A Tensor Framework for Learning in Structured Domains

The aim of this thesis is to build a bridge between tensors and adaptive structured data processing, providing a general framework for learning in structured domains which has tensor theory at its backbone. To this end, we show that tensors arise naturally in model parameters from the formulation of learning problems in structured domains. We propose to approximate such parametrisations leveraging tensor decompositions whose hyper-parameters regulate the trade-off between expressiveness and compression ability. Moreover, we show that each decomposition introduces a specific inductive bias to the model. Another contribution of the thesis is the application of these new approximations to unbounded structures, where tensor decompositions needs combining with weight sharing constraints to control model complexity. The last contribution of our work is the development of two Bayesian non-parametric models for structures which learn to adapt their complexity directly from data.