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Bayesian Nets and Applications

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... (EG=A?GT?UM?S?HW) 18 ... HG are independent given UM. Medical Application of Bayesian Networks: ... on their ability to discriminate between disease classes ... – PowerPoint PPT presentation

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Title: Bayesian Nets and Applications

1
Bayesian Nets and Applications
• Next class machine learning
• C. 18.1, 18.2
• Questions on the homework?

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Why is this useful?
• Useful for assessing diagnostic probability from
causal probability
• P(causeeffect) P(effectcause)P(cause)
P(effect)
• Let M be meningitus, S be stiff
neck P(ms)P(sm)P(m) 0.8 X 0.0001 0.0008
P(s) 0.1
• Note posterior probability of meningitus is
still very small!

9
Naïve Bayes
• What happens if we have more than one piece of
evidence?
• If we can assume conditional independence
• Overslept and trafficjam are independent, given
late
• P(lateoverslept ? trafficjam) aP(overslept ?
trafficjam)late)P(late) aP(overslept)late)
P(trafficjamlate)P(late)
• Naïve Bayes where a single cause directly
influences a number of effects, all conditionally
independent
• Independence often assumed even when not so

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Bayesian Networks
• A directed acyclic graph in which each node is
annotated with quantitative probability
information
• A set of random variables makes up the network
nodes
• A set of directed links connects pairs of nodes.
If there is an arrow from node X to node Y, X is
a parent of Y
• Each node Xi has a conditional probability
distributionP(XiParents(Xi) that quantifies the
effect of the parents on the node

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Example
• Topology of network encodes conditional
independence assumptions

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Hard working
Smart
Good test taker
Understands material
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Smart Smart
True False
.5 .5
Hard Working Hard Working
True False
.7 .3
Hard working
Smart
Good test taker
Understands material
S Good Test Taker Good Test Taker
S True False
True .75 .25
False .25 .75
S HW UM UM
S HW True False
True True .95 .05
True False .6 .4
False True .6 .4
False False .2 .8
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Conditional Probability Tables
Smart Smart
True False
.5 .5
Hard Working Hard Working
True False
.7 .3
S Good Test Taker Good Test Taker
S True False
True .75 .25
False .25 .75
S HW UM UM
S HW True False
True True .95 .05
True False .6 .4
False True .6 .4
False False .2 .8
GTT UM A B C D F
True True .7 .25 .03 .01 .01
True False .3 .4 .2 .05 .05
False True .4 .3 .2 .08 .02
False False .05 .2 .3 .3 .15
UM A B C D F
True .7 .25 .03 .01 .01
False .2 .3 .4 .05 .05
15
Compactness
• A CPT for Boolean Xi with k Boolean parents has
2k rows for the combinations of parent values
• Each row requires one number p for Xitrue (the
number for Xifalse is just 1-p)
• If each variable has no more than k parents, the
complete network requires O(nx2k) numbers
• Grows linearly with n vs O(2n) for the full joint
distribution
• Student net 11225511 numbers (vs. 26-1)31

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Conditional Probability
A general version holds for joint distributions
P(PlayerWins,HostOpensDoor1)P(PlayerWinsHostOpe
nsDoor1)P(HostOpensDoor1)
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Global Semantics/Evaluation
• Global semantics defines the full joint
distribution as the product of the local
conditional distributions P(x1,,xn)?in1P(xi
Parents(Xi)) e.g.,
• P(EGA?GT?UM?S?HW)

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Global Semantics
• Global semantics defines the full joint
distribution as the product of the local
conditional distributions P(X1,,Xn)?in1P(XiP
arents(Xi)) e.g., ObservationsS, HW, not UM,
will I get an A?
• P(EGA?GT?UM?S?HW) P(EGAGT
?UM)P(GTS)P(UM HW ?S)P(S)P(HW)

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Conditional Independence and Network Structure
• The graphical structure of a Bayesian network
forces certain conditional independences to hold
regardless of the CPTs.
• This can be determined by the d-separation
criteria

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a
c
Converging
a
b
b
b
Diverging
Linear
c
c
a
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D-separation (opposite of d-connecting)
• A path from q to r is d-connecting with respect
to the evidence nodes E if every interior node n
in the path has the property that either
• It is linear or diverging and is not a member of
E
• It is converging and either n or one of its
decendents is in E
• If a path is not d-connecting (is d-separated),
the nodes are conditionally independent given E

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Hard working
Smart
Good test taker
Understands material
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• S and EG are not independent given GTT
• S and HG are independent given UM

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Medical Application of Bayesian
Networks Pathfinder
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Pathfinder
• Domain hematopathology diagnosis
• Microscopic interpretation of lymph-node biopsies
• Given 100s of histologic features appearing in
lymph node sections
• Goal identify disease type malignant
or benign
• Difficult for physicians

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Pathfinder System
• Bayesian Net implementation
• Reasons about 60 malignant and benign diseases of
the lymph node
• Considers evidence about status of up to 100
morphological features presenting in lymph node
tissue
• Contains 105,000 subjectively-derived
probabilities

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Commercialization
• Intellipath
• Integrates with videodisc libraries of
histopathology slides
• Pathologists working with the system make
significantly more correct diagnoses than those
working without
• Several hundred commercial systems in place
worldwide

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Sequential Diagnosis
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Features
• Structured into a set of 2-10 mutually exclusive
values
• Pseudofollicularity
• Absent, slight, moderate, prominent
• Represent evidence provided by a feature as
F1,F2, Fn

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Value of information
• User enters findings from microscopic analysis of
tissue
• Probabilistic reasoner assigns level of belief to
different diagnoses
• Value of information determines which tests to
perform next
• Full disease utility model making use of life and
death decision making
• Cost of tests
• Cost of misdiagnoses

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Group Discrimination Strategy
• Select questions based on their ability to
discriminate between disease classes
• For given differential diagnosis, select most
specific level of hierarchy and selects questions
to discriminate among groups
• Less efficient
• Larger number of questions asked

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Other Bayesian Net Applications
• Lumiere Who knows what it is?

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Other Bayesian Net Applications
• Lumiere
• Single most widely distributed application of BN
• Microsoft Office Assistant
• Infer a users goals and needs using evidence
about user background, actions and queries
• VISTA
• Help NASA engineers in round-the-clock monitoring
of each of the Space Shuttles orbiters subsystem
• Time critical, high impact