Probabilistic Tensor Factorization for Tensor Completion

Abstract

Multi-way tensor datasets emerge naturally in a variety of domains, such as recommendation systems, bioinformatics, and retail data analysis. The data in these domains usually contains a large number of missing entries. Therefore, many applications in those domains aim at missing value prediction, which boils down to a tensor completion problem. While tensor factorization algorithms can be a potentially powerful approach to tensor completion, most existing methods have the following limitations: First, some tensor factorization algorithms are unsuitable for tensor completion since they cannot work with incomplete tensors. Second, deterministic tensor factorization algorithms can only generate point estimates for the missing entries, while in some cases, it is desirable to obtain multiple-imputation datasets which are more representative of the joint variability for the predicted missing values. Therefore, we propose probabilistic tensor factorization algorithms, which are naturally applicable to incomplete tensors to provide both point estimate and multiple imputation for the missing entries. In this paper, we mainly focus on the applications to retail sales datasets, but the framework and algorithms are applicable to other domains as well. Through extensive experiments on real-world retail sales data, we show that our models are competitive with state-of-the-art algorithms, both in prediction accuracy and running time.