Graphical Models for Machine Learning and Digital by Brendan J. Frey

By Brendan J. Frey

A number of difficulties in laptop studying and electronic verbal exchange care for advanced yet established typical or man made platforms. during this e-book, Brendan Frey makes use of graphical versions as an overarching framework to explain and remedy difficulties of trend class, unsupervised studying, facts compression, and channel coding. utilizing probabilistic buildings comparable to Bayesian trust networks and Markov random fields, he's capable of describe the relationships among random variables in those platforms and to use graph-based inference concepts to improve new algorithms. one of the algorithms defined are the wake-sleep set of rules for unsupervised studying, the iterative turbodecoding set of rules (currently the easiest error-correcting interpreting algorithm), the bits-back coding approach, the Markov chain Monte Carlo method, and variational inference.

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I take P(zklak, (h) = P(zkl{zj}J�i, Ok)' where in the second expression the parameters are con­ strained so that the function does not depend on nonparents. Also, in order to succinctly account for the bias, I will usually assume that there is a dummy variable Zo that is set to Zo = 1. ) Using these notational simplifications and using g(. 32) where ()kj is set to 0 for each nonparent Zj. 8 Example 2: The bars problem Bayesian networks provide a useful framework for specifying generative mod­ els.

349 ) . 8). 3 Probabilistic Inference in Graphical Models Probability propagation (the sum-product algorithm) The highly regular way that messages are passed in the generalized forward­ backward algorithm can be relaxed to obtain a more general probability prop­ agation algorithm. It turns out that as long as a few simple rules are fol­ lowed, messages may be passed in any order (even in parallel) to obtain con­ ditional probabilities. These rules prescribe how the network is to be initial­ ized for propagation, and how messages are created, propagated, absorbed and buffered.

On the other hand, for pattern classification, unsupervised learning, and data compression, we will usually estimate a pa­ rameterized Bayesian network from some training data and then use proba­ bilistic inference to classify a new pattern, perform perceptual inference, or produce a source codeword for a new pattern. In Chapter 2, I discuss different ways to perform probabilistic inference, including probability propagation, Markov chain Monte Carlo, variational op­ timization, and the Helmholtz machine.

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