BYY harmony learning, independent state space, and generalized APT financial analyses.

First, the relationship between factor analysis (FA) and the well-known arbitrage pricing theory (APT) for financial market is discussed comparatively, with a number of to-be-improved problems listed. An overview is made from a unified perspective on the related studies in the literatures of statistics, control theory, signal processing, and neural networks. Next, we introduce the fundamentals of the Bayesian Ying Yang (BYY) system and the harmony learning principle. We further show that a specific case of the framework, called BYY independent state space (ISS) system, provides a general guide for systematically tackling various FA related learning tasks and the above to-be-improved problems for the APT analyses. Third, on various specific cases of the BYY ISS system in three typical architectures, adaptive algorithms, regularization methods and model selection criteria are provided for either or both of parameter learning with automated model selection and parameter learning followed by model selection. Finally, we introduce some other financial applications that are based on the underlying independent factors via the APT analyses.