Transcript Laskey, 2005 - Computer Science & Engineering

Issues for Discussion and Work Jan 2007
 Choose meeting time for Sp07
 Tuesday 1500-1600 (or earlier, if compatible with Dr. Huhns).
 “MEBN logic includes FOL as a subset” [Laskey 2006,
section 5 (p.36)]. Explain and prove this claim
 Continue work on technical report
 Upgrade Magellan with ACHv2.0.3
 [Marco] Contact PARC for Source Code of ACH version 2.0.3
 [Jingshan] Prepare Magellan for the update
 [JH] Show JW and SL how Magellan works and how it is
organized
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Engineering, University of South Carolina
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Nodes
 Nodes in a Bayesian network are in one-to-one
correspondence with (random) variables.
Variables map states (also known as values) to
subsets of the event space
The probability of a variable having a certain value is
the probability of all the events consistent with that
variable having that value
Variables represent propositions about which the
system reasons; they are therefore sometimes called
propositional variables, even though they may take
values other than true and false.
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Attributes
 Each variable has a set of identifying attributes
 Attributes “play the role of variables in a logic
programming language” [Laskey and Mahoney,
UAI-97]
 Attributes identify a particular instance of a
random variable
 Attributes are used to combine fragments:
Fragments can be combined only if their attributes
unify
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Fragments As Templates
 Fragments are template models:
 “A template model is appropriate for problem domains in which
the relevant variables, their state spaces, and their probabilistic
relationships do not vary from problem instance to problem
instance” [L&M, UAI-97]
 A scenario is a combination of instantiated template
models
 The attributes are used to identify and combine
fragment instances but the probabilistic relationships do
not change from instance to instance:
 The probability distribution described in the Bayesian network is
a joint distribution on the nodes only, not on the nodes and the
attributes
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Medical Illustration
 [A] medical diagnosis template network would contain variables
representing background information about a patient, possible
medical conditions the patient might be experiencing, and clinical
findings that might be observed.
 The network encodes probabilistic relationships among these
variables. To perform diagnosis on a particular patient, background
information and findings for the patient are entered as evidence
and the posterior probabilities of the possible medical conditions
are reported.
 Although values of the evidence variables vary from patient
to patient, the relevant variables and their probabilistic
relationships are assumed to be the same for all patients. It
is this assumption that justifies the use of template models.
Direct quote from [Laskey and Mahoney, UAI-97]
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Guidance for Selection of Nodes
and Attributes
 Nodes represent the variables on which the assessment of
a situation depends. For example:
 State and hypothesis variables
 Observation and test variables
 Intermediate and theoretical variables
 Setting factors
 Attributes identify a particular situation. E.g.:
 Location
 Time
 Name
 Case ID
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Engineering, University of South Carolina
2007-01-05
Use of MEBNs in Magellan and
Evolution of MEBNs
 In Magellan,
No provision is made for the combination of multiple
instances of the same fragment
This simplifies the specification of local probability
distributions
 In later versions of MEBNs:
A language is provided for the description of local
probability distributions
Multiple instances of the same fragments can be
used
Local probability distributions depend on the values
of attributes
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MEBNs As a System Integrating
First-Order Logic and Probability
 Paulo C.G. da Costa and Kathryn B. Laskey. “MultiEntity Bayesian Networks without Multi-Tears.” Available
at http://ite.gmu.edu/~klaskey/publications.html
[Costa, 2005]
 Kathryn B. Laskey. “First-order Bayesian Logic.”
Available at
http://ite.gmu.edu/~klaskey/publications.html [Laskey,
2005]
 Kathryn B. Laskey. “MEBN: A Logic for Open-World
Probabilistic Reasoning.” Available at
http://ite.gmu.edu/~klaskey/publications.html [Laskey,
2006]
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Sample BN Fragments
[Laskey, 2005]
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2007-01-05
Using MEBNs
• Bayesian Network Fragment (BNF)
It is the basic unit. Each network fragment consists of a
set of related variables together with knowledge about
the probabilistic relationships among the variables.
• Multi Entity Bayesian Network (MEBN)
Collection of BNFs specifying probability distribution over
attributes of and relationships among a collection of
interrelated entities
• Situation-Specific Network(SSN)
Ordinary finite Bayesian Network constructed
from an MEBN knowledge base, to reason about
specific target hypothesis, with a particular
evidence.
[Laskey, 2005]
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Formal Specifications
 First-Order Bayesian Logic
 A logical foundation that fully integrates
classical first-order logic with probability theory
 Because first-order Bayesian logic contains
classical first-order logic as a deterministic
subset, it is a natural candidate as a universal
representation for integrating domain
ontologies expressed in languages based on
classical first-order logic or subsets thereof.
[Laskey, 2005]
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Logic in BN Fragments
[Laskey, 2005]
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A Simple Bayesian Network
[Laskey, 2005]
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A Conditional Proabability Table
[Laskey, 2005]
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Multiple Instances
[Laskey, 2005]
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Temporal Repetition
[Laskey, 2005]
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A Fragment (MFrag)
[Laskey, 2005]
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An Instance of an MFrag
[Laskey, 2005]
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2007-01-05
A Temporal MFrag
[Laskey, 2005]
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Temporal Situation-Specific BN
[Laskey, 2005]
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2007-01-05
Other Issues in [Laskey, 2005]
 Generative Theories
 Composition Algorithm
 Related Research:
 HMMs
 DBNs
 Plates
 Object-Oriented BNs
 Probabilistic Relational Models
 Learning
 Decision Making
 Multiple-entity decision graphs (MEDGs) are to influence
diagrams what MEBNs are to Bayesian networks
 OWL-P
 A planned MEBN-based extension to OWL
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Engineering, University of South Carolina
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