hopefully final commit
This commit is contained in:
Alex Blank
+33
-3
@@ -38,7 +38,7 @@
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\begin{titlepage}
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\centering
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{\large \textbf{Leipzig University}}\\[1.5cm]
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{\large Faculty of Mathematics and Computer Science}\\[2cm]
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{\large Faculty of Mathematics and Computer Science}\\[1cm]
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\includegraphics[width=7cm]{leipzig_university_logo}\\[1cm] % Adjust size as needed
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@@ -47,7 +47,9 @@
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\textbf{Master’s Thesis}\\[1cm]
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\textbf{Author:}\\
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Alexander Blank\\[0.5cm]
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Alexander Blank\\ [0.2cm]
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Matriculation Number: \\
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3796505\\ [0.5cm]
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\textbf{Supervisor:}\\
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Prof. Bogdan Franczyk\\
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@@ -62,7 +64,22 @@
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\pagebreak
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\begin{abstract}
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This could be your abstract - call 0800 - ABSTRACT to get your personal quote.
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This thesis investigates the feasibility of predicting fertility from high-resolution body
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core temperature data using machine learning.
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More than 40,000 cycles recorded with an intravaginal sensor were used to train and evaluate recurrent,
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transformer-based, and convolutional model variants.
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Results show that while LSTM models achieved the lowest error on standard metrics,
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transformer-based architectures performed more robustly in use-case evaluations
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for contraception and natural family planning (NFP).
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Predictions were substantially more accurate in regular cycles than in irregular ones,
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underlining both the promise and the limits of temperature-based approaches.
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A pre-ovulatory temperature drop was identified as a relevant physiological marker influencing fertility probability.
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In simulated use cases, model predictions approached the effectiveness of established contraceptive
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methods and enabled more efficient timing for conception efforts.
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Despite the limitations of retrospective labeling, noisy real-world data,
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and the restriction to temperature as a single modality,
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the study demonstrates that machine learning can meaningfully advance individualized fertility prediction.
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These results provide a foundation for future multimodal approaches and for the development of adaptive, user-tailored fertility support tools.
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\end{abstract}
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\pagebreak
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@@ -97,6 +114,19 @@
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Responsibility for the content, structure, and conclusions of this thesis remains entirely my own.
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\pagebreak
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I hereby declare that I have written the present thesis independently and only with the use of the sources and aids indicated.
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In particular, literal or paraphrased quotations are marked as such.
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I am aware that any violation may lead, even retrospectively,
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to the revocation of the degree.
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I further declare that the electronic copy is identical to the printed copies.
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\vspace{2cm}
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\noindent
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\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l c r}
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Location: & Date: & Signature: \\
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\end{tabular*}
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\include{sections/appendix}
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\printbibliography
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@@ -2,6 +2,202 @@
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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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@@ -71,7 +71,7 @@ Over time, the temperature does not show any significant or longer lasting tempe
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To illustrate the diversity of real-world menstrual cycles, Figures~\ref{fig:background_long_cycle} and~\ref{fig:background_short_cycle}
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show examples of cycles that are significantly longer or shorter than a normative 28-day cycle.
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\citeauthor{bull_real-world_2019} have done an extensive study on cycle variability,
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highlighting that women frequently deviate from the normative cycle, especially with age\cite{bull_real-world_2019}.
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highlighting that women frequently deviate from the normative cycle, especially with age~\cite{bull_real-world_2019}.
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\begin{figure}[htbp]
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\centering
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@@ -116,7 +116,7 @@ The distribution of fertility probability is not dependent on the length of the
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.7\textwidth]{resources/figures/background/background_pregnancy_chance_over_time}
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\includegraphics[width=0.7\textwidth]{resources/figures/background/fertility_probability_relative_to_ovulation}
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\caption{Chance of fertilization depending on the day of the menstrual cycle.
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The highest chance is around one day before ovulation~\cite{dunson_day-specific_1999}.}
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\label{fig:background_pregnancy_chance}
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@@ -202,7 +202,8 @@ In addition to temperature measurements, the database includes contextual metada
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These markers provide further physiological context and may include information about intermediate bleeding, sexual intercourse, or positive pregnancy tests.
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At the time of writing, the dataset contains approximately 65{,}000 annotated cycles,
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comprising more than 350 million individual temperature measurements~\footnote{This is the largest dataset of continuous body core temperature data used in any study so far.}.
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comprising more than 350 million individual temperature measurements.
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This is the largest dataset of continuous body core temperature data used in any study so far.
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\subsubsection{Dataset Summary}
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For the present study, the dataset was reduced to approximately 40{,}000 cycles after filtering out entries that were incomplete,
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@@ -281,7 +282,10 @@ Recurrent Neural Networks (RNNs) and the more recent Transformer architecture.
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Recurrent Neural Networks (RNNs) are extensions of classical neural networks that incorporate cyclic connections between neurons.
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These recurrent connections allow the network to retain information from previous inputs by feeding the hidden state
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from a prior time step into the current one, enabling a form of temporal memory.
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They process input \emph{sequentially}, maintaining this hidden state over time.
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Recurrent Neural Networks (RNNs) process sequences in a strictly sequential manner,
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where each token's representation depends on the preceding token.
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This results in a per-layer time complexity of $\mathcal{O}(n \cdot d^2)$, where $n$ is the sequence length and $d$ is the hidden state size.
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In practice, this means that input data is processed sequentially, one step at a time.
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At each step \(t\), the input \(x_t\) is combined with the previous hidden state \(h_{t-1}\) to produce a new
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@@ -324,46 +328,61 @@ information: the \emph{forget gate}, the \emph{input gate}, and the \emph{output
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\item The \emph{output gate} selects relevant parts of the current cell state to produce the output and the next hidden state.
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\end{itemize}
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Each gate employs a sigmoid activation function to regulate the flow of information,
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allowing LSTMs to preserve and update memory over long sequences.
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Each gate uses a sigmoid activation to produce values in \([0, 1]\),
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regulating how much information passes through.
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This gating mechanism enables LSTMs to maintain relevant information over long sequences
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while discarding irrelevant parts.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.6\textwidth]{resources/figures/background/background_lstm_structure}
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\caption{Architecture of a memory cell \( c_j \) and its gate units \( \text{in}_j \) and \( \text{out}_j \).
