Cyclic probabilistic reasoning networks: some exactly solvable iterative error-control structures.

Wai-shing Lee.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 114).Abstracts in English and Chinese.Contents --- p.iList of Figures --- p.ivList of Tables --- p.vAbstract --- p.viAcknowledgement --- p.viiChapter Chapter 1. --- Layout of the thesis --- p.1Chapter Chapter 2. --- Introduction --- p.3Chapter 2.1 --- What is the reasoning problem? --- p.3Chapter 2.2 --- Fundamental nature of Knowledge --- p.4Chapter 2.3 --- Fundamental methodology of Reasoning --- p.7Chapter 2.4 --- Our intended approach --- p.9Chapter Chapter 3. --- Probabilistic reasoning networks --- p.11Chapter 3.1 --- Overview --- p.11Chapter 3.2 --- Causality and influence diagrams --- p.11Chapter 3.3 --- Bayesian networks - influence diagrams endowed with a probability interpretation --- p.13Chapter 3.3.1 --- A detour to the interpretations of probability --- p.13Chapter 3.3.2 --- Bayesian networks --- p.15Chapter 3.3.3 --- Acyclicity and global probability --- p.17Chapter 3.4 --- Reasoning on probabilistic reasoning networks I - local updating formulae --- p.17Chapter 3.4.1 --- Rationale of the intended reasoning strategy --- p.18Chapter 3.4.2 --- Construction of the local updating formula --- p.19Chapter 3.5 --- Cluster graphs - another perspective to reasoning problems --- p.23Chapter 3.6 --- Semi-lattices - another representation of Cluster graphs --- p.26Chapter 3.6.1 --- Construction of semi-lattices --- p.26Chapter 3.7 --- Bayesian networks and semi-lattices --- p.28Chapter 3.7.1 --- Bayesian networks to acyclic semi-lattices --- p.29Chapter 3.8 --- Reasoning on (acyclic) probabilistic reasoning networks II - global updating schedules --- p.29Chapter 3.9 --- Conclusion --- p.30Chapter Chapter 4. --- Cyclic reasoning networks - a possibility? --- p.32Chapter 4.1 --- Overview --- p.32Chapter 4.2 --- A meaningful cyclic structure - derivation of the ideal gas law --- p.32Chapter 4.3 --- "What's ""wrong"" to be in a cyclic world" --- p.35Chapter 4.4 --- Communication - Dynamics - Complexity --- p.39Chapter 4.4.1 --- Communication as dynamics; dynamics to complexity --- p.42Chapter 4.5 --- Conclusion --- p.42Chapter Chapter 5. --- Cyclic reasoning networks ´ؤ error-control application --- p.43Chapter 5.1 --- Overview --- p.43Chapter 5.2 --- Communication schemes on cyclic reasoning networks directed to error-control applications --- p.43Chapter 5.2.1 --- Part I ´ؤ Local updating formulae --- p.44Chapter 5.2.2 --- Part II - Global updating schedules across the network --- p.46Chapter 5.3 --- Probabilistic reasoning based error-control schemes --- p.47Chapter 5.3.1 --- Local sub-universes and global universe underlying the error- control structure --- p.47Chapter 5.4 --- Error-control structure I --- p.48Chapter 5.4.1 --- Decoding algorithm - Communication between local sub- universes in compliance with the global topology --- p.51Chapter 5.4.2 --- Decoding rationales --- p.55Chapter 5.4.3 --- Computational results --- p.55Chapter 5.5 --- Error-control structure II --- p.57Chapter 5.5.1 --- Structure of the code and the corresponding decoding algorithm --- p.57Chapter 5.5.2 --- Computational results --- p.63Chapter 5.6 --- Error-control structure III --- p.66Chapter 5.6.1 --- Computational results --- p.70Chapter 5.7 --- Error-control structure IV --- p.71Chapter 5.7.1 --- Computational results --- p.73Chapter 5.8 --- Conclusion --- p.74Chapter Chapter 6. --- Dynamics on cyclic probabilistic reasoning networks --- p.75Chapter 6.1 --- Overview --- p.75Chapter 6.2 --- Decoding rationales --- p.76Chapter 6.3 --- Error-control structure I - exact solutions --- p.77Chapter 6.3.1 --- Dynamical invariant - a key to tackle many dynamical problems --- p.77Chapter 6.3.2 --- Dynamical invariant for error-control structure I --- p.78Chapter 6.3.3 --- Iteration dynamics --- p.79Chapter 6.3.4 --- Structure preserving property and the maximum a posteriori solutions --- p.86Chapter 6.4 --- Error-control structures III & IV - exact solutions --- p.92Chapter 6.4.1 --- Error-control structure III --- p.92Chapter 6.4.1.1 --- Dynamical invariants for error-control structure III --- p.92Chapter 6.4.1.2 --- Iteration dynamics --- p.93Chapter 6.4.2 --- Error-control structure IV --- p.96Chapter 6.4.3 --- Structure preserving property and the maximum a posteriori solutions --- p.98Chapter 6.5 --- Error-control structure II - exact solutions --- p.101Chapter 6.5.1 --- Iteration dynamics --- p.102Chapter 6.5.2 --- Structure preserving property and the maximum a posteriori solutions --- p.105Chapter 6.6 --- A comparison on the four error-control structures --- p.106Chapter 6.7 --- Conclusion --- p.108Chapter Chapter 7. --- Conclusion --- p.109Chapter 7.1 --- Our thesis --- p.109Chapter 7.2 --- Hind-sights and foresights --- p.110Chapter 7.3 --- Concluding remark --- p.111Appendix A. An alternative derivation of the local updating formula --- p.112Bibliography --- p.11