RajendraAkerkar

1R. Akerkar

Personalisation - user profile and prototypesp p ypto provide: What is received is what is required

EXAMPLESWeb page retrieval to satisfy customerComputer InterfaceNews Services AdvertisingNews Services, AdvertisingRegulation of messages -SMS. E-MailPersonalised Data Mining

AI Machine Learning, Inferenceand Linguistics provides the intelligent agents for this personalisation service

2R. Akerkar

message

P1 P2 P3 P4 P5 prototypes

s1 s2 s3 s4 s5 supports for interest

Personalised Fusion

to users

send ?Final Support3R. Akerkar

Fuzzy Bayesian Netsy y

Fuzzy Decision TreesCan we construct a theory

Fril programsCan we construct a theoryof prototypes ?

Evidential Logic Rules

Neural netsCan be have a theory offusion ?

Fuzzy Conceptual graphs

Cluster over persons to get clusters for prototypes4R. Akerkar

Data Base

WEB

answer fuzzy decisiontree

search agentuser query

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Fril Evidential logic ruleFril Evidential logic rule

x1 is g1 with weight w1x2 is g2 with weight w2l i f IFF

throughfilts g w we g w

. . . .xn is gn with weight wn

class is f IFF filterh

For input {xi = fi}Let i = Pr(gi | fi)

f, gi, fi, h are fuzzy sets

(g | )class is f with probability where = (w11 + w22 + + wnn) = (w11 + w22 + … + wnn)h

6R. Akerkar

Random VariablesOffer Type

RateLoanRate

companysize company

age

Random Variableswith conditionalindependencies

OfferRateSuit

CompS it

MedicalReqSuit

Su t Suit Req

Loan InterestCompany Size : {l di ll}Loan

TimeInterest

Offer : {mortgage, personal loan, car loan, credit card

{large, medium, small}

car insurance, holiday insurance, payment protection,charge card, home insurance}

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Offer : {mortgage personal loan car loan credit cardOffer : {mortgage, personal loan, car loan, credit cardcar insurance, holiday insurance, payment protection,charge card, home insurance}Type Rate : {fixed, variable}LoanRate : {good, fair, bad}Company Size : {large, medium, small}p y { g , , }Company Age : {old, middle, young}Loan Period : {long, medium, short}Rate Suitable : {very average little}Rate Suitable : {very, average, little}Company Suitable : {very, average, little}Medical req : {yes, no}Offer Suit : {good, av, bad}Interest : {high, medium, low}

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X1 X2 X3

X4X5

We update this priorjoint distribution with

t t iX4 5 respect to any givenvariable instantiations

X6

P (X X ) P (X | P t (X ))n

iPr(X1, ..., Xn ) Pr(Xi | Parents(Xi ))i1 Prior

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C0C0 = {Offer*, LoanPeriod*, OfferSuit*}C1 = {OfferSuit,Offer, RateSuit}C2 = {RateSuit*, LoanRate*, Offer, TypeRate*}C3 {CompSuit MedReq * OfferSuit RateSuit

C1C3 = {CompSuit, MedReq,* OfferSuit, RateSuit,

Interest*}C4 = {CompSize*, AgeComp*, CompSuit*}

C2 C3

C4

Compile Clique tree : equivalent to forming prior joint p q q g p jdistribution using an efficient message passing algorithm

10R. Akerkar

Message :4% fixed rate long term mortgages availablefrom 40 year old fairly large Company FRIL

conceptual graph

graph instantiations

Offer = mortgage, Type rate = fixed, loan time = longCompSize = dist, CompAge = dist.

Use message passing algorithm again to update clique distributionswith graph instantiations.

Result will be distribution over interest variable - defuzzify toobtain degree of interest

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w1 w2 w3 w4 w5 w6 w7 X replaced with {w }w1 w2 w3 w4 w5 w6 w7 X replaced with {wi}1

We can also

X0

We can alsofuzzify discretesets

X

Mass Assignment Theory provides:{Pr(wi | x)} where x is point value interval or fuzzy set{Pr(wi | x)} where x is point value, interval or fuzzy seti.e we translate value on X to distribution over {wi}

Mass Assignment Theory provides:Mass Assignment Theory provides:Defuzzification: if {i} is distribution over {wi} thenx i i

i where i is expected value of wi 12R. Akerkar

medium

0 1 2 3 4 5 6

small large

0 1 2 3 4 5 6DICE SCORE

Random Set of Voters %

≤ 3 4 5 6x% accept x as large % 0 20 80 100

large = 4 / 0.2 + 5 / 0.8 + 6 / 1

1 2 3 4 5 6 7 8 9 101 2 3 4 5 6 7 8 9 106 6 6 6 6 6 6 6 6 65 5 5 5 5 5 5 5 4 4

MAlarge ={6} : 0.2, {5, 6} : 0.6, {4, 5, 6} : 0.2

4 4

constant threshold : if voter accepts x and y>x then he must accept y13R. Akerkar

weighted dice is small where small = 1 / 1 + 2 / 0 7 + 3 / 0 3

MA = {1} : 0.3, {1, 2} : 0.4, {1, 2, 3} : 0.3

weighted dice is small where small 1 / 1 + 2 / 0.7 + 3 / 0.3prior for dice : 1:0.1, 2:0.1, 3:0.5, 4 :0.1, 5:0.1, 6:0.1