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At the center, the self-recurrent linear unit (with weight 1.0) maintains the internal state~\cite{hochreiter_long_1997}.
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See text for more details.}
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\includegraphics[width=0.6\textwidth]{resources/figures/background/lstm_cell_diagram}
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\caption{Architecture of a memory cell and its gate units (Image source: \cite{chevalier_english_2018}).}
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\label{fig:lstm_architecture}
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\end{figure}
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The LSTM unit maintains an internal state \( s_{c_j}(t) \) for each cell $c_j$ that evolves over time to capture long-term dependencies.
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Figure~\ref{fig:lstm_architecture} shows the structure of a memory cell along with its input and output gates.
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The \emph{input gate} activation \( y_j^{\text{in}}(t) \) controls the influence of the new candidate input \( g(\text{net}_{c_j}(t)) \) on the state update (Eq.~\eqref{eq:state_update}):
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The LSTM maintains an internal cell state \(c_t\), which is updated at each time step.
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First, the forget gate activation \(f_t\) determines how much of the previous state is retained:
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\begin{equation}
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s_{c_j}(t) = s_{c_j}(t - 1) + y_j^{\text{in}}(t) \cdot g(\text{net}_{c_j}(t))
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f_t = \sigma\left(W_f \cdot [h_{t-1}, x_t] + b_f\right)
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\label{eq:forget_gate}
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\end{equation}
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The input gate \(i_t\) and the candidate cell state \(\tilde{c}_t\) are computed as:
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\begin{align}
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i_t &= \sigma\left(W_i \cdot [h_{t-1}, x_t] + b_i\right)
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\label{eq:input_gate} \\
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\tilde{c}_t &= \tanh\left(W_c \cdot [h_{t-1}, x_t] + b_c\right)
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\label{eq:candidate_state}
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\end{align}
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The new cell state \(c_t\) is then updated by combining the retained previous state
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with the gated candidate state:
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\begin{equation}
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c_t = f_t \cdot c_{t-1} + i_t \cdot \tilde{c}_t
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\label{eq:state_update}
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\end{equation}
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|
||||
The \emph{output gate} \( y_j^{\text{out}}(t) \), computed from \( \text{net}_{\text{out}_j}(t) \), determines how much of the transformed internal state is passed on as visible output (Eq.~\eqref{eq:cell_output}):
|
||||
|
||||
\begin{equation}
|
||||
y_j^{c}(t) = y_j^{\text{out}}(t) \cdot h(s_{c_j}(t))
|
||||
\label{eq:cell_output}
|
||||
\end{equation}
|
||||
|
||||
\(g\) and \(h\) are differentiable functions, here \emph{tanh}.
|
||||
The gate activations themselves are derived from net inputs formed as weighted sums of previous outputs \( y^u(t-1) \), as given by:
|
||||
Next, the output gate \(o_t\) determines how much of the transformed cell state
|
||||
is exposed as hidden state:
|
||||
|
||||
\begin{align}
|
||||
\text{net}_{\text{out}_j}(t) &= \sum_u w_{\text{out}_j,u} \, y^u(t - 1) \label{eq:net_out} \\
|
||||
\text{net}_{\text{in}_j}(t) &= \sum_u w_{\text{in}_j,u} \, y^u(t - 1) \label{eq:net_in} \\
|
||||
\text{net}_{c_j}(t) &= \sum_u w_{c_j,u} \, y^u(t - 1) \label{eq:net_c}
|
||||
o_t &= \sigma\left(W_o \cdot [h_{t-1}, x_t] + b_o\right)
|
||||
\label{eq:output_gate} \\
|
||||
h_t &= o_t \cdot \tanh(c_t)
|
||||
\label{eq:cell_output}
|
||||
\end{align}
|
||||
|
||||
During training, the weights associated with the inputs \( x_t \) and previous outputs \( h_{t-1} \),
|
||||
as well as the biases for each gate in a cell, are learned through backpropagation.
|
||||
To build more expressive models, memory cells can be stacked in multiple layers, and their outputs concatenated or passed sequentially to higher layers.
|
||||
Here, \(\sigma\) denotes the sigmoid function.
|
||||
All gates depend on both the previous hidden state \(h_{t-1}\) and the current input \(x_t\).
|
||||
The weight matrices \(W_f, W_i, W_c, W_o\) and biases \(b_f, b_i, b_c, b_o\)
|
||||
are learned during training via backpropagation through time.
|
||||
|
||||
By combining multiplicative gates and additive memory updates, LSTMs can learn when to forget,
|
||||
update, and expose information, solving key limitations of vanilla RNNs in sequence modeling tasks.
|
||||
|
||||
LSTMs are widely used in biomedical applications due to their capacity to handle sequences of variable length and complexity.
|
||||
In the context of fertility prediction, where hormonal patterns exhibit periodicity but also irregularity,
|
||||
@@ -388,6 +407,9 @@ Unlike recurrent neural networks (RNNs), Transformers process input sequences \e
|
||||
allowing them to model relationships between any pair of input tokens or timesteps directly.
|
||||
This design mitigates the limitations of recurrent models, such as long-term memory constraints
|
||||
and vanishing gradients.
|
||||
However, the per-layer time complexity is $\mathcal{O}(n^2 \cdot d)$, due to the quadratic cost of computing pairwise attention across the $n$ tokens.
|
||||
Unlike RNNs, Transformers also cannot inherently process sequences of variable length.
|
||||
Additional preprocessing steps, such as padding or windowing must be applied to support these.
|
||||
|
||||
Originally introduced for machine translation, Transformers have proven broadly applicable to
|
||||
various sequence modeling tasks due to their flexibility, scalability, and strong performance
|
||||
@@ -401,7 +423,7 @@ linearly projected from the input and used to compute attention scores.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.4\textwidth]{resources/figures/background/background_transformer_architecture}
|
||||
\caption{The Transformer - architecture for an encoder-decoder model~\cite{vaswani_attention_2017}}
|
||||
\caption{The Transformer - architecture for an encoder-decoder model (Image source: \cite{vaswani_attention_2017})}
|
||||
\label{fig:background_transformer_architecture}
|
||||
\end{figure}
|
||||
|
||||
@@ -417,7 +439,7 @@ In the case of machine translation, this input would be a sentence in the source
|
||||
|
||||
|
||||
The input tokens are first mapped to dense continuous vector representations (embeddings).
