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Learning with Weighted Examples - Machine Learning | CSCI 5622, Study notes of Computer Science

University of Colorado Boulder (CU Boulder)Computer Science
Prof. Gregory Grudic

Material Type: Notes; Professor: Grudic; Class: MACHINE LEARNING; Subject: Computer Science; University: University of Colorado - Boulder; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 02/10/2009

koofers-user-wuf
koofers-user-wuf 🇺🇸

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1
Learning With Weighted
Examples
Greg Grudic
Weighted Training Examples
• Training Examples
• Associate a weight
• The greater the weight, the greater the
importance of the training example
– Might come from prior knowledge
–Or a boosting algorithm….
()( )
{
}
11
, ,..., ,
NN
Dy y=xx
{
}
12 3
, ,...,ww w
0
i
w>
pf3
pf4

Partial preview of the text

Download Learning with Weighted Examples - Machine Learning | CSCI 5622 and more Study notes Computer Science in PDF only on Docsity!

Learning With Weighted

Examples

Greg Grudic

Weighted Training Examples

• Training Examples

• Associate a weight

• The greater the weight, the greater the

importance of the training example

– Might come from prior knowledge

– Or a boosting algorithm….

1 1

N N

D = x y x y

1 2 3

w , w ,..., w

i

w >

Weighted Sum of Least Squares

• The Loss Function being minimize:

• The matrixes and outputs become

• The Solution is

2

0

1 1

weighted RSS

N d

i i j ij

i j

w y β βx

= =

1 1 11 1 1 1 1

w

1

d

N N N N Nd N N

w w x w x w y

X

w w x w x w y

Y

1

T T

w

−

β = X X X Y

Weighted Ridge Regression

• The Loss Function being minimize:

• The matrixes and outputs become

• The Solution is

2

2

0

1 1 1

weighted Ridge Loss

N d d

i i j ij j

i j j

w y β β x λ β

= = =

1

0

T T

w

λ I

−

β = X X + X Y

1 1 11 1 1 1 1

w

1

d

N N N N Nd N N

w w x w x w y

X

w w x w x w y

Y

0

I is a (d+1) by (d+1) identity

matrix with the first entry

set to zero

Decision Tree Stump

• Next homework…