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Nguyen (PowerPoint)

VIEWS: 12 PAGES: 27

									Learning with
Knowledge from
Multiple Experts
Matthew Richardson
Pedro Domingos

Represented by Anh Ngoc Nguyen

                                 1
Contents
 Introduction
 Bayesian Network
 Learning Bayesian Network
 Learning Bayesian Network from multiple
  Experts
 Practical Experiments
 Conclusions


                 by Anh Ngoc Nguyen         2
Introduction
 Gaining knowledge for Expert System
 Traditionally knowledge is expected to be
  from a single self-consistent source
 But knowledge from expert is buggy and
  incomplete
 Refining knowledge requires laborious
  process


                  by Anh Ngoc Nguyen          3
Introduction
 Idea of combining knowledge of many
  „weak“ experts into a „strong“ base
 Knowledge in the paper is represented by
  Bayesian Network
 In particular, combining statements of
  experts about structure of a Bayesian
  Network
 Refining using Bayesian network learning
  algorithm
                 by Anh Ngoc Nguyen          4
Bayesian Network
   Most frequently used for coding uncertain
    knowledge in expert systems

   Graphic model encoding the joint
    probability distribution for a large set of
    variables



                      by Anh Ngoc Nguyen          5
Bayesian Network
   Consist of
     Structure:  a directed acyclic graph represent
      relationship between pairs of nodes

     Parameters:    probabilities of each state of the
      variable given every possible combination of
      states of its parents (contained in conditional
      probability tables (CPTs))


                       by Anh Ngoc Nguyen                 6
Bayesian Network




           by Anh Ngoc Nguyen   7
Bayesian Network




           by Anh Ngoc Nguyen   8
Bayesian Network

                                Insurance
                                Bayesian
                                Network




           by Anh Ngoc Nguyen               9
Bayesian Network
   d discrete variable    x1,           , xd 

   Denote: par  xi  : set of parents of                  xi

   Probability of event X   x1 ,                , xd 

      P  X   i 1 P  xi | par  xi  
                      d



                     by Anh Ngoc Nguyen                          10
Learning Bayesian Network (LBN)
 Concerning structure learning and
  parameters estimating
 Structure learning: search over the posible
  structures space to get the „true“ one
 Parameters estimating: find the
  parameters from found structure and
  practical data


                  by Anh Ngoc Nguyen        11
Learning Bayesian Network (LBN)
   Heckerman et al (1995): Structure learning
    algorithm:
     Search   over structures space
     Start from an initial network: empty, random
      or derived from prior knowledge
     Evaluate structure using Bayesian Dirichlet
      (BD) score



                      by Anh Ngoc Nguyen             12
Learning Bayesian Network (LBN)
   Bayesian Dirichlet (BD) score
P S, D  P S  P D | S 
                     d      qi         nij 
                                                   ri      nijk  nijk 
                                                               
            P  S                               
                    i 1   j 1     nij  nij
                                                 k 1        nijk 
                                                                  


   Gamma func.:   x 1  x  x  ;  1  1

                           by Anh Ngoc Nguyen                             13
LBN from multiple Experts
 Take experts‘ statement into account.
 Models:

            Expert 1



                                                  Structure +
    World   Expert 2   Structure        Learner
                                                  parameters
              ...



            Expert n



             Data
                        by Anh Ngoc Nguyen                      14
LBN from multiple Experts
   Basic framework
     Structure   S   s1 ,     , sj,          , sd  
                                  s j  , , , 
     Experts‘s   statement
                  Ei   ei1 ,     , eij , , eid  
                                     eij  , , , 

     Expert   knowlege: E   E1 ,                    , Ei ,   , Em 

                           by Anh Ngoc Nguyen                            15
LBN from multiple Experts
   Basic framework
     By Bayes‘ theorem  probability of
      processing structure given Expert Knowledge
      and Training data

       P  S | E, D    P  E | S  P  S , D 
                       PS | E PD | S 

           New score function
                       by Anh Ngoc Nguyen           16
LBN from multiple Experts
   Expert model
       P  eij | s j 




     Expert      parameters:    pa , pd , pr , pb , pc


                          by Anh Ngoc Nguyen              17
LBN from multiple Experts
   Expert model
       Psj 




     Model
                                   d
        P  S | E    C  S   P  s j   P  eij | s j 
                                                m


                                   j 1         i 1


                           by Anh Ngoc Nguyen                   18
LBN from multiple Experts
   Algorithm
     Search  over structure space, using score
      function P  S | E, D , start with structure that
      maximize P  S | E 
     If expert knowledge is of sufficient quality 
      take structure maximize P  S | E  as the true
      one
     Given expert parameters ( pa , pd , pr , pb , pc )
      and p0

                        by Anh Ngoc Nguyen             19
Practical Experiments
   Simulated Experts
     Use  four networks from Bayesian Network
      repository as ground true
     Simulated Experts‘ statement
     Set initial parameters:
            p0  0.05, pa  0.025, pd  0.4
            pr  0.1, pc  0, pb  0

     Training   set size: 100 examples
                         by Anh Ngoc Nguyen      20
Practical Experiments
   Simulated Experts
     Two  case: varying training set size and
      varying noise level
     20 runs
     Resulting network was evaluated using two
      measures:
       Average KL distance from the true network.
       Structural difference: number of arcs added or
        removed


                       by Anh Ngoc Nguyen                21
Practical Experiments




            by Anh Ngoc Nguyen   22
Practical Experiments
   Real Experts
     Use  the Microsoft printer troubleshooting
      Bayesian Network
     Experts are 9 computer users
     Set initial parameters: set p0  0.02 and
      optimize experts‘ parameters using Powell‘s
      method
     Training set size: 100 examples



                     by Anh Ngoc Nguyen             23
Practical Experiments
   Real Experts
     Two   case:
       „low“: user know nothing about network
       „high“: user have studied about network

     20runs
     Measuring using two methods:
       Average KL distance
       Structural difference




                        by Anh Ngoc Nguyen        24
Practical Experiments




            by Anh Ngoc Nguyen   25
Conclusions
 Learning with knowledge from multiple
  experts showed potential advantages
 Future work:
     Support   more varying types of input from
      experts
     Using more refined models of expert behavior
     Apply to other representation besides
      Bayesian Network
     ...

                       by Anh Ngoc Nguyen          26
References
   Richardson, M. & Domingos, P. (2003) Learning with
    knowledge from Multiple Experts
   Heckerman, D. () A tutorial on learning with Bayesian
    Network
   Myers J. W. & Laskey K. B. & DeJong K. A. () Learning
    Bayesian Networks from Incomplete Data using
    Evolutionary Algorithms
   http://math.fullerton.edu/mathews/n2003/PowellMethodM
    od.html
   http://www.csse.monash.edu.au/~lloyd/tildeMML/KL/




                        by Anh Ngoc Nguyen             27

								
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