Bayesian Networks for Modeling Gene Expression Data. Sushmita Roy BMI/CS 576 www.biostat.wisc.edu/bmi576 firstname.lastname@example.org Nov 19 th , 2013. Bayesian networks (BN). A BN compactly represents a joint probability distribution It has two parts: A graph which is directed and acyclic
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Nov 19th, 2013
Random variables encode expression levels
Parameters of CPD for child given parents.
Assume Xi is binary
Needs 25 measurements
No independence assertions
Needs 23 measurements
P( X4|X1, X2,X3 ) as a table
Parents of X4
For each joint assignment to X1, X2, X3,
estimate the probabilities for each possible value of X4
For example, consider X1=T, X2=F, X3=T
P(X4=T|X1=T, X2=F, X3=T)=2/4
P(X4=F|X1=T, X2=F, X3=T)=2/4
Maximum likelihood parameters
Need approximate methods to search the space of networks
Measures of relevance
P(X), Q(X) are two distributions over X
Measures the mutual information between X and Y, given Z
If Z captures everything about X, knowing Y gives no more information about X.
Thus the conditional mutual information would be zero.
AMutual information can miss some parents
Score 15 seems to perform the best
row independentlyDoes the confidence estimated from bootstrap procedure represent real relationships?
--- Randomized data
One learned Bayesian network
Bootstrapped confidence Bayesian network
Highlights a subnetwork associated with yeast mating