learning regulatory networks from postgenomic data and prior knowledge dirk husmeier 1)...
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Learning regulatory networks from postgenomic data and prior knowledge
Dirk Husmeier
1) Biomathematics & Statistics Scotland
2) Centre for Systems Biology at Edinburgh
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Raf signalling network
From Sachs et al Science 2005
Systems Biology
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unknown
high-throughput experiment
s
postgenomic data
machine learning
statistical methods
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Bayesian networks
A
CB
D
E F
NODES
EDGES
•Marriage between graph theory and probability theory.
•Directed acyclic graph (DAG) representing conditional independence relations.
•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.
),|()|(),|()|()|()(
),,,,,(
DCFPDEPCBDPACPABPAP
FEDCBAP
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Model
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Parameters
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Learning Bayesian networks
P(M|D) = P(D|M) P(M) / Z
M: Network structure. D: Data
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MCMC in structure spaceMadigan & York (1995), Guidici & Castello (2003)
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Alternative paradigm: order MCMC
Machine Learning, 2004
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Successful application of Bayesian networks to the Raf regulatory network
From Sachs et al Science 2005
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Flow cytometry data
• Intracellular multicolour flow cytometry experiments: concentrations of 11 proteins
• 5400 cells have been measured under 9 different cellular conditions (cues)
• Optimzation with hill climbing
• Perfect reconstruction
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Microarray data Spellman et al (1998)Cell cycle73 samples
Tu et al (2005)Metabolic cycle36 samples
Ge
nes
Ge
nes
time time
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AUC scores TP for FP=5
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Part 1
Integration of prior knowledge
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+
+
+
+…
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Use TF binding motifs in promoter sequences
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Biological prior knowledge matrix
Biological Prior Knowledge
Define the energy of a Graph G
Indicates some knowledge aboutthe relationship between genes i and j
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Prior distribution over networks
Deviation between the network G and the prior knowledge B: Graph: є {0,1}
Prior knowledge: є [0,1]“Energy”
Hyperparameter
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New contribution
• Generalization to more sources of prior knowledge
• Inferring the hyperparameters
• Bayesian approach
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Multiple sources of prior knowledge
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Sample networks and hyperparameters from the posterior distribution
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Bayesian networkswith two sources of prior
Data
BNs + MCMC
Recovered Networks and trade off parameters
Source 1 Source 2
1 2
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Bayesian networkswith two sources of prior
Data
BNs + MCMC
Source 1 Source 2
1 2
Recovered Networks and trade off parameters
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Bayesian networkswith two sources of prior
Data
BNs + MCMC
Source 1 Source 2
1 2
Recovered Networks and trade off parameters
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Sample networks and hyperparameters from the posterior distribution with MCMC
Metropolis-Hastings scheme
Proposal probabilities
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Sample networks and hyperparameters from the posterior distribution
Metropolis-Hastings scheme
Proposal probabilities
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Sample networks and hyperparameters from the posterior distribution
Metropolis-Hastings scheme
Proposal probabilities
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Prior distribution
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Rewriting the energy
Energy of a network
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Approximation of the partition function
Partition function of an ideal gas
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Evaluation on the Raf regulatory network
From Sachs et al Science 2005
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Evaluation: Raf signalling pathway
• Cellular signalling network of 11 phosphorylated proteins and phospholipids in human immune systems cell
• Deregulation carcinogenesis
• Extensively studied in the literature gold standard network
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DataPrior knowledge
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Flow cytometry data
• Intracellular multicolour flow cytometry experiments: concentrations of 11 proteins
• 5400 cells have been measured under 9 different cellular conditions (cues)
• Downsampling to 100 instances (5 separate subsets): indicative of microarray experiments
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Microarray example Spellman et al (1998)Cell cycle73 samples
Tu et al (2005)Metabolic cycle36 samples
Ge
nes
Ge
nes
time time
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DataPrior knowledge
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Prior knowledge from KEGG
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Prior distribution
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Prior knowledge from KEGG
Raf network
0.25
00.5
0
0.5
0.87
0
1
0.5
0 0
0.5
0
10.71
0
0
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Data and prior knowledge
+ KEGG
+ Random
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Evaluation
• Can the method automatically evaluate how useful the different sources of prior knowledge are?
• Do we get an improvement in the regulatory network reconstruction?
• Is this improvement optimal?
