Advanced Artifical Intelligence CLPBN: Constraint Logic Programming for Probabilistic Knowledge

1
Advanced Artifical Intelligence-CLP(BN)
Constraint Logic Programming for Probabilistic
Knowledge-
2
Table of Contence
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Introduction
• Example
• Function Principle
• Evaluation
• Results
• Discussion

3
Introduction
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• PRM
• Baysian Network
• Joint Probability Funktion
• Interferences about missing Data
• Datalog
• Skolem Constants

We want both logic and probability funktions
4
Introduction
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• CLP(BN)
• Baysian Network
• Constructed by Skolem funtions
• Representing Joint Probabilities

5
Introduction
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• What is a CLP(BN)?
• logic program
• Defining a set of probability distributions over
  the models of the underlying logic program
• Consists
• Logic portion C
• Probabilistic portion B

6
Introduction
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Probabilistic portion
• Any skolem Funktion has an CPT specifying the
  distributions
• CPT associated with a clause may be thought as
  Bayes net
• Each node is labeled by a variable or term build
  from a Skolem function

7
Example
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion
8
Example
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Probabilistic portion
• Any skolem Funktion has an CPT specifying the
  distributions
• CPT associated with a clause may be thought as
  Bayes net
• Each node is labeled by a variable or term build
  from a Skolem function

9
Example
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion
10
Example
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion
The clause relating a registrations grade to the
courses difficulty and to Students intelligence
resembles a Bayes net
11
Functional Principle
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• A query in CLP(BN) is an ordinary Prolog query
• at each resolution step clauses may be unified
• What if both clauses praticipate in CPT or Bayes
  net constraints?

12
Functional Principle
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Construct a large Bayes net consisting of all the
  smaller Bayes nets that have been unified during
  resolution
• Substitute or rename Variables/Terms
• Use occur-check to guarantee acyclicity
• Possible because one term must be a sub-term of
  the CPT constraint for the other sub-term

13
Functional Principle
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion
14
Functional Principle
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• such constructions are in fact proper defined
  Baysian nets but possibly infinite (Proof compare
  section 3.3)
• -gtBN uniquely defines a joint distribution over
  ground Skolem terms defined by the programm P
• Using minimal Herbrand quotient models
• -gtprobability distributions over models
  consistent with the probability distribution over
  ground Skolem terms
• -gtdenoting CLP(BN)

15
Functional Principle
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• CLP(BN) follows the soundness and completeness
  of SLD-resolution (like Prolog)
• Accompanied by a Bayes net
• the Bayes net will agree with the given answer
  (Proof compare section 3.4)

16
Evaluation
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Learning in CLP(BN) using ILP and sample data
• School Database
• No missing Data
• Methabolic Activity
• Real world relational problem
• Much missing data

17
Evaluation
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• School Database
• Aleph learns clauses independantly
• Cycles may appear
• Postprocessing
• only matches without perfect score are directions
  of arcs
• No information about time and costs

18
Evaluation
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• 2. Metabolic Activity
• Possibility of higher false positives rate
• Ordinary logic only slightly worse in performance

19
Results
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• Any PRM can be represented as an CLP(BN) program
  
• Any Prolog program can be represented in an
  CLP(BN) program
• CLP is an extention of logic programs
• -gtRecursion
• -gtnon determinism
• -gtuse of functions and symbols
• -gtmore expressive than PRM

20
Results
Table of Contence Introduction Example Functional
Principle Evaluation Results Discussion

• ammenable to learn techniques from ILP
• Incorporation of probabilistic methods into ILP
• Interesting viewpoint of adding logic to PRM
  instead of probabilistic knowledge to Logic
  programs

21
Thanks for your attention