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Bayesian Networks - Intro -

MINVOLSET. KINKEDTUBE. PULMEMBOLUS. INTUBATION. VENTMACH. DISCONNECT. PAP. SHUNT. VENTLUNG. VENITUBE. PRESS. MINOVL. FIO2. VENTALV. PVSAT. ANAPHYLAXIS. ARTCO2. EXPCO2. SAO2. TPR. INSUFFANESTH. HYPOVOLEMIA. LVFAILURE. CATECHOL. LVEDVOLUME. STROEVOLUME. ERRCAUTER. HR.

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Bayesian Networks - Intro -

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  1. MINVOLSET KINKEDTUBE PULMEMBOLUS INTUBATION VENTMACH DISCONNECT PAP SHUNT VENTLUNG VENITUBE PRESS MINOVL FIO2 VENTALV PVSAT ANAPHYLAXIS ARTCO2 EXPCO2 SAO2 TPR INSUFFANESTH HYPOVOLEMIA LVFAILURE CATECHOL LVEDVOLUME STROEVOLUME ERRCAUTER HR ERRBLOWOUTPUT HISTORY CO CVP PCWP HREKG HRSAT HRBP BP Mainly based on F. V. Jensen, „Bayesian Networks and Decision Graphs“, Springer-Verlag New York, 2001. Advanced IWS 06/07 Bayesian Networks- Intro - Wolfram Burgard, Luc De Raedt, Kristian Kersting, Bernhard Nebel Albert-Ludwigs University Freiburg, Germany

  2. Why bother with uncertainty? Uncertainty appears in many tasks • Partial knowledge of the state of the world • Noisy observations • Phenomena that are not covered by our models • Inherent stochasticity - Introduction

  3. Recommendation Systems Your friends attended this lecture already and liked it. Therefore, we would like to recommend it to you ! - Introduction Real World

  4. Activity Recognition[Fox et al. IJCAI03] Lecture Hall Will you go to the AdvancedAI lecture or will you visit some friends in a cafe? Cafe - Introduction

  5. 3D Scan Data Segmentation[Anguelov et al. CVPR05, Triebel et al. ICRA06] How do you recognize the lecture hall? - Introduction

  6. Duplicate Identification • L. D. Raedt • L. de Raedt • Luc De Raedt • Wolfram Burgard • W. Burgold • Wolfram Burgold - Introduction Real World

  7. Video event recognition[Fern JAIR02,IJCAI05] • What is going on? • Is the red block on top of the green one? • …

  8. How do we deal with uncertainty? • Implicit: • Ignore what you are uncertain if you can • Build procedures that are robust to uncertainty • Explicit: • Build a model of the world that describes uncertainty about its state, dynamics, and observations • Reason about the effects of actions given the model Graphical models = explicit, model-based - Introduction

  9. Probability • A well-founded framework for uncertainty • Clear semantics: joint prob. distribution • Provides principled answers for: • Combining evidence • Predictive & Diagnostic reasoning • Incorporation of new evidence • Intuitive (at some level) to human experts • Can automatically be estimated from data - Introduction

  10. Joint Probability Distribution • „truth table“ of set of random variables • Any probability we are interested in can be computed from it - Introduction

  11. Representing Prob. Distributions • Probability distribution = probability for each combination of values of these attributes • Naïve representations (such as tables) run into troubles • 20 attributes require more than 220106 parameters • Real applications usually involve hundreds of attributes • Hospital patients described by • Background: age, gender, history of diseases, … • Symptoms: fever, blood pressure, headache, … • Diseases: pneumonia, heart attack, … - Introduction

  12. Bayesian Networks - Key Idea Exploit regularities !!! • Bayesian networks • utilize conditional independence • Graphical Representation of conditional independence respectively “causal” dependencies - Introduction

  13. MINVOLSET KINKEDTUBE PULMEMBOLUS INTUBATION VENTMACH DISCONNECT PAP SHUNT VENTLUNG VENITUBE PRESS MINOVL FIO2 VENTALV PVSAT ANAPHYLAXIS ARTCO2 EXPCO2 SAO2 TPR INSUFFANESTH HYPOVOLEMIA LVFAILURE CATECHOL LVEDVOLUME STROEVOLUME ERRCAUTER HR ERRBLOWOUTPUT HISTORY CO CVP PCWP HREKG HRSAT HRBP BP A Bayesian Network The “ICU alarm” network • 37 binary random variables • 509 parameters instead of - Introduction

  14. E B A J M Bayesian Networks • Finite, acyclic graph • Nodes: (discrete) random variables • Edges: direct influences • Associated with each node: a table representing a conditionalprobability distribution (CPD), quantifying the effect the parents have on the node - Introduction

  15. Bayesian Networks X2 X1 X3 - Introduction

  16. Markov Networks • Undirected Graphs • Nodes = random variables • Cliques = potentials (~ local jpd)

  17. ? Fielded Applications • Expert systems • Medical diagnosis (Mammography) • Fault diagnosis (jet-engines, Windows 98) • Monitoring • Space shuttle engines (Vista project) • Freeway traffic, Activity Recognition • Sequence analysis and classification • Speech recognition (Translation, Paraphrasing • Biological sequences (DNA, Proteins, RNA, ..) • Information access • Collaborative filtering • Information retrieval & extraction • … among others - Introduction

  18. Graphical Models Graphical Models (GM) Other Semantics Causal Models Chain Graphs Dependency Networks Directed GMs Undirected GMs Bayesian Networks Markov Random Fields / Markov networks FST DBNs Mixture Models Decision Trees - Introduction Simple Models HMMs Kalman Segment Models Gibbs/Boltzman Distributions Factorial HMM Mixed Memory Markov Models PCA BMMs LDA

  19. Outline • Introduction • Reminder: Probability theory • Basics of Bayesian Networks • Modeling Bayesian networks • Inference • Excourse: Markov Networks • Learning Bayesian networks • Relational Models - Introduction

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