Node Probability Table Generation Method

8/16/2019 Node Probability Table Generation Method

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A Method for Developing Node

Probability Table Using QualitativeValue of Software Metrics

Department of ComputerApplications

National Institute of Technology

Jamshedpur

Chandan Kumar

Presented By:

[email protected]

Authors !handan "u#ar$ Dr% D% "% &adav


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INTRODUCTION

PROPOSED METHOD

CONCLUSION

REFERENCES

CONTENTS

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Bayesian belief network is te !o"bination of #robability teory an$ %ra# teory& Te 'n!ertainty

of te syste" is "o$ele$ 'sin% #robability teory an$

te %ra# el#s to in$i!ate in$e#en$en!e str'!t're

tat enables te #robability $istrib'tion to be$e!o"#ose$ into s"aller #ie!es

Bayesian belief network is es#e!ially 'sef'l to

re#resent te "o$elin% of an 'n!ertainty an$ a(e

been a##lie$ s'!!essf'lly in (ario's areas like)

"e$i!al $ia%nosti! syste"s* +eater fore!astin%*

Pro,e!t "ana%e"ent* Si%nal #ro!essin%* Software

en%ineerin% et!&

'NT()DU!T')N


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!ont*

In e(ery area were BBN is a##lie$ a(e been

#ro(e$ tat BBN is !a#able to re#resent te

'n!ertainty& Howe(er* tere are two si%nifi!ant

barriers to b'il$ lar%e s!ale BBN)

-. B'il$in% te !a'sal relationsi#s a"on% te no$esan$

/. De(elo#"ent of NPTs&) In Bayesian belief networks fra"ework* te

in$e#en$en!e str'!t're in a ,oint $istrib'tion is!ara!teri0e$ by a $ire!te$ a!y!li! %ra# 1D23.*

wit No$es re#resentin% ran$o" (ariables an$

e$%es re#resentin% !a'sal relationsi#s between

(ariables&


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!ont*

Te !a'sal relationsi#s between (ariables are$efine$ by #robability f'n!tions tat re!ei(e in#'t as

a set of (al'es of te #arent no$es an$ !al!'late te

%i(en no$e4s #robability& Tese #robability f'n!tions

are !o""only re#resente$ by tables 5 na"ely* no$e

#robability tables 1NPTs.&

E6)


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!ont*


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!ont*

Desi%nin% te NPT $ata is one of te f'n$a"entaliss'es asso!iate$ wit te BBN& Tere are no

%'i$elines or r'les tat !an be 'se$ to $e(elo# te

NPT $ata tat is a##ro#riate for all ty#es of #roble"s&

For e6a"#le* "an'ally $efinin% NPT for Bayesian

belief networks is a !o"#le6 task an$ takes

e6#onentially lar%e effort&

Se(eral "eto$s a(e been #ro#ose$ in te literat're

to re$'!e tis !o"#le6 task of $efinin% NPT

"an'ally&


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!ont*

7& H'an% an$ M& Henrion 8-9: #ro#ose$ a "eto$known as Noisy;OR& Te $isa$(anta%e of tis

"eto$ is tat it a##lies only to te Boolean No$es

an$ !o"#letely i%nores te intera!tion effe!ts

between (ariables&F&


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!ont*

by !o"#'tin% a##ro#riate wei%te$ f'n!tions of teeli!ite$ $istrib'tions&

Fenton et al& 8-A: #ro#ose$ an a##roa! wi! is

base$ on te $o'bly tr'n!ate$ nor"al $istrib'tion&

In te literat're* it is obser(e$ tat te "ost of te

a##roa!es te!ni@'es al%orit"s a(e !onsi$ere$ a

#arti!'lar ty#e of statisti!al $istrib'tion& Howe(er* for

$e(elo#in% te NPT of a No$e in BBN* te statisti!al$istrib'tion of assess"ent "ay $e#en$ on te kin$ of

#roble" an$ te ty#e of $ata a(ailable an$ it "ay

follow any ty#e of #robabilisti! statisti!al $istrib'tion&


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!ont*

In fa!t* No$e infor"ation is store$ in te $o"aine6#ert in te for" of knowle$%e tat !an be

$eter"ine$ tro'% te @'alitati(e (al'e in te for"

of low* "e$i'" an$ i% an$ fro" te @'alitati(e

(al'e te !orres#on$in% #robability !an be %enerate$wit less effort&

Tis a##roa! $oes not follow any statisti!al

$istrib'tion an$ refle!ts a tr'e #robability $istrib'tionof te No$e bea(ior&

Terefore* in tis #a#er* a new "eto$ is #ro#ose$ to

$e(elo# te No$e #robability table 'sin% te

@'alitati(e (al'e of software "etri!&


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P()P)S+D M+T,)D

Te no$e #robability tables in a BBN "o$el state testren%ts of 'n!ertain relationsi#s between te

fa!tors& Te n'"ber of #robabilities re@'ire$ for ea!

