Page 204 - Artificial Intelligence for Computational Modeling of the Heart

176 Chapter 5 Machine learning methods for robust parameter estimation

the best CASCADEGEP run 0.1 ± 0.2 ms for QRSd and 11.2 ± 15.8 ◦
for EA, respectively. In summary, all three methods yielded com-
parable performance in terms of EA error, SIMPLEGEP and the
proposed method performed similarly in terms of QRSd and were
outperformed in this regard by CASCADEGEP. However, consid-
ering success rates (successfully personalized patients according
to the defined convergence criteria), both the performance of
Vito (67%) and CASCADEGEP (68%) were equivalent, while SIM-
PLEGEP reached only 49% or less. In terms of run-time, i.e. aver-
age number of forward model runs until convergence, Vito (31.8)
almost reached the high efficiency of SIMPLEGEP (best: 20.1 iter-
ations) and clearly outperformed CASCADEGEP (best: 86.6 itera-
tions), which means Vito was ≈ 2.5× faster.
Residual error after initialization One major advantage over
standard methods is the data-driven initialization step (see sec-
tion 5.3.2.1), which eliminates the need for the user to provide
initial parameter values. To evaluate the utility of this step, we
evaluated the forward model with the computed initialization
without further personalization, then quantified the resulting er-
rors and compared them against the error after initialization when
fixed initial values were used (based on initialization of the best
performing BOBYQA run). This was done for increasing number of
0
5
transition samples per dataset: n samples = 10 ...10 .Fig. 5.7 shows
that by increasing training data, both errors decreased notably. In
fact, only 100 transitions per dataset suffice to become more ac-
curate than the best tested fixed initial values.
In summary, the proposed initialization not only simplifies the
setup, as it removes the need for user-provided initialization, this
experiment also showed that it can reduce initial errors by a large
margin with only few training transitions available. It should be
noted again that in its normal operating mode (continue person-
alization after initialization), the model fit is further improved, as
demonstrated in the previous experiment.
Convergence analysis With the next experiment, we investigated
how much training data (transition samples) were needed to
achieve solid performance of the agent. To this end, we evaluated
the proposed method with varying number of training transition
samples per dataset and found increasing performance with in-
creasing training data (Fig. 5.8), suggesting that the learning pro-
2
cess was working properly. At n samples = 10 samples per patient,
we already outperformed the best version of SIMPLEGEP (49% suc-
cess rate). Starting from n samples ≈ 3000, a plateau at ≈ 66% success
rate was reached, which then remained approximately constant
and almost on par with the top CASCADEGEP performance (68%
success rate). Also the number of model runs until convergence