Ch8.3.4-LoopyBelief

Ch8.3.4-LoopyBelief - Machine Learning ! ! ! ! ! Srihari...

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Unformatted text preview: Machine Learning ! ! ! ! ! Srihari Inference: Loopy Belief Propagation Sargur Srihari srihari@cedar.buffalo.edu 1 Machine Learning ! ! ! ! ! Srihari Loopy belief propagation •  •  In practice exact inference may not be possible Approaches in such cases: 1.  2.  Variational methods, which are deterministic Sampling or Monte Carlo methods Based on stochastic numerical sampling from distributions 3.  Loopy belief propagation –  –  Apply sum product algorithm even though there is no guaranty of good results Message passing schedule is modified –  –  Flood schedule simultaneously passes a message across every link in both direction Serial schedule pass one message at each time step 2 Machine Learning ! ! ! ! ! Srihari 7. Learning the graph structure •  We have assumed that the structure of the graph is known and fixed •  It is interesting to go beyond inference and learn the graph structure from data •  Requires defining a set of possible structures and a measure to score each structure 3 Machine Learning ! ! ! ! ! Srihari Bayesian Learning of graph •  Compute posterior distribution over graph structures –  Make prediction by averaging with respect to this distribution •  If we have prior p(m) over graphs indexed by m then posterior is –  p(m|D) ∝ p(m)p(D|m) –  Where D is the data set •  Model evidence p(D|m) provides score for each model –  Evaluation of evidence involves marginalization over latent variables –  Computationally challenging for many models •  Exploring space of structures is also problemtic –  No of different graph structures grows exponentially with no of nodes –  Necessary to use heuristics to find good candidates 4 ...
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Ch8.3.4-LoopyBelief - Machine Learning ! ! ! ! ! Srihari...

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