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thesis/sections/methodology.tex
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@@ -587,15 +587,17 @@ MAE was selected for its intuitive interpretability.
In particular, the fertility probability target lends itself well to an absolute error interpretation, In particular, the fertility probability target lends itself well to an absolute error interpretation,
making MAE a natural choice for evaluating prediction accuracy. making MAE a natural choice for evaluating prediction accuracy.
To enable a more nuanced comparison of model performance, To complement this, we also report the mean squared error (MSE):
we complement the overall MAE with targeted evaluations at biologically relevant subregions of the prediction sequence. \begin{align}
Rather than relying solely on the aggregate error across the full time series, \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
we compute MAE for specific intervals—such as before, during, and after the fertile window, \end{align}
as well as for individual days relative to ovulation. MSE penalizes larger errors more heavily than MAE, making it useful for highlighting substantial deviations.
This is particularly relevant for model comparison, where disproportionate errors can skew performance.
Moreover, since the fertility probability target was trained using an MSE-based loss function,
this metric directly reflects the optimization objective.
As discussed in Section~\ref{subsubsec:physiological_signs}, To enable a more nuanced comparison of model performance,
the five days leading up to ovulation are the most relevant for both contraception and natural family planning (NFP). we complement the overall error metrics with targeted evaluations at biologically relevant subregions of the prediction sequence.
These days are therefore evaluated individually.
This decomposition allows us to identify localized strengths and weaknesses in different models— This decomposition allows us to identify localized strengths and weaknesses in different models—
for example, a model may accurately capture the onset of fertility but underperform closer to ovulation. for example, a model may accurately capture the onset of fertility but underperform closer to ovulation.
@@ -619,21 +621,22 @@ Tables~\ref{tab:fertility_mae_metrics} and~\ref{tab:ov_over_mae_metrics} summari
\renewcommand{\arraystretch}{1.3} % spacing between rows \renewcommand{\arraystretch}{1.3} % spacing between rows
\begin{tabular}{@{}p{0.35\linewidth}p{0.60\linewidth}@{}} \begin{tabular}{@{}p{0.35\linewidth}p{0.60\linewidth}@{}}
\toprule \toprule
\textbf{Metric Name} & \textbf{Description} \\ \textbf{Metric Name} & \textbf{Description} \\
\midrule \midrule
Fertility Overall & Mean absolute error (MAE) over the entire sequence. \\ \multicolumn{2}{@{}l}{\textbf{Mean Absolute Error}} \\
Pre-Fertility & MAE before the fertile window. \\ \midrule
Post-Fertility & MAE after the fertile window. \\ Fertility Overall & MAE over the entire sequence. \\
During-Fertility & MAE during the fertile phase. \\ During-Fertility & MAE during the fertile phase. \\
First fertile day & MAE on the first fertile day (start of fertile phase). \\ Non-Fertility & MAE on the non-fertile days. \\
Second fertile day & MAE on the second fertile day. \\ \midrule
Third fertile day & MAE on the third fertile day. \\ \multicolumn{2}{@{}l}{\textbf{Mean Squared Error}} \\
Fourth fertile day & MAE on the fourth fertile day. \\ \midrule
Fifth fertile day & MAE on the fifth fertile day. \\ Fertility Overall & MSE over the entire sequence. \\
Sixth fertile day & MAE on the sixth fertile day (end of fertile phase). \\ During-Fertility & MSE during the fertile phase. \\
Non-Fertility & MSE on the non-fertile days. \\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\caption{Evaluation metrics of the fertility probability target based on mean absolute error (MAE) at various points across the predicted fertility window.} \caption{Evaluation metrics of the fertility probability target based on mean absolute error (MAE) at various intervals across the predicted fertility window.}
\label{tab:fertility_mae_metrics} \label{tab:fertility_mae_metrics}
\end{table} \end{table}
@@ -643,23 +646,42 @@ Tables~\ref{tab:fertility_mae_metrics} and~\ref{tab:ov_over_mae_metrics} summari
\renewcommand{\arraystretch}{1.3} % spacing between rows \renewcommand{\arraystretch}{1.3} % spacing between rows
\begin{tabular}{@{}p{0.35\linewidth}p{0.60\linewidth}@{}} \begin{tabular}{@{}p{0.35\linewidth}p{0.60\linewidth}@{}}
\toprule \toprule
\textbf{Metric Name} & \textbf{Description} \\ \textbf{Metric Name} & \textbf{Description} \\
\midrule \midrule
OV-Over Overall & Mean absolute error (MAE) over the entire sequence. \\ \multicolumn{2}{@{}l}{\textbf{Mean Absolute Error}} \\
Pre-OV & MAE before the ovulation. \\ \midrule
Post-OV & MAE after the ovulation. \\ OV-Over Overall & MAE over the entire sequence. \\
Four days before & MAE four days before the ovulation (beginning of fertile phase). \\ Pre-OV & MAE before the ovulation. \\
Three days before & MAE three days before the ovulation. \\ Post-OV & MAE after the ovulation. \\
Two days before & MAE two days before the ovulation. \\ \midrule
One day before & MAE one day before the ovulation. \\ \multicolumn{2}{@{}l}{\textbf{Mean Squared Error}} \\
Day of OV & MAE on the day of the ovulation. \\ \midrule
One day after & MAE one day after the ovulation (end of fertile phase). \\ OV-Over Overall & MSE over the entire sequence. \\
Pre-OV & MSE before the ovulation. \\
Post-OV & MSE after the ovulation. \\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\caption{Evaluation metrics of the ovulation-over target based on mean absolute error (MAE) at various points across the predicted fertility window.} \caption{Evaluation metrics of the ovulation-over target based on mean absolute error (MAE) at various intervals across the predicted fertility window.}
\label{tab:ov_over_mae_metrics} \label{tab:ov_over_mae_metrics}
\end{table} \end{table}
\subsubsection{Regular and Irregular Cycles}\label{subsubsec:methodology_regular_and_irregular_cycles}
A perfectly regular menstrual pattern does not require a sophisticated algorithm to predict ovulation—
the next ovulation day is likely to be identical or very close to the previous one.
To evaluate how different algorithms handle varying degrees of cycle variability,
we compare model performance on two distinct user groups: one with highly regular cycles and another with highly irregular cycles.
These groups are defined by the standard deviation of ovulation day across cycles.
Specifically, we select the 100 users with the lowest standard deviation (regular group)
and the 100 users with the highest standard deviation (irregular group).
This comparison allows us to assess not only overall performance,
but also whether ovulation can be meaningfully predicted in the presence of strong temporal irregularity.
For a user to be included in the analysis, they must have at least five completed cycles.
Additionally, ovulation must occur no later than cycle day 150, as later values likely indicate measurement errors or
biologically atypical cases that fall outside the scope of this study.
\subsubsection{Baseline Comparisons}\label{subsubsec:baseline_comparisons} \subsubsection{Baseline Comparisons}\label{subsubsec:baseline_comparisons}
To place model results into context, a set of simple baseline models was established. To place model results into context, a set of simple baseline models was established.