Abstract
We focus on learning the probability matrix for discrete random variables in factor graphs. We review the problem and its variational approximation and, via entropic priors, we show that soft quantization can be included in a probabilistically-consistent fashion in a factor graph that learns the mutual relationship among the variables involved. The framework is explained with reference the ”Tipper” example and the results of a Matlab simulation are included.
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References
Graphical models emerge. new connections betweeen machine learning and signal processing. Signal Processing Magazine, 27(6) (2010)
Beal, M.J.: Variational algorithms for approximate bayesian inference. Ph.D. thesis, University of London (2003)
Beal, M.J., Ghahramani, Z.: Variational bayesian learning of directed graphical models with hidden variables. Bayesian Analysis 1, 1–44 (2004)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley (2006)
Dauwels, J.: On variational message passing in factor graphs. In: ISIT2007, Nice, France, June 24-June 29 (2007)
Ghahramani, Z.: Unsupervised Learning. Springer (2004)
Heckerman, D.: A tutorial on learning with bayesian networks. Tech. Rep. MSR-TR-95-06, Microsoft Research (1996); March 1995 (Revised November 1996)
Dauwels, J., Eckford, A., Loeliger, S.K., Expectation, H.A.: xpectation maximization as message passing–part i: Principles and gaussian messages. arXiv:0910, 1–14 (2009); Submitted to IEEE Tr. on Information Theory
Jantzen, J.: Foundations of Fuzzy Control. Wiley (2007)
Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press (2003)
Loeliger, H.A.: An introduction to factor graphs. IEEE Signal Processing Magazine 21(1), 28–41 (2004)
Loeliger, H.A., Dauwels, J., Hu, J., Korl, S., Ping, L., Kschischang, F.: The factor graph approach to model-based signal processing. Proceedings of the IEEE 95(6), 1295–1322 (2007)
Choi, M.J., Tan, V.Y.F., Anandkumar, A., Willsky, A.S.: Learning latent tree graphical models. Journal of Machine Learning Research 12, 1771–1812 (2011)
Palmieri, F.A.N., Ciuonzo, D.: Entropic priors for short-term stochastic process classification. In: 14th Int. Conf. on Information Fusion, Chicago, IL (2011)
Palmieri, F.A.N., Ciuonzo, D.: Objective priors from maximum entropy in data classification. In: Information Fusion (2012), doi:10.1016/j.inffus.2012.01.012
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)
Novak, V., Perfilieva, I., Mockor, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Press (1999)
Winn, J., Bishop, C.M.: Variational message passing. Journal of Machine Learning Research 6, 661–694 (2005)
Winn, J.M.: Variational message passing and its applications. Ph.D. thesis, University of Cambridge (2004)
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Palmieri, F.A.N., Cavallo, A. (2013). Probability Learning and Soft Quantization in Bayesian Factor Graphs. In: Apolloni, B., Bassis, S., Esposito, A., Morabito, F. (eds) Neural Nets and Surroundings. Smart Innovation, Systems and Technologies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35467-0_1
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DOI: https://doi.org/10.1007/978-3-642-35467-0_1
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