Supervised learning aims to learn functional relationships between inputs and outputs. Multitask learning tackles supervised learning tasks by performing them simultaneously to exploit commonalities between them. In this thesis, we focus on the problem of eliminating negative transfer in order to achieve better performance in multitask learning. We start by considering a general scenario in which the relationship between tasks is unknown. We then narrow our analysis to the case where data are characterised by a combination of underlying aspects, e.g., a dataset of images of faces, where each face is determined by a person's facial structure, the emotion being expressed, and the lighting conditions. In machine learning there have been numerous efforts based on multilinear models to decouple these aspects but these have primarily used techniques from the field of unsupervised learning. In this thesis we take inspiration from these approaches and hypothesize that supervised learning methods can also benefit from exploiting these aspects. The contributions of this thesis are as follows: 1. A multitask learning and transfer learning method that avoids negative transfer when there is no prescribed information about the relationships between tasks. 2. A multitask learning approach that takes advantage of a lack of overlapping features between known groups of tasks associated with different aspects. 3. A framework which extends multitask learning using multilinear algebra, with the aim of learning tasks associated with a combination of elements from different aspects. 4. A novel convex relaxation approach that can be applied both to the suggested framework and more generally to any tensor recovery problem. Through theoretical validation and experiments on both synthetic and real-world datasets, we show that the proposed approaches allow fast and reliable inferences. Furthermore, when performing learning tasks on an aspect of interest, accounting for secondary aspects leads to significantly more accurate results than using traditional approaches
