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Table 2. AUC and std.errors obtained from the single- and multi-view systems at a
case
level with the one-sided p -values and 95% confidence intervals for the differences
CASE
AUC ± std.err p -value Confidence interval
max
MV-CAD-Causal 0.833 ± 0 . 013
Method
-
-
MV-CAD-LR
0.835 ± 0 . 013
41%
( 0 . 007 , 0 . 005)
MV-CAD-NB
0.826 ± 0 . 014
21%
( 0 . 004 , 0 . 010)
SV-CAD
0.797 ± 0 . 014
1.1%
(0 . 003 , 0 . 040)
train
MV-CAD-Causal 0.847 ± 0 . 013
-
-
0.835 ± 0 . 014
(0 . 002 , 0 . 026)
MV-CAD-LR
1.3%
0.833 ± 0 . 014
(0 . 005 , 0 . 022)
MV-CAD-NB
0.1%
SV-CAD
0.797 ± 0 . 014
0.1%
(0 . 009 , 0 . 043)
The results show that MV-CAD-Causal significantly outperforms SV-CAD at
both breast and case level. With respect to the two multi-view benchmark
methods, our causal model is superior at a breast level and a case level us-
ing training as a combining scheme ( CaseNet ). As expected the case results
for MV-CAD-Causal using the maximum (MAX) out of two breast probabilities
has less satisfactory performance than using training in the causal independence
model. This shows that combining all available information in a proper way is
beneficial for accurate case classification.
Although MV-CAD-NB and MV-CAD-LR are overall less accurate than the last
two stages of the multi-view causal model, it is clear that all three MV-CAD
models achieve superior performance with respect to SV-CAD . This result follows
naturally from the explicit representation of multi-view dependences at a region
and view level of the multi-view model and it clearly indicates the importance
of incorporating multi-view information in the development of CAD systems.
To get more insight into the areas of improvement at a case level we plotted
ROC curves for all systems. For all the plots we observed the same tendency
of an increased true positive rate at low false positive rates ( < 0 . 5)-a result
ultimately desired at the screening practice where the number of normal cases
is considerably larger than the cancerous ones; Figure 8 presents the ROC plot
for the best performing models.
Evaluation of the multi-view model fitness. To have a closer look at the
quality of classification for the three multi-view models, we compute the av-
erage log-likelihood ( ALL ) of the probabilities for different units -link, region,
MLO/CC view, breast and case-by:
N
ALL ( Cl )= 1
N
ln P ( Cl i |E i ) ,
(3)
i =1
 
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