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Bayesian Networks

Learn how Bayesian Networks encode uncertain knowledge, causal relationships, and offer inference methods in AI domains. Discover both qualitative and quantitative aspects, along with learning techniques and practical applications in fault diagnosis and transaction recognition.

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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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