Machine learning 1

unknownlippsAI and Robotics

Oct 16, 2013 (3 years and 5 months ago)

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Machine Learning 2

1

Machine Learning

Basic definitions:



concept
: often described implicitely(„
good politician
“) using
examples, i.e.
training data



hypothesis:
an attempt to describe the concept in an
explicite way



concept / hypothesis are presented in the
corresponding language



hypothesis is verified using
testing data



background knowledge

provides info about the context
(properties of environment)



learning algorithm searches the space of hypothesis to find
consistent and complete h
., the space is restricted by
introducing
bias


Machine Learning 2

2

Goal of inductive ML


Suggest a hypothesis
characterizing
concept
in a
given domain (= the set of
objects in this domain)
implicitely described

through
a limited
set of classified
examples

E
+

and
E
-
.


The hypothesis
:


has to cover
E
+

while avoiding
E
-


be applicable to objects which
do not belong to
E
+

and
E
-
.

Machine Learning 2

3

Basic notions




-

domain
of the concept

K
, ie.
K

.



E




a set of

training examples
is
complemented by a classifcation, i.e. a
function
cl
:

E
--
>

yes
, no

.


E
+

denotes all elements of
E

classified as

yes



E
+

and
E
-

are a disjoint cover of the set
E

Machine Learning 2

4

Example 1 „computer game“:
Is there a way
how to distinguish quickly a friendly robot
from the others?


Friendly r.

Unfriendly r.

Machine Learning 2

5

Concept Language and

Background Knowledge


Examples of concept language:


A set of real or idealised examples expressed in the object language that
represent each of the concepts learned (Nearest Neighbour)


attribute
-
value pairs (propositional logic)


relational concepts (first order logic)



One can extend the concept language with user
-
defined
concepts or
background knowledge
.


BK plays an important role in

Inductive Logic Programming (ILP)


The use of certain BK predicates may be a necessary condition for
learning the right hypothesis.


Redundant or irrelevant BK slows down the learning.


Machine Learning 2

6

Example 1: hypothesis and its testing

Head
shape

Smiling
face

Neck

Body
shape

Holding

Friendly


circle

nothing

tie

circle

sword

yes

triangle

yes

nothing

square

nothing

yes

H1 in the form of a decision tree

if neck( r)

= bow

then „friendly”


= nothing

then



if head_shape ( r) = triangle

then „friendly“



else „unfriendly“


= tie


then



if body_shape( r) = square then „unfriendly“ else




if head_shape( r) = circle then „friendly“




else „unfriendly“

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Example 1: hypothesis and its testing

Machine Learning 2

8

Hypothesis
-

attempt for a formal description

Both

examples

and

hypothesis

have

to

be

specified

in

a

language
.

Hypothesis

has

the

form

of

a

formula


(X)

with

a

single

free

variable

X
.


Let

us

define

extension

Ext


of

a

hypotheis


(X)

wrt
.

the


domain




as

the

set

of

all

elements

of


,

睨楣w

m敥e

瑨t

捯湤楴楯i


,


.
Ext


=


o




⡯(

platí




Properties of hypothesis


hypothesis


is

complete
(úplná), iff
E
+



Ext




h.


is

consistent
, if it covers no negative examples, i.e.
Ext




E
-

=




h.


is correct
, if it is
complete a
nd consistent

Machine Learning 2

9

How many correct hypothesis can be
designed for a fixed training set
E
?


Fact:

the number of possible concepts is much more than
possible hypothesis (a formula)


concequence
: most of the concepts cannot be
characterized by a corresponding hypothesis
-

we have to
accept the hypothesis, which are “approximately correct“
only.


Uniqueness of an
“approximately correct“
hypothesis
cannot be ensured.

Machine Learning 2

10

Choice of a hypthesis and
Ockham
´
s rasor

Williamu of Ockham

recommends the way how
to compare the hypothesis:

Entia non sunt
multiplicanda praeter
necessitatem
“,



Einstein
: „…
the
language should not be
sompler than necessary
.“

Machine Learning 2

11

Machine Learning Biases


The concept/hypothesis language specifies the
language bias
, which limits the set of all
concepts/hypotheses that can be
expressed/considered/learned.


The
preference bias

allows us to decide between
two hypotheses (even if they both classify the
training data equally).


The
search bias

defines the order in which
hypotheses will be considered.


Important if one does not search the whole hypothesis
space.


Machine Learning 2

12

Preference Bias, Search Bias & Version Space

Hypothesis are partially ordered

Version space
:
searches for
the subset of hypotheses that have zero
training error.







+

+

+

+

_

_

_

_

most spec. concept

most gen. concept

Machine Learning 2

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Types of learning


skill

refinement

(swimming,

biking,

...
)




knowledge

acquisition


Rote

Learning

(chess,

checkers),

the

aim

is

to

find

an

appropriate

heuristic

function

evaluating

the

current

state

of

the

game,

e
.
g
.

