Budgeted Machine Learning of

Budgeted Machine Learning of

Bayesian Networks

Michael R.
Gubbels

Dr. Stephen D. Scott

Department of Computer Science and Engineering

University of Nebraska
-
Lincoln

McNair Scholars Program

August 2009

Overview

•
Introduction

•
Methods

•
Results

•
Discussion

•
Conclusions

2

Machine Learning

The concern of
machine learning
is to design
algorithms

for learning
general knowledge from a collection of related special cases called
examples
. A collection of related examples forms a data set for the
concept

relating its examples.


Learning algorithms construct a general
model

for relationships
among the characteristics or
attributes

in data set.


Using this model, the attributes of interest or
labels

of an example
can be learned in terms of its other attributes. This allows the label
of a new example or
instance

to be
predicted

in terms of its
attributes.

3

Machine Learning

A
TTRIBUTES

Smoker

Bronchitis

Fatigue

Chest

X
-
ray

Lung
Cancer

E
XAMPLES

Yes

No

Yes

Negative

No

No

No

No

Positive

No

∙∙∙

Yes

Yes

No

Positive

Yes

4

L
EARNING

A
LGORITHM

observed by

L
EARNED

M
ODEL

Yes

generates

predicts

presented to

(Yes, No, Yes, Positive, ?)

Budgeted Machine Learning

5

In
budgeted machine learning
, an algorithm is given a
budget

and
must pay for the attributes observed during learning. Using the
attributes purchased from examples, the algorithm constructs a
general model for a concept.


The labels of examples are free, so can be observed without penalty,
but the attributes have an associated cost.


Attributes are purchased until the budget is exhausted.

Budgeted Machine Learning

6

A
TTRIBUTES

Smoker

Bronchitis

Fatigue

Chest

X
-
ray

Lung
Cancer

C
OST

$10

$50

$10

$100

E
XAMPLES

?

?

?

?

No

?

?

?

?

No

∙∙∙

?

?

?

?

Yes

B
UDGETED

L
EARNING

A
LGORITHM

L
EARNED

M
ODEL

Yes

purchases from

generates

predicts

observed by

evaluated by

(Yes, No, Yes, Positive, ?)

presented to

Budgeted Machine Learning

•
Attribute selection policies

–
Round robin

Purchases one value at a time from each attribute

e.g., (A
1
, A
2
, A
3
, A
4
, A
1
, A
2
, A
3
, A
4
,

A
1
,

… )


–
Biased robin


Repeatedly purchases values from the same while
those purchases improve the model


e.g., ( A
1
, A
1
, A
2,

A
3,

A
3,

A
3,

A
4,

A
1,
A
1,
… )

7

Budgeted Machine Learning

8

Naïve
Bayes

classifier

Bayesian network









–
卩浰S敲et漠瑲慩a

–
啮U敡汩V瑩c 慳獵浰瑩潮o 潦oat瑲i扵t攠
i湤数敮摥湣n

–
P潯o 敳瑩浡t敳 潦o瑲略⁰ 潢慢ili瑩敳

–
䑩f晩f畬u

t漠瑲慩a

–
䍡C

浯摥l⁣潮摩瑩潮慬o
i湤数敮摥湣攠潦oat瑲i扵t敳

–
䍯浰Ct敳

慣a畲at攠
灲潢慢ili瑩敳

Purpose

•
Evaluate how well existing algorithms learn
Bayesian networks for use in classification

–
Produce more accurate probability estimates

•
Should improve efficacy of existing algorithms that
depend on such estimates

–
Explicitly represent attribute independencies

•
Should facilitate learning of a more accurate model

•
Should improve classification performance of model

9

Methods

1.
Generated data sets

–
Used
Asia

and
ALARM

Bayesian network models

•
Asia

network has 8 attributes:

–
Predicted
Bronchitis

•
ALARM

network has 37 attributes

–
Predicted
Breathing Pressure

2.
Constructed model

3.
Evaluated the learned networks


10

Methods

1.
Generated data sets

2.
Constructed model

–
Used round robin and biased robin policies

–
Learned naïve and complex Bayesian networks

•
Structures were given

•
Uniform and noisy prior knowledge

–
Uniform attribute cost

–
Varied the learning algorithm’s total budget

3.
Evaluated the learned networks

11

Methods

1.
Evaluated the learned networks

2.
Constructed model

3.
Evaluated the learned networks

–
For uniform and noisy prior knowledge

–
For many numbers of purchases

–
Baseline (“best possible”) classification
performance of model


12

Results

13

Results

14

Discussion

•
Naïve Bayesian networks

–
Converge to baseline faster with uniform priors

•
Bayesian networks

–
Have more accurate baseline than naïve networks

–
Converge to baseline faster with noisy priors

15

Conclusions

•
Bayesian networks learned using existing algorithms
converge to baseline

•
Bayesian networks may be preferable to naïve
networks when learning complex concepts or when
prior knowledge is available