|
||||
Since the attention mechanism permutation-invariant, that is, it does not inherently encode the order of tokens in the sequence,
|
||||
Since the attention mechanism is permutation-invariant, that is, it does not inherently encode the order of tokens in the sequence,
|
||||
\emph{positional encodings} are added to the token embeddings to provide information about the token positions in the sequence.
|
||||
|
||||
Without positional encoding, repeated tokens such as `The` would be indistinguishable
|
||||
@@ -564,11 +586,11 @@ For high-resolution time-series data, the input dimensionality can become large,
|
||||
especially in models like Transformers that process the entire sequence in parallel.
|
||||
This can lead to increased memory consumption and slower training.
|
||||
To mitigate this and retain as much information as possible, convolutional layers can be used
|
||||
to reduce the sequence length while preserving important local patterns.
|
||||
to reduce the sequence length while preserving important local patterns~\cite{lecun_gradient-based_nodate}.
|
||||
|
||||
In this context, one-dimensional convolutions act as learnable filters that slide over the input sequence to extract temporal features.
|
||||
Each filter is parameterized to respond to specific local structures in the data, such as peaks, slopes, or short-term motifs.
|
||||
By adjusting the \emph{stride}—the step size of the convolution—the model can control the degree of downsampling,
|
||||
By adjusting the \emph{stride}, the step size of the convolution, the model can control the degree of downsampling,
|
||||
effectively reducing the number of time steps passed to subsequent layers.
|
||||
|
||||
Additional dimensionality reduction can be achieved using pooling operations, such as \emph{max pooling}, which retains only the maximum value within a given window.
|
||||
|
||||
@@ -2,4 +2,34 @@
|
||||
%! Date = 3/6/25
|
||||
|
||||
|
||||
\section{Conclusion}\label{sec:conclusion}
|
||||
\section{Conclusion}\label{sec:conclusion}
|
||||
|
||||
This thesis presented a systematic investigation of different machine learning architectures
|
||||
for fertility prediction based on high-resolution body core temperature data.
|
||||
By comparing LSTM- and Transformer-based models, as well as their convolutional variants,
|
||||
the results show that machine learning can achieve high predictive performance.
|
||||
LSTM models performed best according to standard evaluation metrics, whereas Transformer-based models
|
||||
proved more robust in simulated use-case evaluations for contraception and Natural Family Planning (NFP).
|
||||
Predictions were consistently more reliable in regular cycles than in irregular ones,
|
||||
highlighting both the potential and the inherent limits of temperature-based approaches.
|
||||
|
||||
A characteristic pre-ovulatory temperature drop was identified as correlating with fertility.
|
||||
Both its timing and its magnitude appear to influence fertility probability,
|
||||
pointing to a concrete physiological marker that could be exploited in practice.
|
||||
|
||||
Use-case evaluations indicate that the model outputs could be highly relevant for contraception and NFP\@.
|
||||
In simulations, pregnancy rates approached those reported for commonly used contraceptives such as condoms
|
||||
or oral contraceptives, and with simple additional measures could even approximate the effectiveness of
|
||||
long-term hormonal methods or sterilization.
|
||||
While pregnancy rates for the NFP use-case were not significantly improved,
|
||||
the predictions enabled a four-fold increase in the efficiency of timed intercourse,
|
||||
facilitating more targeted pregnancy efforts for couples.
|
||||
|
||||
Despite the limitations of real-world tracking data, including missing entries, noise,
|
||||
and user heterogeneity, this work underscores the potential of personalized, data-driven predictions
|
||||
in digital reproductive health.
|
||||
Future work should integrate additional physiological signals, expand demographic representation,
|
||||
and validate models in prospective real-world settings.
|
||||
|
||||
In sum, this study contributes a systematic foundation for machine learning-based fertility prediction
|
||||
and sets the stage for adaptive, user-tailored fertility support tools.
|
||||
+83
-173
@@ -4,7 +4,7 @@
|
||||
|
||||
\section{Discussion}\label{sec:discussion}
|
||||
|
||||
\subsection{RQ1: Model Architecture Evuation an Optimization}\label{subsec:discussion_rq1_model_evaluation}
|
||||
\subsection{Objective 1: Model Architecture Evuation an Optimization}\label{subsec:discussion_rq1_model_evaluation}
|
||||
|
||||
|
||||
The first research objective considered different model architectures and how they perform
|
||||
@@ -71,7 +71,7 @@ as a direct regression target, might prove more stable and informative.
|
||||
As we will see in the next section, the current targets are highly sensitive to anomalies,
|
||||
which may not be the case for alternative formulations.
|
||||
|
||||
\subsection{RQ2: Factors and Patterns that Influence Prediction}\label{susbsec:discussion_rq2_factors_and_patterns}
|
||||
\subsection{Objective 2: Factors and Patterns that Influence Prediction}\label{susbsec:discussion_rq2_factors_and_patterns}
|
||||
|
||||
Our second research objective focused on identifying potential factors and patterns in the data
|
||||
that influence fertility prediction.
|
||||
@@ -116,7 +116,7 @@ This could lead to a more biologically grounded interpretation of the patterns u
|
||||
Moreover, improvements in label quality will naturally improve the interpretability and accuracy of predictions.
|
||||
Better labels would also allow more reliable medical interpretation of the prediction outputs and the patterns driving them, as previously discussed.
|
||||
|
||||
\subsection{RQ3: Performance Across Regular and Irregular Cycles}\label{subsec:discussion_rq3_regular_vs_irregular}
|
||||
\subsection{Objective 3: Performance Across Regular and Irregular Cycles}\label{subsec:discussion_rq3_regular_vs_irregular}
|
||||
|
||||
The third research objective of this study was to compare model performance across subsets of users
|
||||
with regular and irregular menstrual cycles.
|
||||
@@ -159,190 +159,100 @@ Ideally, the model would have access to the entire cycle history of a user for t
|
||||
However, this would likely exceed the memory and capacity constraints of the architectures used in this study.
|
||||
Overcoming this limitation may require more efficient or hierarchical time series architectures, as previously discussed.
