hopefully final commit
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Alex Blank
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\appendixpage % prints "Appendices"
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\section{Supplementary Results: Prediction of Ovulation-Over Indicator}\label{sec:appendix_ov_over_results}
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\subsection{Comparative Study of Model Architectures and Parameters}\label{subsec:appendix_ov_over_architecture_results}
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We evaluate prediction of a binary indicator denoting whether ovulation has already occurred.
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We examine the influence of input window length, input resolution, and model capacity.
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\paragraph{Impact of input window length.}
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For predicting whether ovulation has occurred (OV-over),
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optimal window lengths again vary by architecture and target phase (pre- vs post-ovulation).
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The \textbf{Transformer} yields the lowest overall (0.0533) and post-ovulation MSE (0.0520) at 40 days.
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The \textbf{LSTM} performs best before ovulation (MSE 0.0212 at 20 days), while its overall MSE improves with longer context (160 days).
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The \textbf{Convolutional LSTM} favors short windows, with the best overall MSE (0.0699), before-OV (0.0389),
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and after-OV (0.0833) all occurring at 20 days.
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The \textbf{Convolutional Transformer} performs best overall at 40 days and best before ovulation at 160 days (MSE 0.0286).
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See Table~\ref{tab:ovover_windows_compact_mse} for a summary.
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\begin{table}[t]
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\small
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\renewcommand{\arraystretch}{1.15}
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\setlength{\tabcolsep}{6pt}
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\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
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\toprule
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\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
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\cmidrule(r){2-4}
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& \shortstack[c]{Overall best\\(days / MSE)}
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& \shortstack[c]{Before-OV best\\(days / MSE)}
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& \shortstack[c]{After-OV best\\(days / MSE)} \\
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\midrule
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LSTM
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& 160 / 0.0557
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& \textbf{20 / 0.0212}
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& 160 / 0.0580 \\
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Transformer
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& \textbf{40 / 0.0533}
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& 20 / 0.0255
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& \textbf{40 / 0.0520} \\
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Convolutional LSTM
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& 20 / 0.0699
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& 20 / 0.0389
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& 20 / 0.0833 \\
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Convolutional Transformer
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& 40 / 0.0709
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& 160 / 0.0286
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& 40 / 0.0820 \\
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\bottomrule
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\end{tabularx}
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\caption{OV-Over: best input window per architecture (MSE only) at a fixed input resolution of 12 values/day.
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Bold entries are bests within a column.}
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\label{tab:ovover_windows_compact_mse}
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\end{table}
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\paragraph{Impact of input resolution.}
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Fixing the input window to 20 days, we compare input resolutions for LSTM and Transformer models.
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For the \textbf{LSTM}, the lowest overall MSE (0.0633) occurs at 24/day,
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with best before-OV and after-OV MSEs at 12/day (0.0212) and 48/day (0.0550), respectively.
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The \textbf{Transformer} performs best overall at 72/day (0.0585),
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with lowest before-OV MSE at 12/day (0.0255) and after-OV MSE at 288/day (0.0578).
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Results are summarized in Table~\ref{tab:ovover_resolution_compact_mse};
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full resolution grids are in Appendix Table~\ref{tab:ov_over_results_by_resolution}.
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\begin{table}[t]
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\small
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\renewcommand{\arraystretch}{1.15}
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\setlength{\tabcolsep}{6pt}
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\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
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\toprule
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\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
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\cmidrule(r){2-4}
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& \shortstack[c]{Overall best\\(values/day / MSE)}
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& \shortstack[c]{Before-OV best\\(values/day / MSE)}
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& \shortstack[c]{After-OV best\\(values/day / MSE)} \\
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\midrule
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LSTM
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& 24 / 0.0633
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& \textbf{12 / 0.0212}
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& \textbf{48 / 0.0550} \\
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Transformer
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& \textbf{72 / 0.0585}
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& 12 / 0.0255
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& 288 / 0.0578 \\
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\bottomrule
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\end{tabularx}
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\caption{OV-Over: best input resolution per architecture (MSE only) at a fixed input-window length of 20\,days.
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Bold entries are bests within a column. Convolutional models are excluded (they consume 288 values/day internally).}
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\label{tab:ovover_resolution_compact_mse}
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\end{table}
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\paragraph{Impact of model parameters.}
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Using fixed input settings (160 days at 12/day for LSTM/Transformer; 40 days for convolutional models), we evaluate model scaling.
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The \textbf{Transformer} achieves the lowest overall (0.0543) and after-ovulation MSE (0.0410) at a large configuration (512×8×8).
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Before-OV MSE is lowest at 256×4×4 (0.0293).
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For the \textbf{LSTM}, the best overall and after-OV performance is at 512×4,
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while the best before-OV MSE occurs at 128×2 (0.0274).
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The \textbf{Convolutional LSTM} performs best overall and after-OV at 256×4, with the best before-OV MSE at 128×2.
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Finally, the \textbf{Convolutional Transformer} achieves its lowest overall and after-OV MSE at 512×4×4, and best before-OV MSE at 512×8×8.