MA {1} : 0.3, {1, 2} : 0.4, {1, 2, 3} : 0.3small

Pr(dice is x | small) = probability that a randomly chosen voter h l f di f b i ld di l i llchooses x as value of dice after being told dice value is small

Least Prejudiced Probability Distribution for dice value =1 : 0 3 + 0 2 + 0 3(1/7) = 0 54291 : 0.3 + 0.2 + 0.3(1/7) = 0.54292 : 0.2 + 0.3(1/7) = 0.24293 : 0.3(5/7) = 0.2143

Pr(x | small)

For continuous fuzzy set we can derive a least prejudiced density function whose expected value can be used for defuzzification

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What is Pr(dice is about 2 | dice is small) where( _ | )about 2 = 1 / 0.5 + 2 / 1 + 3 / 0.5

small0.3 0 4 0 3Prior1 : 0.1

about_2 {1} {1, 2} {1, 2, 3}

{2}0 5

0.3 0.4 0.3

01/2(0.2)

0 11/7(0.15)

= 0 0214 2 : 0.13 : 0.54 : 0.1

{2}

{1, 2, 3}

0.5

0.5

= 0.1 = 0.0214

0.15 0.2 0.15

5 : 0.16 : 0.1

{ , , }

Pr(about_2 | small) = 0.6214

Point Semantic Unification used to determine Pr(f | g)Point Semantic Unification used to determine Pr(f | g) where f is fuzzy set, g is point, interval or fuzzy set

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output_sm output_me output_laprediction Means of

output_sm, output me

t ll l i f t OUTPUT

output_me, output_laare1, 2, 3mutually exclusive fuzzy sets on OUTPUT

modelinput output {distribution over words} output_sm : 1

output me : 2

1, 2, 3

model output_me : 2output_la : 3

Prediction = 11 + 22 + 33 Defuzzification

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V i bl X lVariable X - value xx is point or fuzzy set defined on R

{fi}

Bayes NodeInstantiate :{fi P (fi | )}

Prior Updated{ }{fi : Pr(fi | x)}Distribution Distribution

NET

Classical probability theory does not allowfor this distribution updatefor this distribution update.

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P’

UpdatedDistribution

onDistribution Constrainton Xk - D P

oX = (X1…Xn)

Minimum Relative Entropy

Pr’(X) ( )Pr’(X)MINPriorDistribution

onX = (X1…Xn)

Pr’(X) Ln ( )Pr(X)MIN

P'(X)D satisfied

Prior Update Updatevar 1 distribution var 2 distribution

until convergence18R. Akerkar

Bayes Net Compiled to give prior probability distributions.

Update Compiled Net with input variables instantiatedto probability distributions usingto probability distributions usingrelative entropy updating

Bayes Net message passing algorithms forClique tree updating modified to be equivalent to this relative entropy updatingbe equivalent to this relative entropy updating

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Fuzzify :A B C

A : {a1, a2, a3}B : [1 10]

Fuzzify :A : same as A aboveB : {small, medium, large}C : {low, av, high}

D

B : [1, 10]C : {1, 2, 3, 4, 5, 6}D : {d1, d2, d3}

D : same as above

small medium large

A B C Da1 x y {d1, d2} 1 10

low = 1 / 1 + 2 / 0.8 + 3 / 0.4av = 2 / 0.2 + 3 / 0.6 + 4 / 1 + 5 / 0.2high = 5 / 0 8 + 6 / 1

= Pr(medium | x) = Pr(large | x) = Pr(low | y) = Pr(av | y)Pr(d1) = 0.5 Pr(d2) = 0.5 high 5 / 0.8 + 6 / 1Pr(small | x) = Pr(high | y) = 0Notex and y can be point values, intervals or fuzzy sets

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Red ced Data Base Joint

A B C DReduced Data Base

a1 medium low d1 5

ProbabilityDistribution

a1 medium low d1a1 medium low d2a1 large low d1a1 large low d2

.5

.5

.5

.5a1 medium av d1a1 medium av d2a1 large av d1a1 large av d2

.5

.5

.5

.5a1 large av d2 .5

Repeat for all lines of database

Calculate Pr(D | A, B, C)

21R. Akerkar

1 Search and Scoring based algorithms1. Search and Scoring based algorithms

2. Dependency Analysis algorithms Complexity

A. Node OrderingB Without node ordering

(a) n2

(b) n4

B. Without node ordering

QueryingQueryingMarkov Cover :Parents of query node + children of queryParents of query node + children of querynode + parents of these children

22R. Akerkar

((prototype p1 (offer Mortgage) ) (evlog disjunctive ((AgeOfCompany old_age) 0.1(CompanySize large_size) 0.15(LoanRate small rate) 0.4(LoanRate small_rate) 0.4(TypeRate quite_fixed) 0.1(LoanPeriod long_period) 0.2(MedicalRequired bias_to_yes) 0.05))) : ((1 1) (0 0))

((prototype p1 (offer PersonalLoan) ) (evlog disjunctive ((AgeOfCompany old_age) 0.1(CompanySize large size) 0.15

Rules can alsobe used forfusion( p y g _ )

(LoanRate medium_rate) 0.4(TypeRate quite_variable) 0.1(LoanPeriod short_period) 0.2(M di lR i d bi t ) 0 05))) ((1 1) (0 0))

fusion

(MedicalRequired bias_to_no) 0.05))) : ((1 1) (0 0))

ETC - rules for other offers and other prototypes23R. Akerkar