|
||||
|
||||
\subsection{RQ4: Use-case Evaluations}\label{subsec:discussion_rq4_use_case_evaluations}
|
||||
\subsection{Objective 4: Use-case Evaluations}\label{subsec:discussion_rq4_use_case_evaluations}
|
||||
|
||||
The fourth research objective was to evaluate two practical use-cases—natural contraception
|
||||
and natural family planning (NFP), using predefined evaluation algorithms.
|
||||
These algorithms approximate the effectiveness of different models across varying fertility thresholds.
|
||||
|
||||
% -------------------------------------------------------------------------------------
|
||||
This study set out to evaluate the predictive value of body temperature for ovulation and fertility,
|
||||
to assess the performance of different model architectures across use cases,
|
||||
and to compare machine learning models with rule-based baselines.
|
||||
Below we discuss the findings in relation to these objectives, their implications, and limitations.
|
||||
We found that for both use-cases, all trained models outperformed the baselines.
|
||||
There was notable variability between model types, with the Transformer model
|
||||
performing best, especially for low fertility thresholds, followed closely by the convolutional variants.
|
||||
The LSTM model consistently showed the weakest performance across all metrics.
|
||||
Still, both trained and baseline models yielded significant
|
||||
improvements over the control group, indicating that all model types offer meaningful predictive value.
|
||||
|
||||
\subsection{Predictive Value of Body Temperature}
|
||||
Our results confirm that body core temperature carries meaningful predictive value for ovulation and fertility,
|
||||
particularly in regular cycles with clear pre-ovulatory dips.
|
||||
This dip before the
|
||||
In such cases, fertility-probability curves aligned closely with the ground truth,
|
||||
demonstrating that models can reliably exploit this physiological marker.
|
||||
However, anomalies in the signal, such as irregular spikes or absent dips, frequently led to erroneous predictions.
|
||||
This suggests that the models strongly rely on short-term temperature fluctuations without
|
||||
distinguishing between ovulation-related and unrelated changes.
|
||||
To our knowledge, no previous work has explicitly evaluated use-cases of natural
|
||||
contraception or NFP with machine learning, or compared them to traditional contraceptive methods.
|
||||
This highlights the exploratory nature of this analysis.
|
||||
|
||||
The irregular-versus-regular cycle analysis reinforces this interpretation:
|
||||
prediction accuracy was consistently higher in regular cycles, indicating that models leverage cyclical regularity in
|
||||
addition to absolute thermal changes.
|
||||
Especially for regular cycles, the performance of the trained models
|
||||
\paragraph{Contraception Use-Case.}
|
||||
For the natural contraception scenario, Transformer-based architectures produced competitive results,
|
||||
achieving fewer than 5 pregnancies per 100 user-years for low thresholds.
|
||||
For context, the expected pregnancy rates per 100 user-years are approximately 12 for male condoms
|
||||
and around 7 for oral contraceptives (e.g., “the pill”).
|
||||
Only implanted hormonal contraceptives and sterilization achieve lower rates (under 1)~\cite{noauthor_birth_nodate}.
|
||||
In contrast, the control group, representing no contraception, resulted in 90 pregnancies per 100 user-years,
|
||||
which closely aligns with literature values (85 pregnancies per 100 women per year)~\cite{trussell_contraceptive_2011}.
|
||||
|
||||
%[continue here: bring in your figure-based examples of temperature drops, anomalies, and unclear cases, with interpretation rather than description.]
|
||||
As expected, the number of denials, i.e.,
|
||||
days on which a potential application would suggest abstinence,increases with the threshold.
|
||||
Therefore, a trade-off exists between minimizing pregnancies and minimizing denials.
|
||||
This trade-off is user-dependent: while some users prefer certainty and are comfortable with frequent denials,
|
||||
others may accept higher risk or use additional protective measures to mitigate it.
|
||||
|
||||
Taken together, these findings highlight both the utility and the limitations of body temperature as a single biomarker.
|
||||
While it provides a strong signal in favorable cases, its variability across users and cycles limits robustness in real-world applications.
|
||||
Additional biomarkers or contextual information are likely required to disambiguate genuine ovulatory patterns from noise.
|
||||
This highlights a critical limitation: all results are based on a naive,
|
||||
rigid denial strategy that did not incorporate any additional measures or contextual information
|
||||
beyond the raw model predictions.
|
||||
When combined with established behavioral protocols,such as abstinence during the early cycle phase,
|
||||
as used in several commercial products~\cite{thigpen_oura_2025, bull_real-world_2019},
|
||||
significantly lower pregnancy rates are likely achievable.
|
||||
|
||||
\subsection{Model Architectures and Use-Case Performance}
|
||||
Across architectures, LSTMs consistently outperformed both Transformers and convolutional models in the fertility-probability task.
|
||||
This was somewhat unexpected given the recent dominance of Transformer-based approaches in sequence modeling.
|
||||
The advantage of LSTMs likely stems from their strong inductive bias for sequential dependencies
|
||||
and the relatively small dataset size, which may limit the benefits of more parameter-heavy architectures.
|
||||
Convolutional models, by contrast, performed competitively on medium-length inputs,
|
||||
suggesting that localized temporal filters can capture useful features when the history is limited.
|
||||
However, they struggled with longer input sequences, where recurrent and attention-based models excelled.
|
||||
As shown in previous sections, irregular cycles require additional caution.
|
||||
All trained models had difficulty accurately predicting fertile days in these cases.
|
||||
Therefore, any real-world application must include mechanisms that warn users about
|
||||
potential inaccuracies and recommend additional precautions when irregular patterns are detected.
|
||||
|
||||
Resolution also proved important: medium-resolution inputs produced the strongest results,
|
||||
suggesting a balance between preserving relevant detail and avoiding noise.
|
||||
Too fine a resolution may amplify random fluctuations, while too coarse a resolution may obscure important cues.
|
||||
Future work could explore models that combine predicted fertility probabilities
|
||||
with contextual features—such as current follicular phase length—to generate
|
||||
more nuanced contraceptive guidance.
|
||||
|
||||
In practical use-case simulations, thresholding had a decisive effect.
|
||||
For contraception, a low threshold produced Pearl-Index equivalents in the range of 4–5,
|
||||
which is competitive with or better than common contraceptive methods under typical use.
