1

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•What is

learning

?

2

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•What is

learning

?

•“That is what learning is. You suddenly understand

something you've understood all your life,

but in a

new way

.”

(Doris Lessing–2007 Nobel Prize in Literature)

3

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•How to construct programs that

automatically

improve

with

experience

.

4

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•How to construct programs that automatically

improve with experience.

•

Learning problem:

–

Task

T

–

Performance measure

P

–

Training experience

E

5

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•

Chess game:

–

Task

T

: playing chess games

–

Performance measure

P

: percent of games won against

opponents

–

Training experience

E

: playing practice games againtsitself

6

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Machine Learning

•

Handwriting recognition:

–

Task

T

: recognizing and classifying handwritten words

–

Performance measure

P

: percent of words correctly

classified

–

Training experience

E

: handwritten words with given

classifications

7

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Choosing the training experience:

–

Direct or indirect feedback

–

Degree of learner's control

–

Representative distribution of examples

8

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Choosing the target function:

–

Type of knowledge to be learned

–

Function approximation

9

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Choosing a representation for the target function:

–

Expressive representation for a close function approximation

–

Simple representation for simple training data and learning

algorithms

10

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Choosing a function approximation algorithm

(learning algorithm)

11

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Chess game:

–

Task

T

: playing chess games

–

Performance measure

P

: percent of games won against

opponents

–

Training experience

E

: playing practice games againtsitself

–

Target function

:

V

: Board →R

12

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Chess game:

–

Target function representation

:

V^

(b) = w

0

+ w

1

x1

+ w

2

x2

+ w

3

x3

+ w

4

x4

+ w

5

x5

+ w

6

x6

x1

: the number of black pieces on the board

x2

: the number of red pieces on the board

x3

: the number of black kings on the board

x4

: the number of red kings on the board

x5

: the number of black pieces threatened by red

x6

: the number of red pieces threatened by black

13

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Chess game:

–

Function approximation algorithm

:

(<

x1

= 3,

x2

= 0,

x3

= 1,

x4

= 0,

x5

= 0,

x6

= 0>, 100)

x1

: the number of black pieces on the board

x2

: the number of red pieces on the board

x3

: the number of black kings on the board

x4

: the number of red kings on the board

x5

: the number of black pieces threatened by red

x6

: the number of red pieces threatened by black

14

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•What is

learning

?

15

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

•

Learning is an (endless)

generalization

or

induction

process.

16

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Designing a Learning System

Experiment

Generator

Performance

System

Generalizer

Critic

New problem

(initial board)

Solution trace

(game history)

Hypothesis

(V

^)

Training examples

{(b

1, V

1), (b

2, V

2), ...}

17

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Issues in Machine Learning

•What learning algorithms to be used?

•How much training data is sufficient?

•When and how prior knowledge can guide the learning process?

•What is the best strategy for choosing a next training experience?

•What is the best way to reduce the learning task to one or more

function approximation problems?

•How can the learner automatically alter its representation to

improve its learning ability?

18

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Example

Yes

ChangeCoolStrongHighWarmSunny4

No

ChangeWarmStrongHighColdRainy3

Yes

SameWarmStrongHighWarmSunny2

Yes

SameWarmStrongNormalWarmSunny1

EnjoySport

ForecastWaterWindHumidityAirTempSky

Example

Experience

Prediction

?

???

ChangeWarmStrongHighColdRainy5

?

???

SameCoolStrongLowWarmSunny7

?

???

SameWarmStrongNormalWarmSunny6

LowWeak

19

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Example

•

Learning problem:

–

Task

T

: classifying days on which my friend enjoys water sport

–

Performance measure

P

: percent of days correctly classified

–

Training experience

E

: days with given attributes and classifications

20

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•Inferring a boolean-valued function from training

examples of its input (

instances

) and output

(

classifications

).

21

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•

Learning problem:

–

Target concept

: a subset of the set of instances X

c

: X →

→→→{0, 1}

–

Target function

:

Sky ×

×××AirTemp×

×××Humidity ×

×××Wind ×

×××Water ×

×××Forecast→

→→→{Yes, No}

–

Hypothesis

:

Characteristics of all instances of the concept to be learned

≡

≡≡≡Constraints on instance attributes

h

: X →

→→→{0, 1}

22

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•

Satisfaction:

h

(x) = 1

iff

x satisfies all the constraints of

h

h

(x) = 0 otherwsie

•

Consistency:

h

(x) =

c

(x) for every instance x of the

training examples

•

Correctness:

h

(x) =

c

(x) for every instance x of X

23

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•

How to represent a hypothesis function?

24

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•

Hypothesis representation

(constraints on instance attributes)

:

<

Sky

,

AirTemp

,

Humidity

,

Wind

,

Water

,

Forecast

>

–

?

