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Goal: Reconstruct Cellular Networks

Explore methods to reconstruct cellular networks through Bayesian networks for gene expression analysis. Learn about Directed Acyclic Graphs, conditional probabilities, and learning algorithms.

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Goal: Reconstruct Cellular Networks

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

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

  3. Qualitative part: Directed acyclic graph (DAG) Nodes - random variables Edges - direct influence Family of Alarm E B P(A | E,B) e b 0.9 0.1 e b 0.2 0.8 e b 0.9 0.1 0.01 0.99 e b Bayesian Networks Compact representation of probability distributions via conditional independence Burglary Earthquake Radio Alarm Call Together: Define a unique distribution in a factored form Quantitative part: Set of conditional probability distributions

  4. E B P(A | E,B) B E .9 .1 e b e b .7 .3 .8 .2 e b R A .99 .01 e b C Learning Bayesian networks Data + Prior Information Learner

  5. E B P(A | E,B) .9 .1 e b e b .7 .3 .8 .2 e b .99 .01 e b E B P(A | E,B) B B E E ? ? e b A A e b ? ? ? ? e b ? ? e b Known Structure, Complete Data E, B, A <Y,N,N> <Y,N,Y> <N,N,Y> <N,Y,Y> . . <N,Y,Y> • Network structure is specified • Inducer needs to estimate parameters • Data does not contain missing values Learner

  6. E B P(A | E,B) .9 .1 e b e b .7 .3 .8 .2 e b B E .99 .01 e b A E B P(A | E,B) B E ? ? e b A e b ? ? ? ? e b ? ? e b Unknown Structure, Complete Data E, B, A <Y,N,N> <Y,N,Y> <N,N,Y> <N,Y,Y> . . <N,Y,Y> • Network structure is not specified • Inducer needs to select arcs & estimate parameters • Data does not contain missing values Learner

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