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Sampled values of the
hyperparameters
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Bayesian networkswith two sources of prior knowledge
Data
BNs + MCMC
Recovered Networks and trade off parameters
Random KEGG
1 2
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Bayesian networkswith two sources of prior knowledge
Data
BNs + MCMC
Random KEGG
1 2
Recovered Networks and trade off parameters
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Evaluation
• Can the method automatically evaluate how useful the different sources of prior knowledge are?
• Do we get an improvement in the regulatory network reconstruction?
• Is this improvement optimal?
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•We use the Area Under the Receiver Operating
Characteristic Curve (AUC).
0.5<AUC<1
AUC=1AUC=0.5
Performance evaluation:ROC curves
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5 FP counts
BN
GGM
RN
Alternative performance evaluation: True positive (TP) scores
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Flow cytometry data and KEGG
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Evaluation
• Can the method automatically evaluate how useful the different sources of prior knowledge are?
• Do we get an improvement in the regulatory network reconstruction?
• Is this improvement optimal?
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Learning the trade-off hyperparameter
• Repeat MCMC simulations for large set of fixed hyperparameters β
• Obtain AUC scores for each value of β
• Compare with the proposed scheme in which β is automatically inferred.
Mean and standard deviation of the sampled trade off parameter
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Flow cytometry data and KEGG
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Part 2
Combining data from different experimental conditions
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What if we have multiple data sets obtained under different experimental conditions?
Example: Cytokine network
• Infection
•Treatment with IFN
•Infection and treatment with IFN
Collaboration with Peter Ghazal, Paul Dickinson, Kevin Robertson, Thorsten Forster & Steve Watterson.
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datadata data datadata data
Monolithic Individual
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datadata data datadata data
Monolithic Individual
Propose a compromise between the two
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M1 M221
D1 D2
M*
MII
DI
. . .
Compromise between the two previous ways of combining the data
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BGe or BDe
Ideal gas approximation
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MCMC
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Empirical evaluation
Real application: macrophages infected with CMV and pre-treated
with IFN-γ
No gold-standard
Simulated data from the Raf signalling network
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Simulated dataRaf network
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Simulated data
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v-Raf network
Simulated data
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Raf network
v-Raf network
Simulated data
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Simulated data
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Simulated Data
Weights between nodes are different for different data sets.
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Simulated Data
Weights between nodes are different for different data sets.
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5 data sets100 data points each
1 random data set (pure noise)
1 data set from the modified network
3 data sets from the Raf network, but with
different regulations strengths
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M1 M221
D1
M*
MII
DI
. . .
Compromise between the two previous ways of combining the data
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Corrupt, noisy data
Modified network
Raf network
Posterior distribution of ß
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M1 M221
D1
M*
MII
DI
. . .
Compromise between the two previous ways of combining the data
0
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5 data sets100 data points each
1 random data set (pure noise)
1 data set from the modified network
3 data sets from the Raf network, but with
different regulations strengths
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Corrupt, noisy data
Modified network
Raf network
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Network reconstruction accuracy
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Convergence problems
Coupling method
Std MCMC
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Data sets:1 rand (blue)3 raf 1 vraf (cyan)
Traceplots of sampled
hyperparameters;
Gaussian data set
log likelihood
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• The MCMC simulations have convergence problems.• If the simulations “converge”:
– Random data set is identified and switched off.– Data from a slightly modified network are also
identified.– The reconstructed network outperforms the two
competing approaches.• Future work:
The convergence problems need to be addressed.
Conclusions – Part 2
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Part 3
Markov chain Monte Carlo
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Learning Bayesian networks
P(M|D) = P(D|M) P(M) / Z
M: Network structure. D: Data
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MCMC in structure spaceMadigan & York (1995), Guidici & Castello (2003)
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Main idea
Propose new parents from the distribution:
•Identify those new parents that are involved in the formation of directed cycles.
•Orphan them, and sample new parents for them subject to the acyclicity constraint.
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1) Select a node
2) Sample new parents 3) Find directed cycles
4) Orphan “loopy” parents
5) Sample new parents for these parents
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Mathematical Challenge:
• Show that condition of detailed balance is satisfied.
• Derive the Hastings factor …
• … which is a function of various partition functions
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Acceptance probability
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Summary
• Learning Bayesian networks from postgenomic data
• Integration of biological prior knowledge
• Learning regulatory networks from heterogeneous data obtained under different experimental conditions
• Improving MCMC
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Acknowledgements
Funding from the
Scottish Government
Rural and Environment Research and Analysis Directorate (RERAD)
Collaboration with
Adriano Werhli
Marco Grzegorczyk
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Adriano Werhli
Marco Grzegorzcyk
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Thank you!
Any questions?