: any value is acceptable

–

single required

value

–

∅

∅∅∅

: no value is acceptable

25

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Concept Learning

•

General-to-specific ordering of hypotheses: hj

≥g

hk

iff

∀

∀∀∀x∈

∈∈∈X: h

k(x) = 1 ⇒

⇒⇒⇒hj(x) = 1

Specific

General

h1

= <Sunny, ?, ?, Strong, ? , ?>

h2

= <Sunny, ?, ?, ? , ? , ?>

h3

= <Sunny, ?, ?, ? , Cool, ?>

H

Lattice

(Partial order)

h1

h3

h2

26

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

Yes

ChangeCoolStrongHighWarmSunny4

No

ChangeWarmStrongHighColdRainy3

Yes

SameWarmStrongHighWarmSunny2

Yes

SameWarmStrongNormalWarmSunny1

EnjoySport

ForecastWaterWindHumidityAirTempSky

Example

h

= < ∅, ∅, ∅, ∅, ∅, ∅>

h

= <Sunny, Warm, Normal, Strong, Warm, Same>

h

= <Sunny, Warm, ? , Strong, Warm, Same>

h

= <Sunny, Warm, ? , Strong, ? , ? >

27

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•Initialize

h

to the most specific hypothesis in

H

:

•For each positive training instance

x

:

For each attribute constraint

ai

in

h

:

If

the constraint is not satisfied by

x

Then

replace

ai

by the next more general

constraint satisfied by

x

•Output hypothesis

h

28

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

Yes

ChangeCoolStrongHighWarmSunny4

No

ChangeWarmStrongHighColdRainy3

Yes

SameWarmStrongHighWarmSunny2

Yes

SameWarmStrongNormalWarmSunny1

EnjoySport

ForecastWaterWindHumidityAirTempSky

Example

h

= <Sunny, Warm, ? , Strong, ? , ? >

Prediction

NoNoNoNo

ChangeWarmStrongHighColdRainy5

YesYesYesYes

SameCoolStrongLowWarmSunny7

YesYesYesYes

SameWarmStrongNormalWarmSunny6

29

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•The output hypothesis is the

most specific

one that

satisfies all positive training examples.

30

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•The result is consistent with the

positive

training examples.

31

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•Is the result is consistent with the

negative

training

examples?

32

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

Yes

ChangeCoolStrongHighWarmSunny4

NoNoNoNo

Change

ChangeChange

ChangeCool

CoolCool

CoolStrongStrongStrongStrongNormal

NormalNormal

NormalWarmWarmWarmWarmSunnySunnySunnySunny5

555

No

ChangeWarmStrongHighColdRainy3

Yes

SameWarmStrongHighWarmSunny2

Yes

SameWarmStrongNormalWarmSunny1

EnjoySport

ForecastWaterWindHumidityAirTempSky

Example

h

= <Sunny, Warm, ? , Strong, ? , ? >

33

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•The result is consistent with the

negative

training examples

if the

target concept

is contained in

H

(and the training

examples are correct).

34

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•The result is consistent with the

negative

training examples

if the

target concept

is contained in

H

(and the training

examples are correct).

•Sizes of the space:

–Size of the instance space:

|X|

= 3.2.2.2.2.2 = 96

–Size of the concept space

C

= 2

|X|

= 2

96

–Size of the hypothesis space

H

= (4.3.3.3.3.3) + 1 = 973 << 2

96

⇒

⇒⇒⇒The target concept (in

C

) may not be contained in

H

.

35

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

FIND-S

•Questions:

–Has the learner

converged

to the target concept, as there can

be several consistent hypotheses (with both positive and

negative training examples)?

–Why the

most specific

hypothesis is preferred?

–What if there are

several maximally specific

consistent

hypotheses?

–What if the training examples are

notcorrect

?

36

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

List-then-Eliminate Algorithm

•

Version space

: a set of all hypotheses that are

consistent with the training examples.

•Algorithm:

–Initial version space = set containing every hypothesis in

H

–For each

training example

<x, c(x)>

, remove from the version

space any hypothesis

h

for which

h(x) ≠

≠≠≠c(x)

–Output the hypotheses in the version space

37

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

List-then-Eliminate Algorithm

•Requires an exhaustive enumeration of all hypotheses

in

H

38

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Compact Representation of

Version Space

•

G

(

the generic boundary

): set of the

most generic

hypotheses of

H

consistent with the training data

D

:

G

= {

g

∈

∈∈∈

H

| consistent(

g

,

D

) ∧

∧∧∧¬∃

¬∃¬∃¬∃

g’

∈

∈∈∈

H

:

g’

>

>>>

g

g

∧

∧∧∧consistent(

g’

,

D

)}

•

S

(

the specific boundary

): set of the

most specific

hypotheses of

H

consistent with the training data

D

:

S

= {

s

∈

H

| consistent(

s

,

D

) ∧

∧∧∧¬∃

¬∃¬∃¬∃

s’

∈

∈∈∈

H

:

s

>

>>>

g

s’

∧

∧∧∧consistent(

s’

