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Bayesian Ying-Yang system, best harmony learning, and five action circling

  • Research Article
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Frontiers of Electrical and Electronic Engineering in China

Abstract

Firstly proposed in 1995 and systematically developed in the past decade, Bayesian Ying-Yang learning1) is a statistical approach for a two pathway featured intelligent system via two complementary Bayesian representations of a joint distribution on the external observation X and its inner representation R, which can be understood from a perspective of the ancient Ying-Yang philosophy. We have q(X,R) = q(X|R)q(R) as Ying that is primary, with its structure designed according to tasks of the system, and p(X,R) = p(R|X)p(X) as Yang that is secondary, with p(X) given by samples of X while the structure of p(R|X) designed from Ying according to a Ying-Yang variety preservation principle, i.e., p(R|X) is designed as a functional with q(X|R), q(R) as its arguments. We call this pair Bayesian Ying-Yang (BYY) system. A Ying-Yang best harmony principle is proposed for learning all the unknowns in the system, in help of an implementation featured by a five action circling under the name of A5 paradigm. Interestingly, it coincides with the famous ancient WuXing theory that provides a general guide to keep the A5 circling well balanced towards a Ying-Yang best harmony. This BYY learning provides not only a general framework that accommodates typical learning approaches from a unified perspective but also a new road that leads to improved model selection criteria, Ying-Yang alternative learning with automatic model selection, as well as coordinated implementation of Ying based model selection and Yang based learning regularization. This paper aims at an introduction of BYY learning in a twofold purpose. On one hand, we introduce fundamentals of BYY learning, including system design principles of least redundancy versus variety preservation, global learning principles of Ying-Yang harmony versus Ying-Yang matching, and local updating mechanisms of rival penalized competitive learning (RPCL) versus maximum a posteriori (MAP) competitive learning, as well as learning regularization by data smoothing and induced bias cancelation (IBC) priori. Also, we introduce basic implementing techniques, including apex approximation, primal gradient flow, Ying-Yang alternation, and Sheng-Ke-Cheng-Hui law. On the other hand, we provide a tutorial on learning algorithms for a number of typical learning tasks, including Gaussian mixture, factor analysis (FA) with independent Gaussian, binary, and non-Gaussian factors, local FA, temporal FA (TFA), hidden Markov model (HMM), hierarchical BYY, three layer networks, mixture of experts, radial basis functions (RBFs), subspace based functions (SBFs). This tutorial aims at introducing BYY learning algorithms in a comparison with typical algorithms, particularly with a benchmark of the expectation maximization (EM) algorithm for the maximum likelihood. These algorithms are summarized in a unified Ying-Yang alternation procedure with major parts in a same expression while differences simply characterized by few options in some subroutines. Additionally, a new insight is provided on the ancient Chinese philosophy of Yin-Yang and WuXing from a perspective of information science and intelligent system.

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  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China

    Lei Xu

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Lei Xu is a chair professor of The Chinese University of Hong Kong (CUHK), a Chang Jiang Chair Professor of Peking University, a guest Research Fellow of Institute of Biophysics, Chinese Academy of Sciences, an honorary Professor of Xidian University. He graduated from Harbin Institute of Technology by the end of 1981, and completed his master and Ph.D thesis at Tsinghua University during 1982–1986. Then, he joined Department Mathematics, Peking University in 1987 first as a postdoc and then exceptionally promoted to associate professor in 1988 and to a full professor in 1992. During 1989–1993, he worked at several universities in Finland, Canada and USA, including Harvard and MIT. He joined CUHK in 1993 as senior lecturer, became professor in 1996 and took the current position since 2002. Prof. Xu has published dozens of journal papers and also many papers in conference proceedings and edited books, covering the areas of statistical learning, neural networks, and pattern recognition, with a number of well-cited papers, e.g., his papers got over 3200 citations according to SCI-Expended (SCI-E) and over 5500 citations according to Google Scholar (GS), and over 2000 (SCI-E) and 3600 (GS) for his 10 most frequently cited papers. He served as associate editor for several journals, including Neural Networks (1995-present) and IEEE Transactions on Neural Networks (1994–1998), and as general chair or program committee chair of a number of international conferences. Moreover, Prof. Xu has served on governing board of International Neural Networks Society (INNS) (2001–2003), INNS Award Committee (2002–2003), and Fellow Committee of IEEE Computational Intelligence Society (2006, 2008), chair of Computational Finance Technical Committee of IEEE Computational Intelligence Society (2001–2003), and a past president of Asian-Pacific Neural Networks Assembly (APNNA). He has also served as an engineering panel member of Hong Kong RGC Research Committee (2001–2006), a selection committee member of Chinese NSFC/HK RGC Joint Research Scheme (2002–2005), external expert for Chinese NSFC Information Science (IS) Panel (2004–2006, 2008), external expert for Chinese NSFC IS Panel for distinguished young scholars (2009–2010), and an nominator for the prestigious Kyoto Prize (2003, 2007). Prof. Xu has received several Chinese national academic awards (including 1993 National Nature Science Award) and international awards (including 1995 INNS Leadership Award and the 2006 APNNA Outstanding Achievement Award). He has been elected to an IEEE Fellow (2001-) and a Fellow of International Association for Pattern Recognition (2002-), and a member of European Academy of Sciences (2002-).

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Xu, L. Bayesian Ying-Yang system, best harmony learning, and five action circling. Front. Electr. Electron. Eng. China 5, 281–328 (2010). https://doi.org/10.1007/s11460-010-0108-9

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