Abstract
The infinite Independent Subspace Analysis (iISA) is presented in this thesis. This model is based on the nested Indian Buffet Process (nIBP), a stochastic process which assigns probability distributions to trees of infinite depth and branching factors. In Bayesian nonparametrics, the theoretical results of nesting strategies, particularly nIBP, are still lacking, so some interesting properties of nIBP are illustrated through various examples to gain insight further into the nIBP and related models such as nested Chinese restaurant process (nCRP). Using the nIBP, the iISA model eliminates the restrictions of classical ISA algorithms on the number of groups and groups sizes by allowing them to be inferred from the data. Moreover, the specialised inference algorithm based on the Metropolis-Hasting method is proposed to handle the increased complexity of the model. The experimental results have not only demonstrated the performance of the iISA model, but also led to a conceptual understanding that can be used to improve the model. Although the application of iISA model on the natural images was not successful, it provides some insights that can be used for further development.