no$e is sown in E@& 1-.&

+ere NP N'"ber of #robabilities of te !il$ no$e" n'"ber of states of te !il$ no$e an$ n n'"ber

of states of #arent no$e&


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!ont*

In its si"#lest for" wen all te no$es a(e te sa"en'"ber of states* ten NPnk * were te k total

n'"ber of #arents* Terefore* if n/ an$ k9* NP

te n'"ber of #robability in!reases e6#onentially

wit te n'"ber of #arent no$es as well te n'"berstates of #arent no$es&


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Steps for obtaining the NPT

Step - Constr'!t (ali$ation table of NPT wit te el#of $o"ain e6#erts&

Substep .-a/ Data Colle!tion ; 2ssess"ent of

$e#en$ent (ariables in ter"s of Hi% 1H.* Me$i'" 1M.

an$ Low 1L. wit wei%t%ae is !olle!te$ fro" te

$o"ain e6#erts in ro'n$ wise 1Ro'n$ -5 -=t of total

assess"ent* Ro'n$ /5 -/ of total assess"ent* Ro'n$ 95

!o"#lete assess"ent.

Substep .-b/ Data 2nalysis 5 Te $ata is !olle!te$ in

ro'n$ wise by te n'"ber of e6#erts& Terefore* it is

ne!essary to !e!k te !onsisten!y of teir o#inion&


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• If te $ifferen!e of #robabilities between te ro'n$s isG* ten te !onsisten!y of te $o"ain e6#erts is

#erfe!t&

• If te $ifferen!e of #robabilities between te ro'n$s is

not e@'al to G* ten te a(era%e (al'e of te

#robabilities of te entire ro'n$ is taken&

Substep .-c/ Esti"ate te !o"#lete set of NPT5 Esti"ate

te !o"#lete assess"ent wit wei%ta%e of $e#en$ent(ariable 'sin% te inter#olation&


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Step 0 3enerate #robability (al'e of te NPT fro"ran$o" f'n!tion&

Step 1 U#$ate te ran$o"i0e$ NPT obtaine$ in ste# /

'ntil it a##ro6i"ately "at!es wit te NPT of ste# -&


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An illustrative e2a#ple

2 BBN "o$el of software $e(elo#"ent is sown in fi%&-

EDT5 E6#erien!e of $e(elo#"ent tea"

CP5 Ca#ability of te #ro%ra""er

S5 'ality of staff

DPF5 Define$ #ro!ess followe$

PD5 'ality of #ro!ess $e(elo#"ent

EDP5 Effort on $e(elo#"ent #ro!ess

ODPE5 O(erall $e(elo#"ent #ro!ess

effe!ti(ely

PODD5 Probability of a(oi$in% $efe!t in

$e(elo#"ent

3ig% -


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!ont*

2 s'b!o"#onent of a "o$el is sown in fi%& / weree6#erien!e of $e(elo#"ent tea" 1EDT. "etri! an$

!a#ability of te #ro%ra""er 1CP. "etri! a(e !alle$ te

#arents of te @'ality of staff 1S. "etri!& In Fi%& - of

BBN* e(ery no$e as tree states 1Hi%* Me$i'" an$

Low.& Terefore* te n'"ber of #robability (al'es for te

no$e @'ality of staff will be 19/.&

3ig% 0


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NPT Develop#ent

Ste# -) Constr'!t (ali$ation table of NPT wit te el#of $o"ain e6#erts&

S'bste# 1-a.) 2ssess"ent of $e#en$ent (ariables in

ter"s of Hi% 1H.* Me$i'" 1M. an$ Low 1L. wit

wei%ta%e is !olle!te$ fro" te $o"ain e6#erts inro'n$ wise& Do"ain e6#erts a##lie$ te f'00y r'le for

te assess"ent& Here te f'00y 2ND r'les of te

IFJTHEN a(e been 'se$&

-& IF EDT is H an$ CP is H ten e6#e!te$ S is H

/& IF EDT is H an$ CP is M ten e6#e!te$ S is M

KKKKKK

& IF EDT is L an$ CP is L ten e6#e!te$ S is L


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!ont*

Te !olle!te$ assess"ent wit wei%ta%e of $e#en$ent(ariable by te $o"ain e6#erts in $ifferent ro'n$s is

sown in Table I&

+DT !P (ound - (ound 0 (ound 1

Hi% Hi%

Hi% Me$i'"

Hi% Low

Me$i'" Hi%

Me$i'" Me$i'"

Me$i'" Low

Low Hi%

Low Me$i'"

Low Low

Table -


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!ont*

S'bste# 1-b.) Data 2nalysis ; Te !olle!te$ $ata ins'bste# 1-a. is analy0e$ an$ re#ro$'!e$ in table /&

Table 0

+DT !P ,'4, M+D'UM 5)6

Hi% Hi% H 1&. 55 L 1&?.

Hi% Me$i'" H 1&=. M 1&?. 55

Hi% Low H 1&-. 55 L 1&A.

Me$i'" Hi% 55 M 1&/. L 1&-.

