CS | 171 | Inroduction to Artificial Int...
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, Multi-layer Neural Networks – Boosting (see papers and Viola-Jones slides on class website) • Applications: learnin
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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, Multi-layer Neural Networks – Boosting (see papers and Viola-Jones slides on class website) • Applications: learnin
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Machine Learning (2)
Other Classifiers
Prof. Alexander Ihler
CS 171: Intro to AI

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Outline
Different types of learning problems
Different types of learning algorithms
Supervised learning
Decision trees
Naïve Bayes
Perceptrons, Multi-layer Neural Networks
– Boosting
(see papers and Viola-Jones slides on class website)
Applications: learning to detect faces in images
(see papers and Viola-Jones slides on class website)

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You will be expected to know
Classifiers:
Decision trees
K-nearest neighbors
Naïve Bayes
Perceptrons, Support vector Machines (SVMs), Neural Networks
Decision Boundaries for various classifiers
What can they represent conveniently?
What not?

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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))

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Training Data for Supervised Learning

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True Tree (left) versus Learned Tree (right)

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Classification Problem with Overlap
0
1
2
3
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5
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7
8
0
1
2
3
4
5
6
7
8
FEATURE 1
FEATURE 2

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Decision Boundaries
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
FEATURE 1
FEATURE 2
Decision
Boundary
Decision
Region 1
Decision
Region 2

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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

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Example: Decision Trees
When applied to real-valued attributes, decision trees produce
“axis-parallel” linear decision boundaries
Each internal node is a binary threshold of the form
x
j
> t ?
converts each real-valued feature into a binary one
requires evaluation of N-1 possible threshold locations for N
data points, for each real-valued attribute, for each internal
node

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