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Dirk Husmeier Frank Dondelinger Sophie Lebre. Inferring gene regulatory networks with non-stationary dynamic Bayesian networks. Biomathematics & Statistics Scotland. Overview. Introduction Non-homogeneous dynamic Bayesian network for non-stationary processes Flexible network structure
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Dirk Husmeier Frank Dondelinger Sophie Lebre Inferring gene regulatory networks with non-stationary dynamic Bayesian networks Biomathematics & Statistics Scotland
Overview • Introduction • Non-homogeneous dynamic Bayesian network for non-stationary processes • Flexible network structure • Open problems
Can we learn signalling pathways from postgenomic data? From Sachs et al Science 2005
Marriage between graph theory and probability theory Friedman et al. (2000), J. Comp. Biol. 7, 601-620
Bayes net ODE model
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
BGe (Linear model) [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4
BDe (Nonlinear discretized model) P P1 Activator P2 Activation Repressor Allow for noise: probabilities P P1 Activator P2 Inhibition Conditional multinomial distribution Repressor
Model Parameters q Integral analytically tractable!
BDe: UAI 1994 BGe: UAI 1995
Example: 2 genes 16 different network structures Best network: maximum score
Identify the best network structure Ideal scenario: Large data sets, low noise
Uncertainty about the best network structure Limited number of experimental replications, high noise
Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges
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
Can we generalize this scheme to more than 2 genes? In principle yes. However …
Number of structures Number of nodes
Sampling from the posterior distribution Find the high-scoring structures Taken from the MSc thesis by Ben Calderhead Configuration space of network structures
Local change MCMC If accept If accept with probability Taken from the MSc thesis by Ben Calderhead Configuration space of network structures
Overview • Introduction • Non-homogeneous dynamic Bayesian networks for non-stationary processes • Flexible network structure • Open problems
Our new model: heterogeneous dynamic Bayesian network. Here: 2 components
Our new model: heterogeneous dynamic Bayesian network. Here: 3 components
Learning with MCMC q Allocation vector h k Number of components (here: 3)
Non-homogeneous model Non-linear model
BGe: Linear model [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4
BDe: Nonlinear discretized model P P1 Activator P2 Activation Repressor Allow for noise: probabilities P P1 Activator P2 Inhibition Conditional multinomial distribution Repressor
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
Can we get an approximate nonlinear model without data discretization? y x
Can we get an approximate nonlinear model without data discretization? Idea: piecewise linear model y x
Inhomogeneous dynamic Bayesian network with common changepoints
Inhomogenous dynamic Bayesian network with node-specific changepoints
Overview • Introduction • Non-homogeneous dynamic Bayesian network for non-stationary processes • Flexible network structure • Open problems
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
Transition probabilities: flexible structure with regularization Morphogenetic transitions: Embryo larva larva pupa pupa adult