Probabilistic tensor factorization for link prediction

Link prediction is the problem of inferring the presence, absence or strength of a link between two entities, based on properties of the other observed links. In the literature, two related types of link prediction problems are considered: (i) missing and (ii) temporal. In both cases, latent variable models have been studied for link prediction tasks that consider link prediction as a noisy matrix and tensor completion problem. By using a low-rank structure of a dataset, it is possible to recover missing entries for matrices and higher-order tensors.In this thesis, we use several approaches based on probabilistic interpretation of tensor factorizations: Probabilistic Latent Tensor Factorization that can realize any arbitrary tensor factorization structure on datasets in the form of single tensor and Generalised Coupled Tensor factorization that can simultaneously fit to higher-order tensors/matrices with common latent factors.We present full Bayesian inference via variational Bayes, then we derive variational inference algorithm for Bayesian coupled tensor factorization to improve the reconstruction over Bayesian factorization of single data tensor and form update equations for these models that handle simultaneous tensor factorizations where multiple observations tensors are available.Previous studies on factorization of heterogeneous data focus on either a single loss function or a specific tensor model of interest. However, one of the main challenges in analyzing heterogeneous data is to find the right tensor model and loss function. So, we consider different tensor models and loss functions for the link prediction.Numerical experiments on synthetic and real datasets demonstrate that joint analysis of data from multiple sources via coupled factorization and variational Bayes approach improves the link prediction performance and the selection of the right loss function and tensor model is crucial for accurate prediction of unobserved links.