Bayesian Nets and Applications

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Bayesian Nets and Applications

• Next class machine learning
• C. 18.1, 18.2
• Homework due next class
• Questions on the homework?
• Prof. McKeown will not hold office hours today

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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
Exam Grade
Homework Grade
5
Hard working
Smart
Good test taker
Understands material
Exam Grade
Homework Grade
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Conditional Probability Tables
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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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Global Semantics/Evaluation

• Global semantics defines the full joint
  distribution as the product of the local
  conditional distributionsP(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 distributionsP(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
  decendants 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
Exam Grade
Homework Grade
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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
NetworksPathfinder
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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 diagnoisis, 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
• Interpret telemetry and provide advice about
  likely failures
• Direct engineers to the best information
• In use for several years
• Microsoft Pregnancy and Child Care
• What questions to ask next to diagnose illness of
  a child

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Other Bayesian Net Applications

• Speech Recognition
• Text Summarization
• Language processing tasks in general