By Michael I. Jordan

ISBN-10: 0262600323

ISBN-13: 9780262600323

Graphical types, a wedding among likelihood conception and graph idea, offer a typical instrument for facing difficulties that happen all through utilized arithmetic and engineering -- uncertainty and complexity. specifically, they play an more and more vital function within the layout and research of desktop studying algorithms. basic to the belief of a graphical version is the proposal of modularity: a posh process is equipped by way of combining less complicated components. likelihood thought serves because the glue wherein the elements are mixed, making sure that the method as a complete is constant and offering how you can interface versions to info. Graph idea offers either an intuitively attractive interface in which people can version hugely interacting units of variables and a knowledge constitution that lends itself clearly to the layout of effective general-purpose algorithms.

This ebook offers an in-depth exploration of matters relating to studying in the graphical version formalism. 4 chapters are educational chapters -- Robert Cowell on Inference for Bayesian Networks, David MacKay on Monte Carlo equipment, Michael I. Jordan et al. on Variational tools, and David Heckerman on studying with Bayesian Networks. the rest chapters hide quite a lot of issues of present study interest.

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Extra info for Learning in Graphical Models (Adaptive Computation and Machine Learning)

Sample text

Assum ing no evidence , then sending the clique marginals as messages results in the clique marginal representation , as for the discrete case: P(U) = II p(Xc )/ll sP(Xs). c Care must be taken to propagate evidence. By evidence [; on a set of nodes Y we mean that each node in Y is observed to take a definite value . ) Evidence about a variable must be entered into every clique and separator in which it occurs . This is because when evidence is entered on a variable it reduces the dimensions of every h vector and K matrix in the cliques and separators in which it occurs .

The * algorithm junction to message marginal is nested message applicability ~ snace - tree approaches . and of time the costs nested with junction those of tree the approach conventional , S331 :IL NOI~~Nflr a3LS~N ' HddV'IVNOI~N'aANOO log . - r L _ 11- - 1881 . 1 1 1 So I . lERULFF space required pass , In be cost The clique , Co of <1>c shall assume is it . ) . For ( m n ) IXcl time during that ' l / Jc , . is is the outward stored in the clique Note potential that if utilized shall , , , , information this however < Pc cost , may refrain from .

Sl messages and 84 the of - messages these triangulated , two on 81 = 82 = 83 = VI = I'\-S3 receives Based already { ( 016 . 57 down potentials induce our has clique associated . The 8 - clique associated the graph break in it , with shown - with on it Figure the . down only other These 3 . the hand potentials . In potential , NESTEDJUNCTIONTREES 59 (Cb n So) \ Ca = { 22, 26, 94, 95} ; that is, 4 x 5 x 5 x 5 = 500 messages must be sentvia separator{83, 84,97, 168} in order to generate80. Sending a message from Cb to Ca involves inward propagation of messages in the (Cc, Cd) junction tree, but , again, since neither Cc nor Cd contain all variables of the (Ca, Cb) separator, we need to send multiple messagefrom Cd to Cc (or vice versa).

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Learning in Graphical Models (Adaptive Computation and Machine Learning) by Michael I. Jordan

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