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CIS 730 Introduction to Artificial Intelligence Lecture 14 of 30

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CIS 730: Introduction to Artificial Intelligence. Lecture ... (Yair Weiss, UAI-2001) Kansas State University. Department of Computing and Information Sciences ... – PowerPoint PPT presentation

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Title: CIS 730 Introduction to Artificial Intelligence Lecture 14 of 30


1
Lecture 26
Introduction to Bayesian Networks
Monday, 27 October 2003 William H.
Hsu Department of Computing and Information
Sciences, KSU http//www.kddresearch.org http//ww
w.cis.ksu.edu/bhsu Reading Chapter 15, Russell
and Norvig
2
Lecture Outline
  • Todays Reading
  • Chapter 14, Russell and Norvig
  • References Readings in Planning Allen,
    Hendler, and Tate
  • Next Week Chapter 15, Russell and Norvig
  • Previously Logical Representations
  • Today Introduction to Reasoning under
    Uncertainty
  • Conditional planning, concluded
  • Monitoring
  • Next Thursday Introduction to Uncertain
    Reasoning
  • Uncertainty in AI
  • Need for uncertain representation
  • Soft computing probabilistic, neural, fuzzy,
    other representations
  • Probabilistic knowledge representation
  • Views of probability
  • Justification

3
ReviewBasic Definitions and Axioms of
Probability
4
ReviewBasic Formulas for Probabilities
A
B
5
Syntax of Probability 1
Adapted from slides by S. Russell, UC Berkeley
6
Syntax of Probability 2
Adapted from slides by S. Russell, UC Berkeley
7
Syntax of Probability 3
Adapted from slides by S. Russell, UC Berkeley
8
ReviewMaking Decisions under Uncertainty
Adapted from slides by S. Russell, UC Berkeley
9
ReviewBayess Theorem
Adapted from slides by S. Russell, UC Berkeley
10
Full Joint Distributions
Adapted from slides by S. Russell, UC Berkeley
11
ReviewExample Bayesian Inference for QA
  • Answering User Queries
  • Suppose we want to perform intelligent inferences
    over a database DB
  • Scenario 1 DB contains records (instances), some
    labeled with answers
  • Scenario 2 DB contains probabilities
    (annotations) over propositions
  • Query Answering (QA) an application of
    probabilistic inference
  • QA Using Prior and Conditional Probabilities
    Example
  • Query Does patient have cancer or not?
  • Suppose patient takes a lab test and result
    comes back positive
  • Correct result in only 98 of the cases in
    which disease is actually present
  • Correct - result in only 97 of the cases in
    which disease is not present
  • Only 0.008 of the entire population has this
    cancer
  • ? ? P(false negative for H0 ? Cancer) 0.02 (NB
    for 1-point sample)
  • ? ? P(false positive for H0 ? Cancer) 0.03 (NB
    for 1-point sample)
  • P( H0) P(H0) 0.0078, P( HA) P(HA)
    0.0298 ? hMAP HA ? ?Cancer

12
Inference from Joint Distributions
Adapted from slides by S. Russell, UC Berkeley
13
Graphical Models to the Rescue 1Independence
Adapted from slides by S. Russell, UC Berkeley
14
Graphical Models to the Rescue 2Conditional
Independence
Adapted from slides by S. Russell, UC Berkeley
15
Graphical Models to the Rescue 3Bayesian
(Belief) Networks
Adapted from slides by S. Russell, UC Berkeley
16
ExampleThe Los Angeles BBN
Attributed to Judea Pearl (Yair Weiss, UAI-2001)
Adapted from slides by S. Russell, UC Berkeley
17
Semantics of Bayesian Networks
Adapted from slides by S. Russell, UC Berkeley
18
Markov Blanket
Adapted from slides by S. Russell, UC Berkeley
19
Constructing Bayesian NetworksThe Chain Rule of
Inference
Adapted from slides by S. Russell, UC Berkeley
20
ExampleEvidential Reasoning for Car Diagnosis
Adapted from slides by S. Russell, UC Berkeley
21
Automated Reasoning using Probabilistic
ModelsInference Tasks
Adapted from slides by S. Russell, UC Berkeley
22
Fusion, Propagation, and Structuring
  • Fusion
  • Methods for combining multiple beliefs
  • Theory more precise than for fuzzy, ANN inference
  • Data and sensor fusion
  • Resolving conflict (vote-taking, winner-take-all,
    mixture estimation)
  • Paraconsistent reasoning
  • Propagation
  • Modeling process of evidential reasoning by
    updating beliefs
  • Source of parallelism
  • Natural object-oriented (message-passing) model
  • Communication asynchronous dynamic workpool
    management problem
  • Concurrency known Petri net dualities
  • Structuring
  • Learning graphical dependencies from scores,
    constraints
  • Two parameter estimation problems structure
    learning, belief revision

Adapted from slides by S. Russell, UC Berkeley
23
Summary Points
  • Graphical Models of Probability
  • Bayesian networks introduction
  • Definition and basic principles
  • Conditional independence (causal Markovity)
    assumptions, tradeoffs
  • Examples LA network, car diagnosis, many more
    (to come)
  • Inference and learning using Bayesian networks
  • Acquiring and applying CPTs
  • Searching the space of trees max likelihood
  • Reasoning under Uncertainty Applications and
    Augmented Models
  • Some Material From http//robotics.Stanford.EDU/
    koller
  • Reference Heckerman Tutorial

24
Terminology
  • Graphical Models of Probability
  • Bayesian belief networks (BBNs) aka belief
    networks aka causal networks
  • Conditional independence, causal Markovity
  • Inference and learning using Bayesian networks
  • Representation of distributions conditional
    probability tables (CPTs)
  • Learning polytrees (singly-connected BBNs) and
    tree-structured BBNs (trees)
  • BBN Inference
  • Type of probabilistic reasoning
  • Finds answer to query about P(x) - aka QA
  • Learning in BBNs In Two Weeks
  • Known structure
  • Partial observability
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