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
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 Spring '09
 yangliu
 Neural Networks, Machine Learning, Unsupervised learning, Artificial neural network, neural network, classifier, unsupervised clustering

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