Me$i'" Me$i'" H 1&-. 55 L 1&9.

Me$i'" Low 55 M 1&/?. L 1&.

Low Hi% H 1&/?. M 1&9?. 55

Low Me$i'" 55 M 1&/. L 1&.

Low Low H 1&?. 55 L 1&?.


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S'bste# 1-!.) Esti"ate te !o"#lete set of NPT tro'%inter#olation& Te esti"ate$ !o"#lete set of NPT is sown

in Table 9& Table 1

+DT !P ,'4, M+D'UM 5)6

Hi% Hi% H 1&. M 1&-?. L 1&?.

Hi% Me$i'" H 1&=. M 1&?. L 1&-.

Hi% Low H 1&-. M 1&9. L 1&A.

Me$i'" Hi% H 1&. M 1&/. L 1&-.

Me$i'" Me$i'" H 1&-. M 1&A. L 1&9.

Me$i'" Low H 1&?. M 1&/?. L 1&.

Low Hi% H 1&/?. M 1&9?. L 1&=.

Low Me$i'" H 1&-. M 1&/. L 1&.

Low Low H 1&?. M 1&-. L 1&?.


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Ste# /) Probabilisti! (al'e is %enerate$ fro" a ran$o"f'n!tion for te $e#en$ent no$e& Te #robabilisti! (al'e

obtaine$ fro" a ran$o" f'n!tion for te $e#en$ent no$e

is sown in Fi%& 9&

3ig% 1


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Ste# 9) U#$ate te ran$o"i0e$ NPT obtaine$ in ste# /'ntil it a##ro6i"ately "at!es wit te NPT of ste# -)

Te NPT is re(ise$ by iteration of ran$o" f'n!tion in

(iew of NPT obtaine$ in ste# -& U#$ate$ ran$o"i0e$ NPT

is sown in Fi%&?&

3ig% 7


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!onclusion

Te no$e #robability table as "a,or i"#a!t on teBBN& Te 'n!ertainty of te !a'sal relationsi# is

@'antifie$ wit te NPT& Tere is not any sin%le

'ni(ersal an$ #ra!ti!al "eto$ a(ailable in te

literat're for !onstr'!tin% NPT for BBN& Te #ro#ose$"eto$olo%y is "ore %eneral an$ !an be 'se$ for any

ty#e of BBN #roble" be!a'se tis "eto$olo%y is te

!olle!ti(e of e6#ert knowle$%e* f'00y lo%i! an$ ran$o"

f'n!tions on iteration basis& Terefore* tis"eto$olo%y is !a#able to $e(elo# te NPT $ata of all

ty#es of a##li!ations&


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(eferences

-. N& E& Fenton an$ M& Neil* 2 Criti@'e of Software Defe!t Pre$i!tion Mo$els*

IEEE Transa!tions on Software En%ineerin%* (ol& /?* ##& A?;A* -/. N& E& Fenton* M& Neil* +& Mar!* P& Hearty* L& Ra$linski an$ P& 7ra'se* On te

effe!ti(eness of early life !y!le $efe!t #re$i!tion wit Bayesian Nets* E"#iri!al

Software En%ineerin%* (ol& -9* ##& = ;?9* /&

9. S& 2"asaki* & Taka%i* O& Mi0'no an$ T& 7ik'no* 2 bayesian belief network for

assessin% te likelioo$ of fa'lt !ontent* Pro!ee$in%s of -=t international

sy"#osi'" on software reliability en%ineerin% 1ISSRE.* ##& /-?5//A* /9&

=. 3anes


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(eferences

. S& Moanta* 3& ino$* 2& 7& 3os* R& Mall* 2n 2##roa! for Early Pre$i!tion

of Software Reliability* 2CM SI3SOFT Software En%ineerin% Notes* (ol& 9?* ##&-;* /-&

. S& Moanta* 3& ino$ an$ R& Mall* 2 te!ni@'e for early #re$i!tion of software

reliability base$ on $esi%n "etri!s* International ian%0o' an%* E&+&T& N%ai* R'i!' Cai* Mei Li'* Software #ro,e!t

risk analysis 'sin% Bayesian networks wit !a'sality !onstraints* De!ision

S'##ort Syste"s* (ol& ?A* ##& =95==* /-9&

-/. P& +eber* 3& Me$ina5Oli(a* C& Si"on* B& I'n%* O(er(iew on Bayesian networksa##li!ations for $e#en$ability* risk analysis an$ "aintenan!e areas* En%ineerin%

2##li!ations of 2rtifi!ial Intelli%en!e* (ol& /?* ##& A-5A/* /-/&

-9. 7& H'an% an$ M& Henrion* Effi!ient Sear!5Base$ Inferen!e for Noisy5OR

BeliefNetworks* Twelft Conferen!e on Un!ertainty in 2rtifi!ial Intelli%en!e*

Portlan$* ##& 9/?599-* -A&


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-9. F&


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-. +an% H


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!uestion""# $

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Node Probability Table Generation Method

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