Biomedical Engineering Reference
In-Depth Information
Table 4.21
Resolution ratio
R
i
for top rank predictors from mutated network (Linear Representa-
tion)
Gene
p
1,
top
R
1
p
2,
top
R
2
p
3,
top
R
3
p
4,
top
R
4
x
2
Rb
x
1
1.394
x
1
,
x
4
1.407
x
1
,
x
4
,
x
9
1.021
x
1
,
x
4
,
x
8
,
x
9
1.034
x
3
E2F
x
7
1.047
x
2
,
x
9
1.009
x
2
,
x
5
,
x
9
1.262
x
2
,
x
5
,
x
8
,
x
9
1.156
x
4
CycE
x
3
1.177
x
2
,
x
3
3.827
x
2
,
x
3
,
x
5
1.222
x
1
,
x
2
,
x
3
,
x
7
1.227
x
5
CycA
x
6
1.006
x
2
,
x
6
1.228
x
2
,
x
6
,
x
7
1.009
x
2
,
x
6
,
x
8
,
x
9
1.019
x
6
Cdc
20
x
9
17.494
x
1
,
x
9
1.255
x
1
,
x
4
,
x
9
1.031
x
3
,
x
4
,
x
7
,
x
9
1.029
x
7
Cdh
1
x
6
1.064
x
6
,
x
9
1.707
x
5
,
x
6
,
x
9
1.384
x
5
,
x
6
,
x
8
,
x
9
1.408
x
8
UbcH
10
x
7
1.959
x
1
,
x
7
1.037
x
1
,
x
4
,
x
7
1.037
x
1
,
x
3
,
x
6
,
x
7
1.036
x
9
CycB
x
7
1.212
x
6
,
x
7
3.373
x
6
,
x
7
,
x
8
1.982
x
3
,
x
6
,
x
7
,
x
8
1.035
Table 4.22
Resolution ratio
R
i
for top rank predictors from mutated network (Sigmoid Represen-
tation)
Gene
p
1,
top
R
1
p
2,
top
R
2
p
3,
top
R
3
p
4,
top
R
4
x
2
Rb
x
1
1.034
x
1
,
x
4
1.185
x
1
,
x
4
,
x
9
1.597
x
1
,
x
4
,
x
7
,
x
9
1.005
x
3
E2F
x
2
1.013
x
2
,
x
5
2.046
x
2
,
x
5
,
x
9
9.160
x
2
,
x
5
,
x
7
,
x
9
1.032
x
4
CycE
x
3
1.547
x
2
,
x
3
81.104
x
2
,
x
3
,
x
6
1.302
x
1
,
x
2
,
x
3
,
x
7
1.056
x
5
CycA
x
3
1.010
x
2
,
x
6
1.388
x
2
,
x
6
,
x
8
1.032
x
2
,
x
3
,
x
6
,
x
8
3.659
x
6
Cdc
20
x
9
298.041
x
1
,
x
9
1.005
x
2
,
x
4
,
x
9
1.112
x
1
,
x
3
,
x
5
,
x
9
1.080
x
7
Cdh
1
x
6
1.058
x
6
,
x
9
2.720
x
5
,
x
6
,
x
9
5.007
x
1
,
x
3
,
x
6
,
x
9
1.052
x
8
UbcH
10
x
7
2.061
x
1
,
x
7
1.526
x
3
,
x
5
,
x
7
1.058
x
3
,
x
5
,
x
6
,
x
7
1.002
x
9
CycB
x
6
1.003
x
6
,
x
7
16.578
x
6
,
x
7
,
x
8
5.424
x
3
,
x
4
,
x
6
,
x
7
1.114
Now let us consider the underfit situation. For the target gene
x
i
, we expect either the
1-input predictor
x
j
or the 1-input predictor
x
k
will have low MSE as both predictors
contain input genes from the actual predictor (
x
j
,
x
k
). However, as the MSE of these
two predictors will be similar, the resolution ratio for the 1-input predictor
R
1
will
be low. Next, we consider the overfit situation. For the target gene
x
i
, we expect
any 3-input or larger predictor that contains
x
j
,
x
k
as a subset will have low MSE
since the that subset is the actual predictor, while any additional input genes only add
noise. As a result, several predictors will have similarly low MSE and the resolution
ratio
R
3
will again be low for the 3-input or 4-input predictor.
Our selection method determines the resolution ratio of all top rank predictors for
each input size, and then selects the top rank predictor with the highest resolution
ratio.
Table
4.21
(linear) and Table
4.22
(sigmoid) lists all the resolution ratios and top
rank predictors for the mutated mammal cell cycle network. The selected predictors
for each gene as chosen by our method is shown in Table
4.23
. In general, we find
the majority of selected predictors are the correct predictors for genes with adequate
expression sampling. Also, we find higher number of correctly select predictors using
the sigmoid representation for gene expression values.