|
||||
These numbers, however, must be treated as theoretical projections, since real-world outcomes depend on user behavior,
|
||||
adherence, and additional protective measures.
|
||||
For pregnancy planning, results were less directly comparable, reflecting the multifactorial nature of conception.
|
||||
Nonetheless, the analysis illustrates how probabilistic outputs could be adapted to individual risk preferences,
|
||||
highlighting the flexibility of machine learning approaches over fixed rules.
|
||||
\paragraph{Pregnancy Use-Case.}
|
||||
For the NFP use-case (i.e., attempting to conceive), all trained models achieved
|
||||
nearly double the pregnancy rate compared to the baselines.
|
||||
However, at low fertility thresholds, the baseline models showed higher efficiency in terms
|
||||
of pregnancies per 1000 intercourse events.
|
||||
Despite this, trained models maintained the overall advantage in total pregnancies per 100 user-years.
|
||||
|
||||
At low thresholds, all models achieved approximately 90 pregnancies per 100 user-years,
|
||||
decreasing to 70--80 at higher thresholds.
|
||||
The number of correct deferrals, days correctly identified as non-fertile, rose with increasing thresholds,
|
||||
again suggesting that users may benefit from personalized thresholds depending
|
||||
on the intensity of their conception efforts.
|
||||
|
||||
Most related studies report pregnancy outcomes over 12 cycles, which we assume to represent roughly one year.
|
||||
We use the 100 user-years metric for consistency.
|
||||
Since fertility status of couples in our dataset is unknown, we assume that all included users are generally fertile.
|
||||
|
||||
%\section{Discussion}\label{sec:discussion}
|
||||
Related research usually refers to pregnancies per 100 women over 12 cycles.
|
||||
We assume that, on average 12 cycles represent one year, and thus use the 100 user-years metric as comparison.
|
||||
We cannot make any assumptions about the fertility of couples in our study, thus we assume that all users sampled
|
||||
are generally able to conceive.
|
||||
|
||||
The model selection study based on the input window length, input resolution and model complexity parameters has shown,
|
||||
longer input windows and higher complexity seem to be favourable for the purposes of this study.
|
||||
The convolutional models show better performance for medium length input windows, which might be a limitation
|
||||
of the model or its convolutional layers.
|
||||
It thus seems like, the more historical measurements are available, the better
|
||||
Among commercial fertility monitors, pregnancy rates over 12 cycles range
|
||||
from 68\% to 72\% (with additional cervical mucus tracking)~\cite{bouchard_achieving_2018}.
|
||||
Our method reaches approximately 80\%, without requiring additional measures,
|
||||
placing it at the upper end of current non-invasive fertility prediction tools.
|
||||
|
||||
The LSTM and Transformer models also work better with medium resolution input, which suggests a sweet-spot of information.
|
||||
Too small a resolution might omit important information, while the opposite might introduce too much noise,
|
||||
that the models in the current configuration cannot handle.
|
||||
It could be worth investigating how more complex models handle more complex input data,
|
||||
as this grid-search was not possible in this study due to time and resource limitations.
|
||||
Interestingly, control group results show that high pregnancy rates are achievable
|
||||
even without targeted timing: random intercourse (approximately 6 times per month)
|
||||
resulted in 90 out of 100 women becoming pregnant within one year, which aligns
|
||||
with literature estimates that ~85\% of couples conceive within a year without
|
||||
timing-based intervention~\cite{pfeifer_optimizing_2017}.
|
||||
|
||||
The study also showed, that the LSTM and Transformer base models outperform the convolutional models.
|
||||
However, this is only the case for longer input sequences.
|
||||
When isolating a 40-day input window, the convolutional models outperform the non-convolution models,
|
||||
which suggests, that there is an informational benefit in the convolution.
|
||||
However, the convolutional models seem to struggle with longer input windows,
|
||||
which clearly represent a benefit for the predictive tasks, as the normal LSTM and Transformer models perform better
|
||||
on longer input windows.
|
||||
Additional work might be necessary to investigate, whether the convolutional models need additional complexity
|
||||
or an optimized convolutional pre-processing to deal with longer input sequences.
|
||||
The benefit of model-based prediction becomes more evident when examining efficiency.
|
||||
While most related work ignores intercourse frequency, our results show that
|
||||
trained and baseline models significantly outperform the control group in pregnancies per 1000 intercourse events.
|
||||
At mid-range threshold values, trained models demonstrated a four-fold increase in efficiency,
|
||||
indicating that model guidance can substantially optimize the effort-to-outcome ratio for couples trying to conceive.
|
||||
|
||||
Overall, the standard LSTM showed the best performance on the fertility-probability target.
|
||||
This came to our surprise, as we expected the Transformer based architecture to outperform the LSTM based architectures.
|
||||
The convolutional Transformer had a lower error rate than the convolutional LSTM, which aligned with our expectations.
|
||||
But it is hard to interpret the results to thoroughly, as they have been taken on single measurement basis.
|
||||
For a further evaluation, each model should be evaluated multiple times to get statistically more significant and comparable results.
|
||||
The resource and time limitations of this study did not permit this.
|
||||
Another useful metric could be time-to-pregnancy across different models and the control group.
|
||||
The same pregnancy rate over one year can represent conception in the first or twelfth month,
|
||||
which has practical significance for users.
|
||||
Including this temporal dimension would allow for a more detailed comparative analysis.
|
||||
|
||||
We will be focusing mainly on the predictive quality of the fertility-probability target,
|
||||
as most selections and evaluations were based on it and the fertility-probability contains the most relevant information
|
||||
for potential users of the predictions.
|
||||
|
||||
All prediction curve in this section have been generated with the best model selected in section~\ref{subsubsec:results_best_model_config_selection},
|
||||
i.e., the LSTM model.
|
||||
Figure~\ref{fig:discussion_regular_cycle_fertility_prediction} shows the prediction curve for the fertility-probability target
|
||||
for a user with a regular cycle pattern.
|
||||
For such a regular cycle pattern, the predictions almost exactly match the targets.
|
||||
Another noteworthy observation is the correlation between a clear temperature drop preceding ovulation and
|
||||
the fertility rising.
|
||||
This can be seen more prominently in Figure~\ref{fig:discussion_temperature_drop_fertility_prediction}.
