tensor decomposition is a fundamental tool for multiway data analysis. While most decomposition algorithms operate a collection of static data and perform batch processes, many applications produce data in a streaming manner - every time a subset of entries are generated, and previously seen entries cannot be revisited. In such scenarios, traditional decomposition approaches will be inappropriate, because they cannot provide timely updates when new data come in, and they need to access the whole dataset many times for batch optimization. To address this issue, we propose POST, a PrObabilistic Streaming Tensor decomposition algorithm, which enables real-time updates and predictions upon receiving new tensor entries, and supports dynamic growth of all the modes. Compared with the state-of-the-art streaming decomposition approach MAST, POST is more flexible in that it can handle arbitrary orders of streaming entries, and hence is more widely applicable. In addition, as a Bayesian inference algorithm, POST can quantify the uncertainty of the latent embeddings via their posterior distributions, and the confidence levels of the missing entry value predictions. On several real-world datasets, POST exhibits better or comparable predictive performance than MAST and other static decomposition algorithms.

Tensor decompositions are fundamental tools for multiway data analysis. Existing approaches, however, ignore the valuable temporal information along with data, or simply discretize them into time steps so that important temporal patterns are easily missed. Moreover, most methods are limited to multilinear decomposition forms, and hence are unable to capture intricate, nonlinear relationships in data. To address these issues, we formulate event-tensors, to preserve the complete temporal information for multiway data, and propose a novel Bayesian nonparametric decomposition model. Our model can (1) fully exploit the time stamps to capture the critical, causal/triggering effects between the interaction events, (2) flexibly estimate the complex relationships between the entities in tensor modes, and (3) uncover hidden structures from their temporal interactions. For scalable inference, we develop a doubly stochastic variational Expectation-Maximization algorithm to conduct an online decomposition. Evaluations on both synthetic and real-world datasets show that our model not only improves upon the predictive performance of existing methods, but also discovers interesting clusters underlying the data.