ISC Operator for reconstructing Bayesian Network in gene networks context. Jimmy Vandel & Simon de Givry
Outlines: ➢ Biological motivation ➢ Bayesian Networks framework ➢ Learning Algorithms ➢ Local Operators ➢ Comet language ➢ Experimentation Vandel Jimmy Plan 1 /17
Biological motivation DNA Gene 1 Gene 2 Gene 3 Vandel Jimmy 1. Biological motivation 2 /17
Biological motivation DNA Gene 1 Gene 2 Gene 3 → gene expressions (mRNA concentrations) Vandel Jimmy 1. Biological motivation 2 /17
Biological motivation DNA Gene 1 Gene 2 Gene 3 → gene expressions (mRNA concentrations) → gene regulations Vandel Jimmy 1. Biological motivation 2 /17
Biological motivation DNA Gene 1 Gene 2 Gene 3 → gene expressions (mRNA concentrations) → gene regulations Vandel Jimmy 1. Biological motivation 2 /17
Goal : Reconstruction of gene regulatory network. Escherichia coli (423 genes, 578 regulations) (SS. Shen-Orr and al., 2002) Vandel Jimmy 1. Biological motivation 3 /17
Polymorphism Vandel Jimmy 1. Biological motivation 4 /17
Polymorphism G1 G2 G3 Vandel Jimmy 1. Biological motivation 4 /17
Polymorphism G1 G2 G3 G1 G2 G3 Vandel Jimmy 1. Biological motivation 4 /17
Polymorphism G1 G2 G3 G1 G2 G3 DNA mutations in genes : in promoter region → impact on its gene activity Vandel Jimmy 1. Biological motivation 4 /17
Polymorphism G1 G2 G3 G1 G2 G3 DNA mutations in genes: in promoter region → impact on its gene activity in coding region → impact on others gene activities Vandel Jimmy 1. Biological motivation 4 /17
Polymorphism G1 G2 G3 G1 G2 G3 M1 M2 M3 DNA mutations in genes: in promoter region → impact on its gene activity in coding region → impact on others gene activities Genetic data from one genetic marker (SNP) for each gene Vandel Jimmy 1. Biological motivation 4 /17
Discrete Bayesian network X i ={ G i , M i } G n Directed acyclic graph composed of variables M 1 M 1 M 2 M 3 Genetic data G 1 G 1 G 2 G 3 Gene expressions Vandel Jimmy 2. Bayesian Networks framework 5/17
Discrete Bayesian network X i ={ G i , M i } G n Directed acyclic graph composed of variables M 1 M 1 M 2 M 3 Genetic data G 1 G 1 G 2 G 3 Gene expressions P G G 3 / G 2, M 2 Conditional distribution G 3 !G 3 G 2 M 2 0.72 0.28 G 2 ! M 2 0.59 0.41 !G 2 M 2 0.63 0.37 !G 2 ! M 2 0.10 0.90 Graphic representation of a joint probability distribution n P G X = ∏ i = 1 P G X i / Pa i Vandel Jimmy 2. Bayesian Networks framework 5/17
Learning strategy G score = argmax G i P G i / D D We look for the graph with dataset . P G i / D = P D / G i P G i P D ∝ P D / G i P G i P D / G i : :marginal likelihood of Gi ➢ P G i ➢ :prior probability of the graph G i → assumed to be uniform Objective function easy to evaluate and avoids over-fitting ➢ decomposable and penalized scores ➢ BDe score ( D.Heckerman Machine learning 1995) ➢ BIC score ( G.Schwartz Annals of statistics 1978) Vandel Jimmy 3. Learning algorithms 6/17
Local search components 1. Search space ➢ Directed Acyclic Graph ➢ Partial DAG (PDAG) ➢ variable orders Vandel Jimmy 3. Learning algorithms 7/17
Local search components 1. Search space 2. Initial structure ➢ Directed Acyclic Graph ➢ empty structure ➢ Partial DAG (PDAG) ➢ random structure ➢ informed structure (MWST, expert...) ➢ variable orders Vandel Jimmy 3. Learning algorithms 7/17
Local search components 1. Search space 2. Initial structure 3. Neighborhood operators ➢ Directed Acyclic Graph ➢ empty structure ➢ addition of an edge ➢ Partial DAG (PDAG) ➢ random structure ➢ deletion of an edge ➢ informed structure ➢ reversal of an edge ➢ k look-ahead (MWST, expert...) ➢ variable orders ➢ optimal reinsertion Vandel Jimmy 3. Learning algorithms 7/17
