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Alex
2025-08-06 15:14:19 +02:00
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thesis/sections/methodology.tex
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@@ -607,16 +607,10 @@ This is particularly relevant for model comparison, where disproportionate error
Moreover, since the fertility probability target was trained using an MSE-based loss function,
this metric directly reflects the optimization objective.
Additionally, we add the coefficient of determination (\(R^2\)) regression score:
\begin{align}
R^2 = 1 - \frac{\sum_{i=1}^n (y_i - \hat{y}_i)^2}{\sum_{i=1}^n (y_i - \bar{y})^2}
\end{align}
where \(y_i\) is the observed value, \(\hat{y}_i\) the predicted value,
\(\bar{y}\) is the mean of observed values and \(n\) is the number of observations.
This coefficient indicates the proportion of total variance in the target that is explained by the model.
Since \( R^2 \) is specific to regression tasks, it is only applied to the fertility probability target.
All models operate on the same inputs and targets, so adjusted \( R^2 \) is not required.
We considered including the coefficient of determination (\(R^2\)) as an evaluation metric.
However, we found that the target windows frequently exhibited very low variance,
a condition under which \(R^2\) becomes unstable and potentially misleading.
As a result, we decided to exclude it from our evaluation.
To enable a more nuanced comparison of model performance,
we complement the overall error metrics with targeted evaluations at biologically relevant subregions of the prediction sequence.
@@ -643,25 +637,19 @@ Tables~\ref{tab:fertility_mae_metrics} and~\ref{tab:ov_over_mae_metrics} summari
\renewcommand{\arraystretch}{1.3} % spacing between rows
\begin{tabular}{@{}p{0.35\linewidth}p{0.60\linewidth}@{}}
\toprule
\textbf{Metric Name} & \textbf{Description} \\
\textbf{Metric Name} & \textbf{Description} \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Mean Absolute Error}} \\
\midrule
Fertility Overall & MAE over the entire sequence. \\
During-Fertility & MAE during the fertile phase. \\
Non-Fertility & MAE on the non-fertile days. \\
Fertility Overall & MAE over the entire sequence. \\
During-Fertility & MAE during the fertile phase. \\
Non-Fertility & MAE on the non-fertile days. \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Mean Squared Error}} \\
\midrule
Fertility Overall & MSE over the entire sequence. \\
During-Fertility & MSE during the fertile phase. \\
Non-Fertility & MSE on the non-fertile days. \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Coefficient of Determination (\(R^2\))}} \\
\midrule
Fertility Overall & \(R^2\) over the entire sequence. \\
During-Fertility & \(R^2\) during the fertile phase. \\
Non-Fertility & \(R^2\) on the non-fertile days. \\
Fertility Overall & MSE over the entire sequence. \\
During-Fertility & MSE during the fertile phase. \\
Non-Fertility & MSE on the non-fertile days. \\
\bottomrule
\end{tabular}
\caption{Evaluation metrics of the fertility probability target based on mean absolute error (MAE) at various intervals across the predicted fertility window.}
@@ -717,7 +705,7 @@ enabling comparability between models and providing interpretable performance me
\paragraph{Contraception Use-Case:}
For evaluating contraceptive effectiveness, we developed an algorithm inspired by the classical \emph{Pearl Index},
initially proposed by~\citeauthor{pearl_factors_1933} in~\citeyear{pearl_factors_1933}.
initially proposed by~\citeauthor{pearl_factors_1933} in~\citeyear{pearl_factors_1933}\cite{pearl_factors_1933}.
\begin{figure}[htbp]
\centering