1. Graphical Models - Inference - Wolfram Burgard, Luc De Raedt, Kristian Kersting, Bernhard Nebel Albert-Ludwigs University Freiburg, Germany PCWP CO HRBP HREKG HRSAT ERRCAUTER HR HISTORY CATECHOL SAO2 EXPCO2 ARTCO2 VENTALV VENTLUNG VENITUBE DISCONNECT MINVOLSET VENTMACH KINKEDTUBE INTUBATIONPULMEMBOLUS PAPSHUNT ANAPHYLAXIS MINOVL PVSAT FIO2 PRESS INSUFFANESTHTPR LVFAILURE ERRBLOWOUTPUT STROEVOLUMELVEDVOLUME HYPOVOLEMIA CVP BP Mainly based on F. V. Jensen, „Bayesian Networks and Decision Graphs“, Springer-Verlag New York, 2001. Advanced I WS 06/07 Most Probable Explanation

2. Bayesian Networks Advanced I WS 06/07 Outline Introduction Reminder: Probability theory Basics of Bayesian Networks Modeling Bayesian networks Inference (VE, Junction tree,MPE) Excourse: Markov Networks Learning Bayesian networks Relational Models

3. Bayesian Networks Advanced I WS 06/07 Elimination operator P(a|e=0) factor B: P(a) P(c|a) P(b|a) P(d|b,a) P(e|b,c) facotr C: factor D: factor E: factor A: e=0 B C D E A VE, Bucket elimination [Dechter ‘96] - Inference (MPE)

4. Bayesian Networks Advanced I WS 06/07 Finding MPE [Dechter ‘96] Elimination operator MPE factor B: P(a) P(c|a) P(b|a) P(d|b,a) P(e|b,c) factor C: factor D: factor E: factor A: e=0 B C D E A - Inference (MPE)

5. Bayesian Networks Advanced I WS 06/07 Generating the MPE-tuple C: E: P(b|a) P(d|b,a) P(e|b,c)B: D: A: P(a) P(c|a) e=0 - Inference (MPE)