Scalable Bayesian Matrix and Tensor Factorization for Discrete Data

Abstract

Matrix and tensor factorization methods decompose the observed matrix and tensor data into a set of factor matrices. They provide a useful way to extract latent factors or features from complex data, and also to predict missing data. Matrix and tensor factorization has drawn significant attentions in a wide variety of applications, such as topic modeling, recommender system, and learning from social network and knowledge base. However, developing factorization methods for massive and sparse observations remains a challenge, especially when the data are binary or count-valued (which is true of most real-world data). In this thesis, we present a set of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The side-information along a certain dimension, such as pairwise relationships (e.g., an adjacency network) between entities, can be easily leveraged to handle issues such as data sparsity, and the cold-start problem; (3) The proposed models have full local conjugacy, leading to simple, closed-form batch inference as well as online inference; (4) In contrast to many existing matrix and tensor factorization methods, in which factor matrices are usually assumed to be real-valued, we assume non-negativity on factor matrices. The non-negative factor matrices in our model provide easy interpretability; (5) For tensor factorization, the number of "topics", or in other words, the rank of tensor, can be inferred from the data. In this thesis, we evaluate the proposed models on a variety of real-world data sets, from diverse domains, such as analyzing scholarly text data, political science data, large-scale market transaction data and knowledge-graphs, etc.