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Bayesian Networks

Bayesian Networks. Motivation. encode uncertain expert knowledge other approaches: possibility theory, fuzzy arithmetic, … encode causality relationships truly “understand” a domain (AI) given a set of random variables, what is their Joint Probability Distribution (JPD) ?

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Bayesian Networks

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  1. Bayesian Networks

  2. Motivation • encode uncertain expert knowledge • other approaches: possibility theory, fuzzy arithmetic, … • encode causality relationships • truly “understand” a domain (AI) • given a set of random variables, what is their Joint Probability Distribution (JPD)? • Bayesian approach:prior probability + likelihood  posterior probability

  3. Qualitative (topology) C {sc1, sc2} Discrete Random Variables A {sa1, sa2} B {sb1, sb2} “C is independent of A and B” Quantitative(probabilities) “A influences B” “If I observe certain states of A,I can draw consequences regarding B”

  4. A {sa1, sa2} B {sb1, sb2} C {sc1, sc2}

  5. Inference • predictive, top-down reasoning: P(symptom | cause) • diagnostic, bottom-up reasoning: P(cause | symptom) • exact inference: NP-hard • Message Passing Algorithm • Cycle-Cutset Conditioning • approximate inference • Monte Carlo sampling (e.g. MCMC) • Loopy Belief Propagation cause symptom

  6. Learning training data + expert knowledge  structure & parameters of BN • known structure + full observations: • Maximum Likelihood Estimation • known structure + partial observations: • Expectation Maximization (EM): local optimum of maximum likelihood • Markov Chain Monte Carlo (MCMC) • unknown structure: NP-hard (many possible graph topologies) • K2: find most probable structures based on some expert knowledge • simplifying assumption: independent variables with common parent node

  7. Applications: Dependability Modelling

  8. Applications: Online Fault Diagnosis http://www.research.ibm.com/people/r/rish/papers/AAAI02symp-probe.pdf

  9. Applications: Transaction Recognition • predict transitions based on server-side RPC sequences • http://www.google.de/patents/US6925452

  10. A statistical battlefield… BN inference  Bayesian approach BN learning  Frequentist approach http://oikosjournal.wordpress.com/2011/10/11/frequentist-vs-bayesian-statistics-resources-to-help-you-choose/

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