Local search components 1. Search space 2. Initial structure 3. Neighborhood operators ➢ Directed Acyclic Graph ➢ empty structure ➢ addition of an edge ➢ Partial DAG (PDAG) ➢ random structure ➢ deletion of an edge ➢ informed structure ➢ reversal of an edge ➢ k look-ahead (MWST, expert...) ➢ variable orders ➢ optimal reinsertion 4. Meta-heuristics ➢ hill climbing (with restarts) ➢ tabu search ➢ simulated annealing ➢ MCMC ➢ genetic algorithms ➢ ... Vandel Jimmy 3. Learning algorithms 7/17
Local Operators ➢ addition ➢ deletion ➢ reversal (deletion + addition on the same pair) ➢ swap (deletion + addition including an extra node) Vandel Jimmy 4. Local operators 8/17
Local Operators ➢ addition ➢ deletion ➢ reversal (deletion + addition on the same pair) ➢ swap (deletion + addition including an extra node) Example: Current situation Target situation G 1 G 2 G 1 G 2 G 3 G 3 score Add G 2, G 3 score Add G 1, G 3 0 Vandel Jimmy 4. Local operators 8/17
Local Operators ➢ addition ➢ deletion ➢ reversal (deletion + addition on the same pair) ➢ swap (deletion + addition including an extra node) Example: Deletion G 1, G 3 Add G 2, G 3 G 1 G 2 Current situation Target situation G 1 G 2 G 1 G 2 G 3 G 3 G 3 score Add G 2, G 3 score Add G 1, G 3 0 Vandel Jimmy 4. Local operators 8/17
Local Operators ➢ addition ➢ deletion ➢ reversal (deletion + addition on the same pair) ➢ swap (deletion + addition including an extra node) Example: Deletion G 1, G 3 Add G 2, G 3 G 1 G 2 score Add G 1, G 3 0 Current situation Target situation G 1 G 2 G 1 G 2 G 3 G 3 G 3 score Add G 2, G 3 score Add G 1, G 3 0 Vandel Jimmy 4. Local operators 8/17
Local Operators ➢ addition ➢ deletion ➢ reversal (deletion + addition on the same pair) ➢ swap (deletion + addition including an extra node) Example: Deletion G 1, G 3 Add G 2, G 3 G 1 G 2 score Add G 1, G 3 0 Current situation Target situation G 1 G 2 G 1 G 2 G 3 G 3 G 3 Swap G 1, G 3, G 2 score Add G 2, G 3 score Add G 1, G 3 0 score Add G 2, G 3 − score Add G 1, G 3 0 → escape from some local maxima Vandel Jimmy 4. Local operators 8/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 G 1 G 2 G 3 G 7 G 4 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 G 1 G 2 G 3 G 7 G 4 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 While there exist a cycle and ! STOP Select the edge of the cycle minimizing score Add G 1 G 2 G 3 G 7 G 4 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 While there exist a cycle and ! STOP Select the edge of the cycle minimizing score Add G 1 Try to delete it G 2 G 3 G 7 G 4 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 While there exist a cycle and ! STOP Select the edge of the cycle minimizing score Add G 1 Try to delete it If score Swap G 2, G 3, G 7 score Deletion G 4, G 6 ≤ 0 G 2 G 3 G 7 G 4 Else Record Deletion G 4, G 6 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 While there exist a cycle and ! STOP Select the edge of the cycle minimizing score Add G 1 Try to delete it If score Swap G 2, G 3, G 7 score Deletion G 4, G 6 ≤ 0 Try to swap this edge G 2 G 3 G 7 G 4 Else Record Deletion G 4, G 6 G 6 G 5 Vandel Jimmy 4. Local operators 9/17
ISC Operator (Iterative Swap Operator) Swap G 2, G 3, G 7 ? Cycle { G 3, G 4, G 6, G 7 } Current situation score Add G 7, G 3 ∣ G 1 score Add G 2, G 3 ∣ G 1 0 While there exist a cycle and ! STOP Select the edge of the cycle minimizing score Add G 1 Try to delete it If score Swap G 2, G 3, G 7 score Deletion G 4, G 6 ≤ 0 Try to swap this edge G 2 G 3 score Swap G 2, G 3, G 7 score Swap G 4, G 6, G 5 ≤ 0 If STOP Else G 7 G 4 Swap G 4, G 6, G 5 Record Else Deletion G 4, G 6 Record G 6 G 5 Vandel Jimmy 4. Local operators 9/17
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