|
||||
The model seems to identify that this drop must be an indication for a heightened fertility.
|
||||
However, this decrease in temperature is not visible for all cycles, and thus significantly impacts the prediction qualities of the model.
|
||||
Figure~\ref{fig:discussion_spike_in_temperature_drop} shows an anomaly that results in a temperature spike during
|
||||
the pre-ovulatory temperature dip.
|
||||
This confuses the model into ending the fertile phase earlier.
|
||||
|
||||
This suggests that the model may interpret the termination of the pre-ovulatory temperature decline as a
|
||||
signal that ovulation is imminent or has just occurred, thus marking the end of the fertile window.
|
||||
Another pattern that is visible for many users is a cycle with no clear temperature drop.
|
||||
Figure~\ref{fig:discussion_unclear_temperature_drop} shows such a curve.
|
||||
Here, potentially unrelated circumstances lead to a drop in temperature that the model incorrectly identifies as fertile days.
|
||||
The actual fertile days don't result in an equally visible temperature drop.
|
||||
This indicates, that a clear temperature drop is a precursor to the ovulation and comes with the fertile days,
|
||||
but its intensity varies between users and also between cycles of the same user.
|
||||
Such a pattern can turn out to be a useful predictor for ovulation / fertility, but the models we trained don't seem
|
||||
to be able to differentiate between ovulation-related and unrelated temperature drops.
|
||||
|
||||
This also points to a potential flaw in our workflow.
|
||||
We don't yet have clinically accurate labels for the cycles that were used for the training of our models.
|
||||
In fact, we cannot guarantee an ovulation, not even for the cycles with a clear temperature rise after the apparent ovulation.
|
||||
The identified temperature drop and the fertility that seems to come with it could be a base for further research
|
||||
with more accurate ovulation labeling.
|
||||
It might be an indicator for a successful upcoming ovulation.
|
||||
|
||||
|
||||
The results of the irregular vs regular cycle study, as shown in~\ref{subsubsec:regular_vs_irregular_cycles},
|
||||
indicate, that the models seem to learn recurrent cycle pattern on a per-user basis.
|
||||
We conclude this based on the fact, that regular cycle performance is significantly better than the performance on the irregular cycle set.
|
||||
If there is a reliable indicator in the temperature data, or its ablations, then there would not be a large difference between the two subsets.
|
||||
The temperature patterns should show up in both regular and irregular cycle users.
|
||||
Thus, all models must learn or extract information beyond the actual temperature data, which they seem to rely on more than
|
||||
the temperature related features.
|
||||
This is likely information indicating some form of regularity, which the models then use to predict the targets for new cycles.
|
||||
It would be interesting to take a close look at how and in what intensity the models use certain features,
|
||||
and whether the performance changes upon omitting certain features.
|
||||
|
||||
\paragraph{Use-Case Study.}
|
||||
|
||||
The threshold has a large effect on the overall effectiveness of the different use cases.
|
||||
For the contraception use case, changing the threshold doubles and even quadruples the pregnancy rate.
|
||||
It has to be noted, that the contraception use case is naive use-case, where the woman does not take any other
|
||||
measures next to the prediction of our models.
|
||||
In a real-world scenario, this is largely not the case, and thus the pregnancy rates should be even lower.
|
||||
A measure often taken is abstinence during the first cycle phase (luteal phase), which should significantly lower
|
||||
unwanted pregnancies.
|
||||
Even without additional measures, a threshold of 0.05 leads to an approximate \emph{Pearl-Index} (pregnancy rate over 1 year for 100 women)
|
||||
of 4--5, which is significantly better than methods such as the contraceptive pill (7) or the condom (13) for a typical use case.
|
||||
However, these numbers have to be taken with caution, as this is not an actual study, but a naive theoretical projection.
|
||||
Further research is necessary to find more reliable results.
|
||||
|
||||
The pregnancy use case is harder to contextualize, as there are no comparable results for other methods,
|
||||
and the actual pregnancy probability is subject to many more factors, we could not take into consideration for this study.
|
||||
|
||||
|
||||
Overall, we conclude, that the body core temperature itself might be a sufficient indicator for pre-ovulation fertility.
|
||||
However, this marker by itself is prone to anomalies in the data.
|
||||
When anomalies intercept with the fertile phase and result in unusual temperature shifts,
|
||||
none of our models were able to avoid erroneous predictions, and we think it will be nearly impossible to do so
|
||||
just based on the temperature data.
|
||||
Measuring and correlating other biomarkers or context information could turn out highly effective in detecting such
|
||||
anomalies and improving the predictive quality of the temperature measurements.
|
||||
The biological mechanisms that influence body core temperature are highly complex and not yet fully understood.
|
||||
Many factors can affect it and the resulting temperature curve.
|
||||
We were not yet able to isolate the ovulation-related temperature fluctuations over time reliably,
|
||||
but in many cases, they provide highly useful information for NFP or natural contraception.
|
||||
|
||||
For a practical use case of any model's prediction, a medical interpretation should be performed.
|
||||
While the results themselves can give a clear indication of both the fertility probability and whether the ovulation
|
||||
of a given cycle is already over for any given day, there a variety of external factors that should be taken into
|
||||
consideration for a direct output to the user.
|
||||
|
||||
|
||||
% talk about whether bbt / temperature can be used for such a task, discuss bbt doubt papers
|
||||
% While previous work has argued against the predictive value of BBT~\cite{some_author_2010}, our findings suggest otherwise.
|
||||
%Using continuous core body temperature data from 40,000 cycles, we demonstrate that temperature-based models can reliably detect ovulatory patterns, even in the presence of physiological noise or mild irregularity.
|
||||
% explain the need for further medical interpretation of the results of either model
|
||||
|
||||
|
||||
% regular vs irregular cycles: mean baselines perform well on regular cycles as expected, as they get closer to the regularities with every past cycle
|
||||
|
||||
% transformer can deal with more data and does also perform better for some cases
|
||||
% lstm outperforms
|
||||
|
||||
%The findings do not show a clear indication, that the temperature can be used as a predictive target.
|
||||
%The results of irregular cycles should be significantly better to infer, that there are usable patters in the
|
||||
%temperature readings before the ovulation or the fertile days.
