Lecture17-annotated - 1 Eric Xing © Eric Xing CMU 2006-2008 1 Machine Learning Machine-701/15 701/15-781 Fall 2008 781 Fall 2008 Bayesian Networks

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Unformatted text preview: 1 Eric Xing © Eric Xing @ CMU, 2006-2008 1 Machine Learning Machine Learning 10 10-701/15 701/15-781, Fall 2008 781, Fall 2008 Bayesian Networks Bayesian Networks Eric Xing Eric Xing Lecture 17, November 10, 2008 Reading: Chap. 8, C.B book Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B X1 X2 X3 X4 X5 X6 X7 X8 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B X1 X2 X3 X4 X5 X6 X7 X8 X1 X2 X3 X4 X5 X6 X7 X8 Eric Xing © Eric Xing @ CMU, 2006-2008 2 2 Eric Xing © Eric Xing @ CMU, 2006-2008 3 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 What is a Bayesian Network?--- example from a signal transduction pathway z A possible world for cellular signal transduction: Eric Xing © Eric Xing @ CMU, 2006-2008 4 z Representation: what is the joint probability dist. on multiple variables? z How many state configurations in total? --- 2 8 z Are they all needed to be represented? z Do we get any scientific/medical insight? z Learning: where do we get all this probabilities? z Maximal-likelihood estimation? but how many data do we need? z Where do we put domain knowledge in terms of plausible relationships between variables, and plausible values of the probabilities? z Inference: If not all variables are observable, how to compute the conditional distribution of latent variables given evidence? z Computing p ( H | A ) would require summing over all 2 6 configurations of the unobserved variables ) , , , , , , , , ( 8 7 6 5 4 3 2 1 X X X X X X X X P Recap of Basic Prob. Concepts A C F G H E D B A C F G H E D B A C F G H E D B A C F G H E D B 3 Eric Xing © Eric Xing @ CMU, 2006-2008 5 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 What is a Bayesian Network?--- example from a signal transduction pathway z A possible world for cellular signal transduction: Eric Xing © Eric Xing @ CMU, 2006-2008 6 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B Membrane Cytosol Nucleus X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 BN: Structure Simplifies Representation z Dependencies among variables 4 Eric Xing © Eric Xing @ CMU, 2006-2008 7 ¡ If X i 's are conditionally independent (as described by a BN ), the joint can be factored to a product of simpler terms, e.g., ¡ Why we may favor a BN? ¢ Representation cost: how many probability statements are needed? ¢ Algorithms for systematic and efficient inference/learning computation • Exploring the graph structure and probabilistic semantics ¢ Incorporation of domain knowledge and causal (logical) structures P ( X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 ) = P ( X 1 ) P ( X 2 ) P ( X 3 | X 1 ) P ( X 4 | X 2 ) P ( X 5 | X 2 ) P ( X 6 | X 3 , X 4 ) P ( X 7 | X 6 ) P ( X 8 | X 5 , X 6 ) Bayesian Network 2+2+4+4+4+8+4+8=36, an 8-fold reduction from 2 8 !...
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This note was uploaded on 01/26/2010 for the course MACHINE LE 10701 taught by Professor Ericp.xing during the Fall '08 term at Carnegie Mellon.

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Lecture17-annotated - 1 Eric Xing © Eric Xing CMU 2006-2008 1 Machine Learning Machine-701/15 701/15-781 Fall 2008 781 Fall 2008 Bayesian Networks

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