MIN
-
MAX

approach


Case
-
Based

Reasoning
:

past

experience

is

stored

in

a

database
.

To

solve

a

new

problem,

the

systém

searches

the

DB

to

find

„the

closest

(the

most

similar)

case“

-

its

solution

is

modified

for

the

current

problem



Advice

Taking
,

learning

to

use

"interpret"

or

"operacionalize"

an

abstract

advice



search

for

„applicability

conditions“


Induction.
Difference Analysis
: candidate
-
elimination or version
space approach, decision trees induction etc.

Machine Learning 2

14

Decision tree induction

Given:

Training examples uniformly described by a single set
of the same attributes and classified into a small set of
classes (most often into 2 classes: positive X negative
examples)

Find:

a decision tree allowing to characterize the new species


Simple example:
robots described by 5 discrete atributes and classified
into 2 classes (friendly, unfriendly)


Is_smiling

{no, yes},


Holding


{sword,

balloon,

flag},



Has_tie


{no,

yes},



Head_shape


{round,

square,

octagone},



Body_shape


{round,

square,

octagone}
.




Machine Learning 2

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Machine Learning 2

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TDIDT
: Top
-
Down Ind
.

of Decision Trees


given
:
S

... the set of classified examples

goal
: design a decision tree
DT
ensuring the same classification
as
S

1.


The root is denoted by
S

2.



Find the "best" attribute
at
to be used for splitting the
current set
S

3
.


Split the set
S

into the subsets
S
1
, S
2
, ..., S
n

wrt. value of
at

(all examples in the subset
S
i
have the same value
at = v
i

).
This set denotes a node of the
DT

4
.


For each
S
i

do:

If
all examples in
S
i

belong to the same class


or

then
create a leaf with the same label,

else

go to 1 with
S = S
i


Machine Learning 2

17

TDIDT
:
How to choose the "best" attribute?



minimize the
entropy

(Shanon)

H(S
i
) =
-

p
i
+


log p
i
+


-

p
i
-


log p
i
-



p
i
+


=

the probability that a
random example

in
S
i
is


,

estimated by frequency



Let
the attribute
at
split
S

into the subsets
S
1
, S
2
, ..., S
n

. T
he
entropy of this system is

defined


H(S,at) =


i
n

= 1
P(S

i
) H (S
i

)


where
P(S

i
)

is probability of the event S

i
, approx. by relative
size
|S

i
| / |S
|



Choose

at

with the minimal

H(S,at)

Machine Learning 2

18

Learning to fly simulator F16 [Samuel, 95]


Design an automatic controller for F16 for following complex task:

1.

Start up and rise upto the heigth 2000 feet

2.

Fly 32000 feet north

3.

Turn right 330
°

4.

When 42000 feet from the starting point (direction N
-
S) turn left and head
towards the starting point, the rotation is finished when the course is between
140
°

and 180
°
.

5.

Adjust the flight direction so that it is paralel to the landing course, tolerance 5


for flight direction and 10
°

for wing twist wrt. horizont

6.

Decrease the heigth and move towards the start of the landing path

7.

Lend

Training data
:
3 skilled pilots performed the assigned mission, each 30 times

Each flight is described by 1000 vectors characterizing ( total of 90000 training
examples):



Position and state of the plane





Pilot

s control action


Machine Learning 2

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Learning to fly simulator F16 [Samuel, 95]


Position and state



on_gound

boolean: is the plane on the ground?


g_limit

boolean: acceleration limit exceeded?


wing_stall (is the plane stabile?), twist (int: 0
°
-
360
°
, wings wrt. horizont)


elevation (angle „body wrt. horizont“), azimuth, roll_speed

(wings deflection),
elevation_speed, azimuth_speed

, airspeed, climbspeed, E/W distance, N/S
distance, fuel (weight of current supply)


Control:



rollers and elevator: position of horizontal/ vertical deflection


thrust

integer: 0
-
100%, force


flaps


integer: 0
°
, 10
°

or 20
°
, wing twist


Each of the 7 phases calls for a specific type of control.

The

training

data

are

divided

into

7

disjunctive

sets

which

are

used

to

design

specific

decision

trees

(independently

for

each

task

phase

and

each

control

action)
.

Control

ensured

by

7

*

4

decison

trees
.



Machine Learning 2

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Tasks adressed by ML applications


Classification/prediction


diagnosis (troubleshooting motor pumps, medicine,.., SKICAT
-

astronomical cataloguing)


execution/control (GASOIL
-

separation of hydrocarbons)


configuration/design (Siemens: equipment c., Boeing)


language understanding


vision and speech


planning and schedulling


Why? Important speed up of the development and maintenace


180 man
-
years to develop ES XCON with 8000 rules, 30 m
-
y needed for
maint.


1 man
-
year to develop BP GASOIL (MLbased) with 2800 rules, 0,1 m
-
y
needed for maint.