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```					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
 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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