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chapter 6




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1 . Inferring Regulatory Pathways: Bayesian Networks Model Based Approach  Step 1: define class of potential models  Step 2: reconstruct a specific model  Step 3: visualization & testable hypotheses  Emphasis on the choice of model and how to use it  The data manipulation steps are derived from the model Kin Z TF X Gene A TF Y TF X Gene A USV1 Hap4 Msn2 Hap4 Atp16 Reconstruction Interpretation Additional Biological Knowledge Data Kin Z TF X Gene A TF Y TF X Gene A Kin Z TF X Gene A TF Y TF X Gene A Kin Z TF X Gene A TF Y TF X Gene A What is a model? “A description of a process that could have generated the observed data” stochastic 2 From Data to Signaling Pathways Ra f Er k p3 8 PK A PK C Jn k PI P2 PI P3 Pl cγ Ak t .. . Cell x Cell1 Cell2 Cell3 Cell4 Automated de-novo reconstruction from high throughput data. Flow cytometry Computational analysis Datasets of cells • condition ‘a’ • condition ‘b’ •condition…‘n’ Ra f M ek 1/ 2 Er k p3 8 PK A PK C Jn k PI P2 PI P3 Pl cγ Ak t 12 Color Flow Cytometry perturbation a perturbation n perturbation b Conditions (96 well format) Primary Human T-Lymphocyte Data Simultaneous information measured individual primary human cells. Thousands of data points. 15 Bayesian Networks P(A,B,C,D,E) = P(A) P(B | A ) P(C | A, B) P(D | A, B, C) P(E | A, B, C, D ) P(A,B,C,D,E) = P(A) P(B | A ) P(C | A, B) P(D | A, B, C) P(E | A, B, C, D ) Bayesian Networks A B C D E X Ind( C ; B | A) Ind( D ; A, B | C) Ind( E ; B, C | A, D) … X X X X X X X X X 16 Bayesian Networks  Flexible language to capture a range Maximal independence  Full dependence  Formal correspondence between  Acyclic directed graph structure  Factorization of joint distribution as a product of conditional probabilities  A set of (conditional) independence statements Equivalence Class  These graphs have equivalent independence assumptions:  All 3 pairs are statistically dependent.  Grandpa and Bart become independent of each other given Homer  We can not tell them apart from the data alone. Grandpa Homer Bart Bart Homer Grandpa Grandpa Homer Bart 17 V-Structure  Homer and Marge are independent.  They become dependent given Bart Homer Bart Marge Grandpa Lisa Equivalent Bayesian Networks  Networks are equivalent if their structures encode the same independence statements  Theorem: Networks are equivalent iff they have the same skeleton and the same “V” structures E A R E A R E A R S C E D F G S C E D F G NOT I-equivalent 32 Score Decomposition A B C D E • We use the ...





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