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Table~\ref{tab:ovover_params_compact_mse} summarizes these parameter-dependent results;
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full comparisons are included in Appendix Tables~\ref{tab:ov_over_results_by_model_parameters_lstm}–\ref{tab:ov_over_results_by_model_parameters_conv_transformer}.
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\begin{table}[t]
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\scriptsize
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\renewcommand{\arraystretch}{1.15}
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\setlength{\tabcolsep}{6pt}
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\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
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\toprule
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\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
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\cmidrule(r){2-4}
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& \shortstack[c]{Overall best\\(params / MSE)}
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& \shortstack[c]{Before-OV best\\(params / MSE)}
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& \shortstack[c]{After-OV best\\(params / MSE)} \\
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\midrule
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LSTM
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& \(512\times4\) / 0.0616
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& \textbf{\(128\times2\) / 0.0274}
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& \(512\times4\) / 0.0613 \\
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Transformer
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& \textbf{\(512\times8\times8\) / 0.0543}
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& \(256\times4\times4\) / 0.0293
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& \textbf{\(512\times8\times8\) / 0.0410} \\
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Convolutional LSTM
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& \(256\times4\) / 0.0687
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& \(128\times2\) / 0.0357
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& \(256\times4\) / 0.0715 \\
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Convolutional Transformer
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& \(512\times4\times4\) / 0.0703
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& \(512\times8\times8\) / 0.0339
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& \(512\times4\times4\) / 0.0814 \\
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\bottomrule
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\end{tabularx}
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\caption{OV-Over: best parameter settings per architecture (MSE only).
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Parameters are formatted as \(\text{hidden}\times\text{layers}\) (LSTM/Conv.\ LSTM) and \(\text{embedding}\times\text{encoder layers}\times\text{heads}\) (Transformer/Conv.\ Transformer).
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Bold values indicate bests within a column. Fixed input settings: 160\,days with 12 values/day for LSTM/Transformer; 40\,days for convolutional models.}
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\label{tab:ovover_params_compact_mse}
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\end{table}
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\subsection{Regular vs. Irregular Cycles}\label{subsec:appendix_ov_over_regular_vs_irregular}
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\begin{table}[htbp]
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\centering
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\small
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\begin{tabularx}{\linewidth}{l*{3}{X}}
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\toprule
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\multirow{2}{*}{Model} & \multicolumn{3}{c}{MSE} \\
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\cmidrule(r){2-4}
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& OV-Over Overall & OV-Over Before OV & OV-Over After OV \\
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\midrule
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\multicolumn{4}{c}{\textbf{Regular Cycle Group}} \\
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\midrule
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LSTM & \textbf{0.028519} & 0.031695 & \textbf{0.026116} \\
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Transformer & 0.032929 & \textbf{0.024774} & 0.033411 \\
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Convolutional LSTM & 0.034224 & 0.028962 & 0.033929 \\
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Convolutional Transformer & 0.033333 & 0.039045 & 0.029329 \\
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Last-Cycle Baseline & 0.087916 & 0.093465 & 0.074191 \\
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Population Mean Baseline & 0.285887 & 0.008876 & 0.418879 \\
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User Mean Baseline & 0.069245 & 0.069152 & 0.055724 \\
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\midrule
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\multicolumn{4}{c}{\textbf{Irregular Cycle Group}} \\
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\midrule
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LSTM & \textbf{0.051747} & \textbf{0.016777} & 0.070419 \\
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Transformer & 0.055990 & 0.026159 & 0.067520 \\
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Convolutional LSTM & 0.054523 & 0.030092 & \textbf{0.066643} \\
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Convolutional Transformer & 0.056075 & 0.029638 & 0.067965 \\
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Last-Cycle Baseline & 0.222906 & 0.134945 & 0.258047 \\
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Population Mean Baseline & 0.171368 & 0.130366 & 0.140363 \\
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User Mean Baseline & 0.180702 & 0.088884 & 0.217144 \\
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\bottomrule
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\end{tabularx}
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\caption{MSEs for ovulation-over target across different model architectures for regular and irregular cycle groups. Bold values denote the best scores per column.}
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\label{tab:ov_over_mse_regular_irregular}
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\end{table}
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\noindent
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Table~\ref{tab:ov_over_mse_regular_irregular} shows the MSE metric results for all models on the regular and irregular cycle groups for the OV-over target.
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For this target, performance patterns differ more distinctly across phases.
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In the regular group, the LSTM performs best overall and after ovulation, while the Transformer performs best before ovulation.
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Convolutional models perform slightly worse than their recurrent and transformer-based counterparts across all phases.
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The population mean baseline shows a spurious low MSE before ovulation, but this is not consistent across phases, suggesting it is not reliable.
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In general, baselines are notably weaker than learned models across all splits.
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For irregular cycles, all model performances deteriorate relative to regular cycles.
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The LSTM remains the most robust, achieving the best MSEs both overall and before ovulation.
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Convolutional LSTM performs best after ovulation.
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Transformer-based models perform less consistently in this group, suggesting decreased robustness to cycle irregularity.
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As before, all learned models outperform the baselines by a wide margin.
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The full table with MSE and MAE for all models can be found in the appendix, Table~\ref{tab:regular_vs_irregular_ov_over_results}.
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\section{Extra Figures}\label{app:figs}
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\begin{landscape}
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