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10bLearnClassifiers.pdf
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CS  171  Inroduction to Artificial Intelligence ...
CS  171  Inroduction to Artificial Intelligence  lecture_notes Machine Learning (2) Other Classifiers Prof. Alexander Ihler CS 171: Intro to AI Outline • Different types of learning problems • Different types of learning algorithms • Supervised learning – Decision trees – Naïve Bayes – Perceptrons, Multilayer Neural Networks – Boosting (see papers and ViolaJones slides on class website) • Applications: learnin
CS  171  Inroduction to Artificia...
CS  171  Inroduction to Artificial Intelligence  lecture_notes Machine Learning (2) Other Classifiers Prof. Alexander Ihler CS 171: Intro to AI Outline • Different types of learning problems • Different types of learning algorithms • Supervised learning – Decision trees – Naïve Bayes – Perceptrons, Multilayer Neural Networks – Boosting (see papers and ViolaJones slides on class website) • Applications: learnin
Page 1
Machine Learning (2)
Other Classifiers
Prof. Alexander Ihler
CS 171: Intro to AI
Page 2
Outline
•
Different types of learning problems
•
Different types of learning algorithms
•
Supervised learning
–
Decision trees
–
Naïve Bayes
–
Perceptrons, Multilayer Neural Networks
– Boosting
(see papers and ViolaJones slides on class website)
•
Applications: learning to detect faces in images
–
(see papers and ViolaJones slides on class website)
Page 3
You will be expected to know
•
Classifiers:
–
Decision trees
–
Knearest neighbors
–
Naïve Bayes
–
Perceptrons, Support vector Machines (SVMs), Neural Networks
•
Decision Boundaries for various classifiers
–
What can they represent conveniently?
What not?
Page 4
Inductive learning
•
Let x
represent the input vector of attributes
–x
j
is the jth component of the vector x
–x
j
is the value of the jth attribute, j = 1,…d
•
Let f(x
) represent the value of the target variable for x
–
The implicit mapping from x to f(x
) is unknown to us
–
We just have training data pairs, D = {x
, f(x
)} available
•
We want to learn a mapping from x
to f, i.e.,
h(x
;
θ
) is “close” to f(x) for all training data points x
θ
are the parameters of our predictor h(..)
•
Examples:
– h(x
;
θ
) = sign(w
1
x
1
+ w
2
x
2
+ w
3
)
–h
k
(x
) = (x1 OR x2) AND (x3 OR NOT(x4))
Page 5
Training Data for Supervised Learning
Page 6
True Tree (left) versus Learned Tree (right)
Page 7
Classification Problem with Overlap
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1
2
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FEATURE 1
FEATURE 2
Page 8
Decision Boundaries
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8
0
1
2
3
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5
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7
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FEATURE 1
FEATURE 2
Decision
Boundary
Decision
Region 1
Decision
Region 2
Page 9
Classification in Euclidean Space
•
A classifier is a partition of the space x
into disjoint decision
regions
–
Each region has a label attached
–
Regions with the same label need not be contiguous
–
For a new test point, find what decision region it is in, and predict
the corresponding label
•
Decision boundaries = boundaries between decision regions
–
The “dual representation” of decision regions
•
We can characterize a classifier by the equations for its
decision boundaries
•
Learning a classifier
ó
searching for the decision boundaries
that optimize our objective function
Page 10
Example: Decision Trees
•
When applied to realvalued attributes, decision trees produce
“axisparallel” linear decision boundaries
•
Each internal node is a binary threshold of the form
x
j
> t ?
converts each realvalued feature into a binary one
requires evaluation of N1 possible threshold locations for N
data points, for each realvalued attribute, for each internal
node
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