Create Presentation
Download Presentation

Download

Download Presentation

Inferring gene regulatory networks with non-stationary dynamic Bayesian networks

274 Views
Download Presentation

Download Presentation
## Inferring gene regulatory networks with non-stationary dynamic Bayesian networks

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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