|
||||
%
|
||||
|
||||
% add improvements in experiments / comparison
|
||||
% add better decision base
|
||||
As in the contraception use-case, all results are based on statistical assumptions
|
||||
that may not fully hold in real-world scenarios.
|
||||
Therefore, findings should be interpreted accordingly.
|
||||
A more detailed investigation of these assumptions, along with further medical interpretation,
|
||||
would improve the reliability and applicability of the predictions.
|
||||
@@ -3,6 +3,14 @@
|
||||
|
||||
|
||||
\section{Introduction}\label{sec:introduction}
|
||||
Reproductive health and fertility prediction are of increasing importance at both the individual and societal level.
|
||||
Globally, maternal age at first pregnancy continues to rise, driven by social and economic factors~\cite{sauer_reproduction_2015}.
|
||||
This trend increases the prevalence of cycle irregularity and subfertility, amplifying the need for reliable,
|
||||
non-invasive methods of fertility tracking.
|
||||
At the same time, many individuals seek alternatives to hormonal contraception, fueling the growth of so-called
|
||||
\emph{FemTech} applications for digital health.
|
||||
Accurate fertility prediction thus carries implications not only for individual reproductive autonomy,
|
||||
but also for public health, demographic trends, and the development of safe, data-driven fertility support tools.
|
||||
|
||||
While textbooks often describe a menstrual cycle as lasting 28 to 30 days with ovulation around day 14~\cite{owen_physiology_nodate},
|
||||
such regularity is the exception rather than the rule~\cite{munster_length_1992, bull_real-world_2019}.
|
||||
@@ -31,9 +39,14 @@ others suggest its predictive value for ovulation~\cite{sato_novel_2024, royston
|
||||
However, most existing studies rely on small, idealized datasets that exclude cycles with irregular lengths or late ovulation.
|
||||
While such restrictions simplify the prediction task and yield high accuracy, they give a misleading impression of real-world model performance.
|
||||
It is thus not yet fully clear whether temperature can reliably be used as a predictive marker for ovulation or fertility.
|
||||
|
||||
Additionally, other studies have focused on peripheral temperature measurements of skin or in-ear temperature,
|
||||
which are subject to many sources of noise that can significantly affect the quality of the resulting predictions.
|
||||
|
||||
To date, no study has systematically evaluated machine learning architectures on a large-scale,
|
||||
high-resolution dataset of intravaginal core body temperature across both regular and irregular cycles.
|
||||
Such an evaluation is crucial to determine whether temperature-based models can provide robust predictions
|
||||
under real-world variability, rather than only on highly regular, curated subsets of data.
|
||||
|
||||
Intravaginal temperature reflects true core body temperature and offers higher resolution and stability,
|
||||
as it is largely unaffected by external circumstances.
|
||||
This allows for more reliable detection of subtle thermal shifts associated with ovulation, especially in irregular cycles.
|
||||
@@ -44,8 +57,10 @@ an intravaginal wearable device that continuously measures core body temperature
|
||||
The objective is to develop a machine learning model that performs reliably across diverse cycle types, including irregular ones.
|
||||
To this end, we compare a set of time series-based machine learning architectures and evaluate their performance for
|
||||
NFP and contraception.
|
||||
Finally, we demonstrate that high predictive accuracy on highly regular, curated datasets, as commonly reported in prior work,
|
||||
may overestimate real-world applicability, since such datasets tend to favor even simple, rule-based approaches.
|
||||
|
||||
This thesis addresses this gap by providing the first large-scale, systematic comparison of LSTM and
|
||||
Transformer architectures on high-resolution intravaginal temperature data.
|
||||
It evaluates robustness across diverse cycle types and demonstrates their practical relevance for contraception and NFP\@.
|
||||
|
||||
The main research objective is to evaluate the fundamental feasibility of predicting fertility and
|
||||
ovulation from body temperature data using machine learning,
|
||||
@@ -60,4 +75,4 @@ across real-world variability in cycle patterns and user needs:
|
||||
\item To compare prediction performance across regular and irregular cycles to assess how cycle variability affects feasibility.
|
||||
\item To evaluate model outputs in the context of practical use cases,
|
||||
such as contraception and natural family planning, using task-specific evaluation criteria.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
@@ -28,12 +28,12 @@ as they typically indicate erroneous entries, pregnancies, sensor failures, or d
|
||||
In addition, incomplete cycles are filtered out, since new cycles continuously arrive from active users
|
||||
and may not contain the full sequence of data required for retrospective labeling.
|
||||
|
||||
Temperature values outside the physiologically plausible range—below 35\textdegree C or above 43\textdegree C—are also excluded,
|
||||
as they typically result from sensor malfunction or transmission errors.
|
||||
Temperature values outside the physiologically plausible range, below 35\textdegree C or above 43\textdegree C,
|
||||
are also excluded, as they typically result from sensor malfunction or transmission errors.
|
||||
|
||||
\subsubsection{Data Labeling}\label{subsubsec:data_labeling}
|
||||
|
||||
Supervised machine learning requires labeled data—i.e., known target values for each input.
|
||||
Supervised machine learning requires labeled data, i.e., known target values for each input.
|
||||
In the context of this study, the relevant target is the ovulation day within each menstrual cycle.
|
||||
|
||||
The dataset contains over 40{,}000 cycles, making manual annotation unfeasible.
|
||||
@@ -65,9 +65,9 @@ The next section details how these labels are incorporated into feature represen
|
||||
|
||||
The features used as model inputs have been divided into three categories:
|
||||
\begin{itemize}
|
||||
\item \textbf{Static features} - Characteristics, that remain constant across a user's cycle, such as age, height, or average ovulation day
|
||||
\item \textbf{Known features} — Inputs known a priori at each time step, such as time of day or calendar-based variables (e.g., month of the year).
|
||||
\item \textbf{Observable features} — Inputs available at the current time step, including raw and derived temperature values (e.g, rolling averages).
|
||||
\item \textbf{Static features:} Characteristics, that remain constant across a user's cycle, such as age, height, or average ovulation day
|
||||
\item \textbf{Known features:} Inputs known a priori at each time step, such as time of day or calendar-based variables (e.g., month of the year).
