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Inferring gene regulatory networks with non-stationary dynamic Bayesian networks

Inferring gene regulatory networks with non-stationary dynamic Bayesian networks

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Inferring gene regulatory networks with non-stationary dynamic Bayesian networks

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  1. Dirk Husmeier Frank Dondelinger Sophie Lebre Inferring gene regulatory networks with non-stationary dynamic Bayesian networks Biomathematics & Statistics Scotland

  2. Overview • Introduction • Non-homogeneous dynamic Bayesian network for non-stationary processes • Flexible network structure • Open problems

  3. Can we learn signalling pathways from postgenomic data? From Sachs et al Science 2005

  4. Network reconstruction from postgenomic data

  5. Marriage between graph theory and probability theory Friedman et al. (2000), J. Comp. Biol. 7, 601-620

  6. Bayes net ODE model

  7. Graph theory • Directed acyclic graph (DAG) representing conditional independence relations. • Probability theory • It is possible to score a network in light of the data: P(D|M), D:data, M: network structure. • We can infer how well a particular network explains the observed data. NODES A B C EDGES D E F

  8. BGe (Linear model) [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4

  9. BDe (Nonlinear discretized model) P P1 Activator P2 Activation Repressor Allow for noise: probabilities P P1 Activator P2 Inhibition Conditional multinomial distribution Repressor

  10. Model Parameters q Integral analytically tractable!

  11. BDe: UAI 1994 BGe: UAI 1995

  12. Dynamic Bayesian network

  13. Example: 2 genes 16 different network structures Best network: maximum score

  14. Identify the best network structure Ideal scenario: Large data sets, low noise

  15. Uncertainty about the best network structure Limited number of experimental replications, high noise

  16. Sample of high-scoring networks

  17. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges

  18. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges Uncertainty about edges High-confident edge High-confident non-edge

  19. Can we generalize this scheme to more than 2 genes? In principle yes. However …

  20. Number of structures Number of nodes

  21. Sampling from the posterior distribution Find the high-scoring structures Taken from the MSc thesis by Ben Calderhead Configuration space of network structures

  22. Madigan & York (1995), Guidici & Castello (2003)

  23. Local change MCMC If accept If accept with probability Taken from the MSc thesis by Ben Calderhead Configuration space of network structures

  24. Overview • Introduction • Non-homogeneous dynamic Bayesian networks for non-stationary processes • Flexible network structure • Open problems

  25. Dynamic Bayesian network

  26. Example: 4 genes, 10 time points

  27. Standard dynamic Bayesian network: homogeneous model

  28. Limitations of the homogeneity assumption

  29. Our new model: heterogeneous dynamic Bayesian network. Here: 2 components

  30. Our new model: heterogeneous dynamic Bayesian network. Here: 3 components

  31. Learning with MCMC q Allocation vector h k Number of components (here: 3)

  32. Non-homogeneous model  Non-linear model

  33. BGe: Linear model [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4

  34. BDe: Nonlinear discretized model P P1 Activator P2 Activation Repressor Allow for noise: probabilities P P1 Activator P2 Inhibition Conditional multinomial distribution Repressor

  35. Linear Gaussian model Restriction to linear processes Original data  no information loss Multinomial model Nonlinear model Discretization  information loss Pros and cons of the two models

  36. Can we get an approximate nonlinear model without data discretization? y x

  37. Can we get an approximate nonlinear model without data discretization? Idea: piecewise linear model y x

  38. Inhomogeneous dynamic Bayesian network with common changepoints

  39. Inhomogenous dynamic Bayesian network with node-specific changepoints

  40. NIPS 2009

  41. Overview • Introduction • Non-homogeneous dynamic Bayesian network for non-stationary processes • Flexible network structure • Open problems

  42. Non-stationarity in the regulatory process

  43. Non-stationarity in the network structure

  44. ICML 2010

  45. Flexible network structure with regularization

  46. Flexible network structure with regularization

  47. Flexible network structure with regularization

  48. Morphogenesis in Drosophila melanogaster • Gene expression measurements over 66 time steps of 4028 genes (Arbeitman et al., Science, 2002). • Selection of 11 genes involved in muscle development. Zhao et al. (2006), Bioinformatics22

  49. Transition probabilities: flexible structure with regularization Morphogenetic transitions: Embryo  larva larva pupa pupa  adult