1

1. IntroductionBackgroundKey questions

2. Probabilistic Exemplar Based Model

RepresentationClassification processLearning process

3. Empirical Evaluation

4. Related Work

A Probabilistic Exemplar Based Model for Case-Based Reasoning

Andrés Rodríguez, Sunil Vadera, Enrique SucarIns. Inv. Eléctricas, University of Salford, ITESM Morelos

MICAI 2000 Abril 2000

OUTLINE

2

Introduction

Case Base Reasoning Cycle

case base

Adaptation

EvaluationRetention

Retrieval

How do we assess

similarity?

Is the proposala likely

solution ?

Which cases

do we retain ?

How do we adapt the old solution?

Representation?

Case Base Reasoning Paradigm

New cases can be solved by adapting solutions that were used to solve similar cases in the past.

3

A

Bcategory

case

C

Interesting when• categories not defined by nec/suf conds.• data is unstructured• categories not disjoint• not all the data exists in advance• uncertainty involved

A

B

exemplar

category

prototypical case

C

4

Key Questions

The objective.

A

B

exemplar

category

newexemplar

What is a good representation for an EBM?

What notion of similarity can be adopted?

How can a new case be classified?

How can it be learned incrementally?

5

Representation

...

... ...

...... ...

C1 Cw

e1 ei ek eq

f1 f2 fm fj fn

P(f1 | parents(f1)) P(fn | parents(fn))

P(e1 | C1) P(ei | C1) P(eq | Cw)

...

C1

Cw

Cie1 ei

ek

eq

6

Classification Process

fa, ..., fh

new case

...

...

CmC1

ec

fk fj

Stage 1

Rank the categories.

Rank(ei) =

Stage 2Determination of an Exemplar

P(ei | fa, ..., fh)

P(f | ei)

nfei

...

... ...

...... ...

C1 Cw

e1 ei ek eq

f1 f2 fm fj fn

P(f1 | parents(f1)) P(fn | parents(fn))

P(e1 | C1) P(eq | Cw)

...

... .

......

C1

e1 ei ek

f1 f2 fm fj

P(f1 | parents(f1))

P(e1 | C1)

...

fei

7

Learning Process

Classification process

new training case

Add exemplar Retain ?

C

e1e2 e3

C

e1e2 e3

C

e1e2 e3

8

What makes a good exemplar?

A prototypical member [Rosch and Mervis (1974)]

1. High family resemblance in the region

2. Low family resemblance with other regions.

Summary representation

is a Bayesian net consisting of the features

of all the cases represented by the exemplar.

Prototypical case

Cij ))|eP(Sr(ek

,C)Peri(ek

jiji

1

1

)|)((),( iii eeSrPCeFoc Focality

Peripherality

),(),( CePeriCeFoc ii Prototypicality

New caseei

C

9

Estimating the Parameters

Need to estimate P(fi| parents(fi))

• Requires 2n+1 values for n parents.• Intersection may not have many examples

Noisy OR model

Exception IndependenceAbsence of fi given e1 is independentof absence of a feature given e2

Accountability ConditionIf a case is not represented by any of theexemplars, then it does not have any of the exemplars’ features.

...

... ...

...... ...

C1 Cw

e1 ei ek eq

f1 f2 fm fj fn

P(f1 | parents(f1)) P(fn | parents(fn))

P(e1 | C1) P(eq | Cw)

...

10

...

A

e6 e8 e9

f1 f2 f4 fn-1f3 fn

Ve

P(e6 | A) P(e9 | A)

P(f1 | e6,Ve) P(fn | e9,Ve)

Virtual Exemplar

Estimate of P(f | Ve)

)1.0,()|( .. nemaxVefP

Where

n : number of cases in the category

and parameters that determine the rate of decay

11

Empirical Evaluation

• Tested on Votes, Zoo, Audiology• Decay: = 0.6, = 0.1, threshold = 0.75 • 70/30 training/testing split• Good accuracy for Votes (89%) & Zoo (92%) • Poor for Audiology (50%)

Audiology: Compression & Accuracy

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11

Category

Pe

rce

nt

Compression Accuracy

Category Training Exemplars Accuracy

Repubilicans 119 2 96

Democrats 185 4 84

12

Bayesian models

Inductive models with supervised learning

Case-based models

PROTOS

CASEY

REMIND

OC1

C4.5

COBWEB

Inductive modelsunsupervised learning

AutoClass

IBLCBR-Express

Naive Bayes

Heckerman's Tirri's

PEBM

Protos• Use of remindings, censors, difference links• Learns from failure by user explanation• Uses many heuristics

Tirri and Myllymäkis’ model• Uses all cases not exemplars• Assumes cases are mutually exclusive• Assumes features are independent given case

Related Work

13

Conclusion

Developed a model with:• probabilistic exemplars• foundations in Bayesian nets• is incremental• promising results

FutureNeed to:• develop quicker propagation• test on more data sets• evaluate it relative to others• investigate , , threshold• multilevel features• dependent features