Transcript X1, X2, X3, X4, X5

Chapter 10
Machine Learning
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Learning
1. Rote learning
2. Learning by taking advice
3. Learning by problem solving
Parameter adjustment
Macro-Operators
4. Learning from examples
Induction : Winston’s learning program p.458
Version Spaces : Candidate eliminate algorithm
Decision tree
5. Explanation-based learning p 482
6. Formal learning theory
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Winston’s learning program
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Winston’s learning program
Concept : P.459
Begin with a structural description of one known
instance of the concept. Call the description the
concept definition.
Examine descriptions of other known instances of
the concepts. Generalize the definition to
include them.
Examine descriptions of near misses of concept,
Restrict the definition to exclude these.
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Winston’s learning program
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Winston’s learning program
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Winston’s learning program
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Winston’s learning program p.458
Block world concept : Figure 17.2 p. 459
Structure description : Figure 17.3 p. 460
The comparison of two arches : Figure 17.4 p. 461
The arch description after two examples : Figure 17.5 p.
462
The arch “description after a near miss : Figure 17.6 p.
463
use semantic networks to describe block structures
use matching process to detect similarities and
differences between structures
use isa hierarchy to describe relationship among
already known objects
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Version Spaces
The goal : to produce a description that is consistent with all
positive examples but no negative examples in the training
set.
use frame representing concept for car see Figure 17.7 p. 463
Features/Slots : { value1, value2,...,valueN }
origin : { Japan, USA, Britain }
Variables : X1, X2, X3
concept space : see Figure 17.11 Concept of Version Spaces p. 466
variables
target concept
all training instance
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Version Spaces
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Version Spaces
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version space = current hypothesis = subset of concept space = largest
collection
of descriptions that is consistent with all the training
examples seen so far.
concept space = G or S
G = contain the most general descriptions consistent with the training
example seen so far.
S = contain the most specific descriptions consistent with training
exaples
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positive example (+)  move S to more specific
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negative example (-)  move G to more specific
if G and S sets converge  the hypothesis is a single concept
description
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Version Spaces
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Candidate Eliminate Algorithm p.466-467
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 algorithm that use to narrow down the version
space
 by remove any descriptions that are inconsistent
with set G and set S
Car Example
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Figure 17.7 Concept Car : p. 463
Figure 17.8 Representation language for car : p. 464
Figure 17.9 The concept Japanese car : p. 464
Figure 17.10 Partial ordering of concepts : p. 465
Figure 17.12 Positive and negative examples of car : p. 467
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Version Spaces
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Version Spaces
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Version Spaces
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Candidate Eliminate Algorithm
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Candidate Eliminate Algorithm
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Version Spaces
We want “Japanese economy car”
From Figure 17.12 Positive and negative examples of car : p. 467
[origin = X1, manufacture = X2, color = X3, decade = X4, type = X5]
GET EX1 (+)
GET EX2 (-)
GET EX3 (+)
GET EX4 (-)
GET EX5 (+)
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G = {(X1, X2, X3, X4, X5)}
S = {(Japan,Honda, Blue,1980,Economy}) =Figure 17.12 in EX1
G = {(X1, Honda, X3, X4, X5), (X1, X2, Blue, X4, X5) ,
(X1, X2, X3, 1980, X5), (X1, X2, X3, X4, Economy)}
S = {(Japan,Honda, Blue,1980,Economy})
** the same because (-) example
check G first, G = {(X1, X2, Blue, X4, X5) ,(X1, X2, X3, X4, Economy)}
S = {(Japan,X2, Blue,X4,Economy})
check G first, G = {(Japan, X2, Blue, X4, X5) ,
(Japan, X2, X3, X4, Economy)}
S = {(Japan,X2, Blue,X4,Economy})
** the same because (-) example
check G first, G = {(Japan, X2, X3, X4, Economy)}
S = {(Japan,X2, X3,X4, Economy})
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Version Spaces
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Note : The algorithm is least commitment algorithm : produce as
little as possible at each step
Problems
1.) S and G may not converge to a single hypothesis
2. ) if there is a noise (inconsistent data)  the algorithm will be
premature, we may prune the target concept too fast
* For example if the data number three given the negative sign (-)
instance of positive sign (+) ... no matter how much the data is we
can not find the concept....
* How to fix this problem is to maintain several G and S sets
BUT it is costly and may have the bounded inconsistency
problem
3.) We can not use OR in the questions ask
* For example : Italian sport car or German luxury car”
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Decision Tree
ID3 Program = to classify a particular input, we start at the top of the tree
and answer questions until we reach a leaf, where the classification is
stored. See Figure 17.13 Decision tree p. 470
1. Choose window = random subset of training examples to train
2. Outside window = use to test the decision tree
3. Use empirical evidence (iterative method) to build up decision tree
4. Building a node = choosing some attribute to divide training instance into
subset
consider (+) sign
Can use with OR .... just change (-) sign into (+) sign
Problems : noisy input, attribute value may be unknown, may have large
decision tree and hard to understand relationship See Figure 17.13
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Decision Tree
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Explanation-Based Learning
 provide
explanation
 depend on domain theory/
domain knowledge
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Formal Learning Theory
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Given positive and negative examples
produce algorithm that will classify future
examples correctly with probability 1/h
Complexity of learning :
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the error tolerance (h)
the number of binary features present in the examples (t)
the size of the rule necessary to make the discrimination (f)
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if the number of training examples required is
polynomial in h,t, and f  then the concept is
learnable.
few training examples are needed  learnable
we restrict the learner to the positive examples
only.
See Figure 12.22 Concept of elephant P. 483
elephant = “gray, mammal, large”
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Induction
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emphasis to all BEANS : all instances
induction : A method of reasoning by which one infers a
generalization from a series of instances.
Inductive syllogisms are of the following form:
1. These beans are from this bag. (and these beans..., and these
beans..., etc.)
2. These beans are (all) white.
# 3 Therefore, all beans from this bag are white.
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In a much broader sense, induction can be thought to include various
other forms of reasoning including reasoning, inference to cause form
symptoms, and confirmation of laws and theories.
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Deduction
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emphasis to one BEAN : one instance
deduction - A method of reasoning by which one infers a
conclusion from a set of sentences by employing the axioms
and rules of inference for a given logical system.
Use the term 'deduction' in a general sense to denote the fact
that a conclusion follows necessarily from the premises.
Deductive syllogisms in quantificational predicate calculus
are of the following form:
1
1. All beans from this bag are white....
2. These beans are from this bag.
#4 Therefore, these beans are white.....
2
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Abduction
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emphasis to one BEANS
abduction -A method of reasoning by which one infers to
the ......best explanation.....
- A heuristic procedure that reasons
inductively from available empirical evidence to the
discovery of the probable hypotheses that would best
explain its occurrence.
Abductive syllogisms are of the following form:
#3 All beans from this bag are white
#4 These beans are white.
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The End
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