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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

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

why bother with uncertainty
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

recommendation systems
Recommendation Systems

Your friends

attended this

lecture already

and liked it.

Therefore, we

would like to

recommend it

to you !

- Introduction

Real World

activity recognition fox et al ijcai03
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

3d scan data segmentation anguelov et al cvpr05 triebel et al icra06
3D Scan Data Segmentation[Anguelov et al. CVPR05, Triebel et al. ICRA06]

How do you recognize the lecture hall?

- Introduction

duplicate identification
Duplicate Identification
  • L. D. Raedt
  • L. de Raedt
  • Luc De Raedt
  • Wolfram Burgard
  • W. Burgold
  • Wolfram Burgold

- Introduction

Real World

video event recognition fern jair02 ijcai05
Video event recognition[Fern JAIR02,IJCAI05]
  • What is going on?
  • Is the red block on top of the green one?
how do we deal with uncertainty
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

probability
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

joint probability distribution
Joint Probability Distribution
  • „truth table“ of set of random variables
  • Any probability we are interested in can be computed from it

- Introduction

representing prob distributions
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

bayesian networks key idea
Bayesian Networks - Key Idea

Exploit regularities !!!

  • Bayesian networks
    • utilize conditional independence
    • Graphical Representation of conditional independence respectively “causal” dependencies

- Introduction

a bayesian network

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

bayesian networks

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

bayesian networks1
Bayesian Networks

X2

X1

X3

- Introduction

markov networks
Markov Networks
  • Undirected Graphs
  • Nodes = random variables
  • Cliques = potentials (~ local jpd)
fielded applications

?

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

graphical models
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

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

- Introduction