•
Future work

–
Evaluate more existing policies with Bayesian networks

–
Analysis of models learned for complex concepts

–
New algorithms to exploit Bayesian network structure

–
Learning from data with different cost models

16

Acknowledgements

•
Dr. Stephen D. Scott

Research Mentor

•
Kun Deng

Graduate Student

•
Amy Lehman

Graduate Student Mentor

•
UNL McNair Scholars Program

17

Bibliography

Lizotte
, D. J.,
Madani
, O., & Greiner, R. (2003). Budgeted learning of
naïve
-
Bayes

classifiers.
Uncertainty in Artificial Intelligence
, 378
-
385.

Tong, S., &
Koller
, D. (2001). Active learning for parameter estimation
in Bayesian networks.
International Joint
Converences

on
Artificial Intelligence.

Deng, K., Bourke, C., Scott, S.,
Sunderman
, J., &
Zheng
, Y. (2007).
Bandit
-
based algorithms for budgeted learning.
Seventh IEEE
International Conference on Data Mining
, 463
-
468.

Neapolitan, R. E. (2004).
Learning
bayesian

networks.

New Jersey:
Pearson Prentice Hall.

Mitchell, T. M. (1997).
Machine learning.

New York: McGraw
-
Hill.

18

Pseudocode

A
TTRIBUTE

S
ELECTION

P
OLICIES

R
OUND

R
OBIN

B
IASED

R
OBIN

R
ANDOM

a
←
S
ELECT
(
M
IN
-
C
OST
(A)
)


U
NTIL
(
B
UDGET
-
E
XHAUSTED
?)
:


e
←

S
ELECT
(
R
ANDOM
(E)
)


v
←
P
URCHASE
(
a,e
)


M
←
L
EARN
M
(v)


a
←

S
ELECT
(
N
EXT
(A)
)

a
←
S
ELECT
(
M
IN
-
C
OST
(A)
)


U
NTIL
(
B
UDGET
-
E
XHAUSTED
?)
:


e
←

S
ELECT
(
R
ANDOM
(E)
)


m
old
←

C
ORRECTNESS
(M
)


v
←
P
URCHASE
(
a,e
)


M
←
L
EARN
M
(v)


m
new
←

C
ORRECTNESS
(M
)


I
F
(
m
new
< m
old
):


a
←

S
ELECT
(
N
EXT
(A)
)

a
←
S
ELECT
(
R
ANDOM
(A)
)


U
NTIL
(
B
UDGET
-
E
XHAUSTED
?)
:


e
←

S
ELECT
(
R
ANDOM
(E)
)


v
←
P
URCHASE
(
a,e
)


M
←
L
EARN
M
(v)


a
←

S
ELECT
(
R
ANDOM
(A)
)

Figure 4.
Pseudocode

for the round robin, biased robin, and random data selection policies.
A

is the set of
attributes available to purchase values from, and
a

is a particular attribute in
A
.
E

is the set of examples,
and
e

is a particular example in
E
.
v

is an attribute value in an example.
M

denotes the specific model
being learned, and the variables
m
old

and
m
new

represent the correctness of model
M

before and after
learning new information.

19

Pseudocode

A
TTRIBUTE

S
ELECTION

P
OLICIES

R
OUND

R
OBIN

B
IASED

R
OBIN

a
←
S
ELECT
(
M
IN
-
C
OST
(A)
)


U
NTIL
(
B
UDGET
-
E
XHAUSTED
?)
:


e
←

S
ELECT
(
R
ANDOM
(E)
)


v
←
P
URCHASE
(
a,e
)


M
←
L
EARN
M
(v)


a
←

S
ELECT
(
N
EXT
(A)
)

a
←
S
ELECT
(
M
IN
-
C
OST
(A)
)


U
NTIL
(
B
UDGET
-
E
XHAUSTED
?)
:


e
←

S
ELECT
(
R
ANDOM
(E)
)


m
old
←

C
ORRECTNESS
(M
)


v
←
P
URCHASE
(
a,e
)


M
←
L
EARN
M
(v)


m
new
←

C
ORRECTNESS
(M
)


I
F
(
m
new
< m
old
):


a
←

S
ELECT
(
N
EXT
(A)
)

20