Contributions and structure of the thesis

This thesis consists of eight publications and an introductory part with literature survey. The aim of the thesis is to develop a computationally efficient algorithm for a nonlinear extension of the linear factor analysis model.

• The main result of this thesis is the development of an algorithm which is able to learn nonlinear factor analysis models with a relatively high number of factors. The computational complexity scales quadratically with respect to the dimension of factor space which is already efficient enough for many interesting applications, but it is also possible to use the model as an elementary module in larger models which scale linearly in the total size of the representation.
• Bayesian probability theory and decision theory provide the theoretical framework for learning, inference and decision making. In this thesis, a computationally feasible approximation of the exact Bayesian learning, termed ensemble learning, is used. The manner in which ensemble learning can be applied to nonlinear factor analysis is presented.
• It is shown how the nonlinear model can be combined with other extensions of factor analysis which relax the Gaussianity assumption of the factors and include a model for the dynamics of the factors.

Section 2 of the introductory part summarises the publications of the thesis, with the contributions of the author explained. Section 3 outlines the theoretical framework of Bayesian probability theory and decision theory. Practical methods and approximations together with their connection to information theory are discussed in section 4. Section 5 introduces the basic static Gaussian linear factor analysis model and its non-Gaussian, nonlinear and dynamic extensions. Publication V serves as a detailed account on the nonlinear factor analysis method developed in this thesis but section 6 gives a brief summary. Biological relevance and further lines of research are discussed in section 7.