Probabilistic Models For Incomplete Multi-dimensional Arrays

Abstract

In multiway data, each sample is measured by multiple sets of correlated attributes. We develop a probabilistic framework for modeling structural dependency from partially observed multi-dimensional array data, known as pTucker. Latent components associated with individual array dimensions are jointly retrieved while the core tensor is integrated out. The resulting algorithm is capable of handling large-scale data sets. We verify the usefulness of this approach by comparing against classical models on applications to modeling amino acid fluorescence, collaborative filtering and a number of benchmark multiway array data.