,

D

)}

39

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Compact Representation of

Version Space

•Version space = <

G

,

S

> = {

h

∈

∈∈∈H| ∃

∃∃∃g∈

∈∈∈

G

∃

∃∃∃s∈

∈∈∈

S

: g ≥

≥≥≥g

h

≥

≥≥≥g

s}

S G

40

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

S0

= {<∅, ∅, ∅, ∅, ∅, ∅>}

G0

= {<?, ?, ?, ?, ?, ?>}

S1

= {<Sunny, Warm, Normal, Strong, Warm, Same>}

G1

= {<?, ?, ?, ?, ?, ?>}

S2

= {<Sunny, Warm, ?, Strong, Warm, Same>}

G2

= {<?, ?, ?, ?, ?, ?>}

S3

= {<Sunny, Warm, ?, Strong, Warm, Same>}

G3

= {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>, <?, ?, ?, ?, ?, Same>}

S4

= {<Sunny, Warm, ?, Strong, ?, ?>}

G4

= {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>}

Yes

Change

Cool

Strong

High

Warm

Sunny

4

No

Change

Warm

Strong

High

Cold

Rainy

3

Yes

Same

Warm

Strong

High

Warm

Sunny

2

Yes

Same

Warm

Strong

Normal

Warm

Sunny

1

EnjoySport

Forecast

Water

Wind

Humidity

AirTemp

Sky

Example

S G

41

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

S4

= {<Sunny, Warm, ?, Strong, ?, ?>}

<Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?>

G4

= {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>}

42

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

•Initialize

G

to the set of

maximally general

hypotheses

in

H

•Initialize

S

to the set of

maximally specific

hypotheses

in

H

43

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

•For each

positive

example

d

:

–Remove from

G

any hypothesis inconsistent with

d

–For each

s

in

S

that is inconsistent with

d

:

Remove

s

from

S

Add

to

S

all least generalizations

h

of

s

, such that

h

is consistent with

d

and some hypothesis in

G

is more general than

h

Remove

from

S

any hypothesis that is more general than another

hypothesis in

S

44

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

•For each

negative

example

d

:

–Remove from

S

any hypothesis inconsistent with

d

–For each

g

in

G

that is inconsistent with

d

:

Remove

g

from

G

Add

to

G

all least specializations

h

of

g

, such that

h

is consistent with

d

and some hypothesis in

S

is more specific than

h

Remove

from

G

any hypothesis that is more specific than another

hypothesis in

G

45

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

•The version space will

converge

toward the correct

target concepts if:

–

H

contains the correct target concept

–There are no errors in the training examples

•A training instance to be

requested next

should

discriminate among the alternative hypotheses in the

current version space:

46

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Candidate-Elimination Algorithm

•

Partially learned

concept can be used to classify new

instances using the majority rule.

S4

= {<Sunny, Warm, ?, Strong, ?, ?>}

<Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?>

G4

= {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>}

?

???

SameCoolStrongHighWarmRainy5

⊕

⊕⊕⊕

⊕

⊕⊕⊕

47

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

•Size of the instance space:

|X|

= 3.2.2.2.2.2 = 96

•Number of possible concepts = 2

|X|

= 2

96

•Size of

H

= (4.3.3.3.3.3) + 1 = 973 << 2

96

48

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

•Size of the instance space:

|X|

= 3.2.2.2.2.2 = 96

•Number of possible concepts = 2

|X|

= 2

96

•Size of

H

= (4.3.3.3.3.3) + 1 = 973 << 2

96

⇒a

biased

hypothesis space

49

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

•An

unbiased

hypothesis space

H’

that can represent

every subset of the instance space

X

:

Propositional

logic sentences

•Positive examples:

x1

,

x2

,

x3

Negative examples:

x4

,

x5

h(x)

≡

≡≡≡

(x = x

1)

∨

∨∨∨

(x = x

2)

∨

∨∨∨

(x = x

3)

≡

≡≡≡

x1

∨

∨∨∨

x2

∨

∨∨∨

x3

50

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

x1

∨

x2

∨

x3

∨

x6

x1

∨

x2

∨

x3

Any new instance

x

is classified positive

by half

of the version space,

and negative by the other half ⇒

⇒⇒⇒

not classifiable

x1

∨

x2

∨

x3

∨

x

6

∨…

(not including

x4

and

x5

)

51

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

?

CheapFamousWed9

No

CheapFamousSat8

Yes

CheapInfamousThu6

No

ExpensiveFamousSun5

Yes

ModerateInfamousWed4

No

CheapInfamousSun3

No

ModerateFamousSat2

Yes

ExpensiveFamousTue7

ExpensiveExpensive

Price

?

InfamousSat10

Yes

FamousMon1

EasyTicket

ActorDayExample

52

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

No

HighBad2

Yes

LowGood1

Buy

PriceQualityExample

?

LowBad4

?

HighGood3

53

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Inductive Bias

•A learner that

makes no prior assumptions

regarding

the identity of the target concept

cannot classify any

unseen instances

.

54

05 January 2010

Cao Hoang Tru

CSE Faculty -HCMUT

Homework

Exercises

2-1 →2.5 (Chapter 2, ML textbook)

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