Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Lecture 24 of 41Lecture 24 of 41
Monday, 18 October 2004
William H. Hsu
Department of Computing and Information Sciences, KSU
Reading:
Chapter 13, Russell and Norvig 2e
Review: Classical and Modern Planning
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Lecture OutlineLecture Outline
•Today’s Reading
–Chapter 13, Russell and Norvig 2e
–References: Readings in Planning – Allen, Hendler, and Tate
•Next Week: Chapter 14, Russell and Norvig 2e
•Previously: Logical Representations
•Today and Wednesday: Introduction to Reasoning under Uncertainty
–Conditional planning, concluded
–Monitoring
•Friday and Next Week: 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
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Review:How Things Go WrongReview:How Things Go Wrong
Adapted from slides by S. Russell, UC Berkeley
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Review:SolutionsReview:Solutions
Adapted from slides by S. Russell, UC Berkeley
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Adapted from slides by S. Russell, UC Berkeley
Example:Preconditions for Remaining PlanExample:Preconditions for Remaining Plan
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Adapted from slides by S. Russell, UC Berkeley
Example:ReplanningExample:Replanning
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Review:Uncertain Reasoning RequirementsReview:Uncertain Reasoning Requirements
Adapted from slides by S. Russell, UC Berkeley
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Methods for Handling UncertaintyMethods for Handling Uncertainty
Adapted from slides by S. Russell, UC Berkeley
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
ProbabilityProbability
Adapted from slides by S. Russell, UC Berkeley
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
The Probabilistic (Bayesian) FrameworkThe Probabilistic (Bayesian) Framework
•Framework: Interpretations of Probability [Cheeseman, 1985]
–Bayesian subjectivist view
•A measure of an agent’s belief in a proposition
•Proposition denoted by random variable (sample space: range)
•e.g., Pr(Outlook = Sunny) = 0.8
–Frequentist view: probability is the frequency of observations of an event
–Logicist view: probability is inferential evidence in favor of a proposition
•Some Applications
–HCI: learning natural language; intelligent displays; decision support
–Approaches: prediction; sensor and data fusion (e.g., bioinformatics)
•Prediction: Examples
–Measure relevant parameters: temperature, barometric pressure, wind speed
–Make statement of the form Pr(Tomorrow’s-Weather = Rain) = 0.5
–College admissions: Pr(Acceptance) p
•Plain beliefs: unconditional acceptance (p = 1) or categorical rejection (p = 0)
•Conditional beliefs: depends on reviewer (use probabilistic model)
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
TerminologyTerminology
•Introduction to Reasoning under Uncertainty
–Probability foundations
–Definitions: subjectivist, frequentist, logicist
–(3) Kolmogorov axioms
•Bayes’s Theorem
–Prior probability of an event
–Joint probability of an event
–Conditional (posterior) probability of an event
•Maximum A Posteriori (MAP) and Maximum Likelihood (ML) Hypotheses
–MAP hypothesis: highest conditional probability given observations (data)
–ML: highest likelihood of generating the observed data
–ML estimation (MLE): estimating parameters to find ML hypothesis
•Bayesian Inference: Computing Conditional Probabilities (CPs) in A Model
•Bayesian Learning: Searching Model (Hypothesis) Space using CPs
Kansas State University
Department of Computing and Information Sciences
CIS 730: Introduction to Artificial Intelligence
Summary PointsSummary Points
•Introduction to Probabilistic Reasoning
–Framework: using probabilistic criteria to search H
–Probability foundations
•Definitions: subjectivist, objectivist; Bayesian, frequentist, logicist
•Kolmogorov axioms
•Bayes’s Theorem
–Definition of conditional (posterior) probability
–Product rule
•Maximum A Posteriori (MAP) and Maximum Likelihood (ML) Hypotheses
–Bayes’s Rule and MAP
–Uniform priors: allow use of MLE to generate MAP hypotheses
–Relation to version spaces, candidate elimination
•Next Week: Chapter 14, Russell and Norvig
–Later: Bayesian learning: MDL, BOC, Gibbs, Simple (Naïve) Bayes
–Categorizing text and documents, other applications