Applications of High-Performance Computing to Functional Magnetic Resonance Imaging (fMRI) Data - High-Throughput Image Reconstruction and Analysis - page 275

were scaled down uniformly until the process became convergent. We obtained
500 time points of the realization. This realization was used to estimate the model
parameters using the Lasso regression. We report results only for k = 1inthis

paper.

12.4.3 Results
Figure 12.3 shows the precision and recall curves as a function of the Lasso regu-
larization penalty l [see (12.8)]. As the penalty is increased, the Lasso regression
estimates fewer nonzero coefficients. This improves the precision (i.e., the coeffi-
cients estimated to be nonzero are more likely to be nonzero) at the cost of recall
(i.e., many nonzero coefficients are estimated to be zero). Figure 12.4 shows the
precision-recall trade-off for different thresholds. It is evident from these figures
that as the threshold increases the precision and recall improves. Thus, the regres-
sion consistently makes less errors in estimating larger MAR coefficients.
The precision and recall measures only indicate the accuracy in estimating
whether a coefficient is nonzero or not. These measures do not convey any infor-
mation about the accuracy in the values of the MAR coefficients. The correlation
measures indicate the accuracy in estimating MAR coefficient values. Figure 12.5
shows the c true as a function of regularization penalty l for different thresholds.
For all thresholds, c true increases as l is increased. This indicates that higher regu-
larization penalty (l) results in fewer nonzero estimates, but with better accuracy.
This measure might be a bit misleading because it is only based on true positives
and does not consider false positives and false negatives. The measure c non-zero

Figure 12.3 Precision and recall as a function of l .