Bayesian Methods for Nonlinear Process Modelling

I have been working in the Bayes research group of the Neural Network Research Centre, HUT. In our group, we apply variational Bayesian learning to identify different types of latent variable models such as (non)linear factor analysis, independent component analysis and their extensions. The resulting algorithms can be used for data compression, feature extraction or blind source separation. My research is mostly concentrated on examining the properties and limitations of the variational learning method and proposed algorithms, developing new types of models like post-nonlinear factor analysis and applying the proposed techniques to real world problems. I. BACKGROUND AND MOTIVATION Independent component analysis (ICA) is a statistical signal processing method that is based on higher-order statistics [1]. It can solve efficiently the so-called blind source separation (BSS) problem in which a number of signals is mixed and should be separated without knowing the detailed mixture model. The hidden factors revealed from the observable random variables are called independent components or sources. ICA is a very powerful technique which is able to find the underlying sources when the classical methods such as principal component analysis (PCA) or factor analysis (FA) fail completely. Examples of problems where the ICA methods can be applied include: • the cocktail-party problem (where several microphones pick up speech waveforms of several people speaking simultaneously), • biomedical signal processing: separation of artifacts from EEG or MEG recordings, • financial time series analysis: finding hidden factors in financial data, • telecommunication applications: separation of the user’s own signal from the interfering other user’s signals in CDMA (Code-Division Multiple Access) mobile communications. The standard ICA model assumes a linear mixture of independent random variables s(t):