1. Goal: Reconstruct Cellular Networks Biocarta. http://www.biocarta.com/ Conditions Genes

2. Causal Reconstruction for Gene Expression u Use language of Bayesian networks to reconstruct causal connections Gene A Gene C Gene D Gene E Gene B Friedman et al, JCB 2000

3. Family of Alarm Bayesian Networks Qualitative part: Directed acyclic graph (DAG) u Nodes - random variables u Edges - direct influence Quantitative part: Set of conditional probability distributions 0.90.1 e b e 0.20.8 0.01 0.99 0.90.1 be b b e BE P(A | E,B) Earthquake Radio Burglary Alarm Call Compact representation of probability distributions via conditional independence Together: Define a unique distribution in a factored form

4. Learning Bayesian networks E R B A C.9.1 e b e.7.3.99.01.8.2 be b b e BEP(A | E,B) Data + Prior Information Learner

5. Known Structure, Complete Data E B A.9.1 e b e.7.3.99.01.8.2 be b b e BEP(A | E,B) ?? e b e ?? ? ? ?? be b b e BE E B A u Network structure is specified l Inducer needs to estimate parameters u Data does not contain missing values Learner E, B, A.

6. Unknown Structure, Complete Data E B A.9.1 e b e.7.3.99.01.8.2 be b b e BEP(A | E,B) ?? e b e ?? ? ? ?? be b b e BE E B A u Network structure is not specified l Inducer needs to select arcs & estimate parameters u Data does not contain missing values E, B, A. Learner