CS 6375 Homework 5
Chenxi Zeng, UTD ID: 11124236
1.
Given the samples
i
X
=
{
,
}
t
t
i
i
x r
, i.e.
(
)
t
i
f x
=
t
i
r
.
(i) If
( )
i
g x
=
1
i
r
, then
( )
i
g x
=
1
i
r
(the mean is regarding to all the
i
), the bias is
( )
(
)
t
i
i
g x
f x

=
1
t
i
i
r
r

, and the variance is
2
[(
( )
( )) ]
i
i
E g x
g x

=
1
1
2
[(
) ]
i
i
E r
r

=
1
2
1
2
[(
) ]
(
)
i
i
E r
r

.
(ii)If
( )
i
g x
=2, then
( )
i
g x
=2, the bias is
2
t
i
r

, and the variance is 0. The
variance is smaller than the one in (i), but it depends on the
1
i
r
(>2 or <2 or =2)
about the bias comparison.
(iii)If
( )
i
g x
=
/
t
i
t
r
N
∑
, then
( )
i
g x
=
/
t
i
t
r
N
∑
, the bias is
/
t
t
i
i
t
r
N
r

∑
, and the
variance is
2
2
[(
/
) ]
(
/
)
t
t
i
i
t
t
E
r
N
r
N

∑
∑
. To be honest, it is very difficult to
compare them with (i).
(iv) Unfortunately, I don’t understand it…
2.
We divide the 1000 training examples to 4 groups: G1, G2, G3 and G4. The
numbers of the groups are 200, 200, 100 and 500. They have attributes in the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 yangliu
 Neural Networks, Machine Learning, Unsupervised learning, Artificial neural network, neural network, classifier, unsupervised clustering

Click to edit the document details