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Listgarten & Heckerman

Determining the Number of Non-Spurious Arcs in a Learned DAG Model: Investigation of a Bayesian and a Frequentist Approach. Listgarten & Heckerman. Purpose. Design a vaccine for HIV

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Listgarten & Heckerman

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  1. Determining the Number of Non-Spurious Arcs in a Learned DAG Model: Investigation of a Bayesian and a Frequentist Approach Listgarten & Heckerman

  2. Purpose • Design a vaccine for HIV • By considering many patients and observing which HLA molekyles causes the T-killer cells of the imune system to react

  3. Definitions • HLA = Human leukocyte antigen • Each person usally has [3;6] • Epitopes = bits of protein • Results of T-cell attacking HIV-peptide • Peptide = “small digestible” • Link between amino acids

  4. How? • Find out which HIV peptides interact with which HLA molekyles by using a graphical model.

  5. Solution • A directed acyclic graph representing HLA and peptides HLA h1 HLA h2 HLA h3 HLA h4 HLA hN ... peptide y1 peptide y2 peptide y3 peptide yM ... Model for one patient. A design of a vaccine is to identify a set of peptide-HLA-pairs, which are epitopes for a large number of the population

  6. Properties • Bi-partite model(2 levels) • HLA can have zero or several outgoing archs • Peptide can have zero or several ingoing archs • Each patient will have [3;6] HLA nodes that are “on” • Answers: which HLA molekyle(s) are(is) responsible for a given immune system reaction

  7. Two approaches • Bayesian • Frequentist

  8. Bayesian Approach cont. 1(2)

  9. Bayesian Approach cont. 2(2) • Exponentional complexity…! • Can be improved by limiting |Parent set| • Limit=5, gives identical results

  10. Frequentist Approach • FDR = False Discovery Rate • Given a set of hypotheses • Hypothesis i has a test score • s: assumed to be independent in a given hypotheses

  11. FDR cont. 1(4)

  12. FDR cont. 2(4) Rewrite Where is a structure search algorithm

  13. FDR cont. 3(4) – multiple data sets Q - – number of archs found by applying to real data, D

  14. FDR cont. 4(4) • Standard FDR: • The average over multiple datasets • +1 – smooths the estimate

  15. Results • PPV – positive predictive value • Frequentist method: • Bayesian method:

  16. Results on non-HIV data

  17. Results on non-HIV data

  18. Results on synthetic HIV data

  19. Results on real HIV data • 8 results…. all matches

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