|
||||
\item \textbf{Observable features:} Inputs available at the current time step, including raw and derived temperature values (e.g, rolling averages).
|
||||
\end{itemize}
|
||||
The target variables predicted by the model—like ovulation status or fertility probability—are described separately.
|
||||
|
||||
@@ -208,6 +208,12 @@ Together, the two outputs offer complementary information and improve interpreta
|
||||
As discussed in Section~\ref{sec:discussion}, all predictions are subject to further interpretation before presentation in the product interface.
|
||||
The model outputs represent data-driven estimates and do not constitute medical advice or diagnostic statements.
|
||||
|
||||
Although the models were trained to predict both targets, and fertility-probability as well as the ovulation-over indicator
|
||||
are relevant for actual application of the models, the primary focus of this thesis lies on the fertility-probability target,
|
||||
which is more central to the research objectives.
|
||||
The ovulation-over indicator is included due to its practical relevance for potential real-world applications,
|
||||
but it is not analyzed in depth, as it lies outsize the core scope of scientific investigation.
|
||||
|
||||
\begin{table}[htbp]
|
||||
\centering
|
||||
\begin{tabular}{@{}lp{0.62\linewidth}@{}}
|
||||
@@ -355,7 +361,7 @@ Additionally, we'll show, how the convolutional hybrids extend their functionali
|
||||
\label{fig:methodology_lstm_architecture}
|
||||
\end{figure}
|
||||
|
||||
Recurrent neural networks, particularly GRUs and LSTMs, were tested for their ability to model long-term dependencies in the time series.
|
||||
Recurrent neural networks, particularly LSTMs, were tested for their ability to model long-term dependencies in the time series.
|
||||
Their sequential memory structure allows them to retain information across cycle days, but they may struggle with high-resolution input and longer sequences.
|
||||
LSTMs, in particular, have a long history of strong performance in sequence prediction tasks.
|
||||
For this study, a stack of LSTM layers was followed by a linear projection layer, mapping the hidden state at the final time
|
||||
@@ -779,7 +785,7 @@ 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}\cite{pearl_factors_1933}.
|
||||
initially proposed by~\citeauthor{pearl_factors_1933} in~\citeyear{pearl_factors_1933}~\cite{pearl_factors_1933}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
@@ -796,16 +802,14 @@ A day-specific probability of intercourse is computed for each user based on age
|
||||
We assume, that the users don't have any health-related or non-health-related issues affecting fertility.
|
||||
If a user's age is unknown, it is randomly drawn from the overall dataset distribution.
|
||||
Only users with at least one continuous year of data are included.
|
||||
To get a representative result, we use 500 randomly selected user years.
|
||||
To get a representative result, we use 100 randomly selected user years.
|
||||
|
||||
Each day of data for a full year we count the following states by the algorithm:
|
||||
\begin{itemize}
|
||||
\item \emph{Sex}: Intercourse occurred.
|
||||
\item \emph{No Sex}: no intercourse occurred.
|
||||
\item \emph{Pregnancy}: fertility prediction allowed intercourse during a potentially fertile period, and it led to a pregnancy.
|
||||
\item \emph{Correct Denial}: fertility prediction correctly indicated abstinence during a fertile period.
|
||||
\item \emph{Incorrect Denial}: fertility prediction incorrectly indicated abstinence during an infertile period.
|
||||
\item \emph{Pregnancy}: fertility prediction allowed intercourse during a potentially fertile period, and it led to a pregnancy.
|
||||
\item \emph{No Pregnancy}: fertility prediction allowed intercourse during an infertile or potentially fertile period, but it did not lead to a pregnancy.
|
||||
\end{itemize}
|
||||
|
||||
This categorization captures both the contraceptive accuracy (avoiding pregnancy) and the practicality
|
||||
@@ -813,6 +817,10 @@ This categorization captures both the contraceptive accuracy (avoiding pregnancy
|
||||
An algorithm achieving perfect contraceptive accuracy by always recommending abstinence would score highly but
|
||||
significantly limit user acceptability and utility.
|
||||
|
||||
To add a control group, we compute the potential pregnancies and number of sexual intercourse without using the models predictions,
|
||||
i.e., the group does not use any contraception.
|
||||
In this case, sexual intercourse can happen unrestricted on every day.
|
||||
|
||||
\paragraph{Pregnancy Use-Case:}
|
||||
|
||||
For the pregnancy use-case, we developed a complementary algorithm to evaluate model performance for users attempting to conceive.
|
||||
@@ -834,21 +842,22 @@ we assume an average frequency of six times per month.
|
||||
We assume no health-related fertility impairments for comparative simplicity,
|
||||
though we acknowledge that real-world fertility is influenced by numerous complex factors.
|
||||
Similar to the contraception scenario, only users with at least one continuous year of data are considered.
|
||||
For representative results, we use 500 randomly selected user years.
|
||||
For representative results, we use 100 randomly selected user years.
|
||||
|
||||
For each day in a full year we count occurrences of the following states:
|
||||
\begin{itemize}
|
||||
\item \emph{Sex}: Intercourse occurred
|
||||
\item \emph{No Sex}: No intercourse
|
||||
\item \emph{Pregnancy}: Correct fertile prediction, intercourse occurred, resulting in pregnancy.
|
||||
\item \emph{No Pregnancy}: Correct fertile prediction, intercourse occurred, but no pregnancy occurred.
|
||||
\item \emph{Incorrect Deferral}: Incorrect non-fertile prediction, actual fertility was above threshold.
|
||||
\item \emph{Correct Deferral}: Correct non-fertile prediction.
|
||||
\item \emph{Incorrect Deferral}: Incorrect non-fertile prediction, actual fertility was above threshold.
|
||||
\end{itemize}
|
||||
|
||||
This classification measures both fertility prediction accuracy and the impact of incorrect deferrals.
|
||||
A model overly predicting fertility would increase potential pregnancy rates but negatively affect usability and trust due to misdirected efforts.
|
||||
|
||||
For the pregnancy case, we also compute a control group.
|
||||
Here, every day is considered potentially fertile and thus allows for intercourse.
|
||||
|
||||
\subsection{Ethical Considerations}\label{subsec:ethical_considerations}
|
||||
|
||||
This study was conducted using pseudonymized data collected in accordance with the terms of service and privacy policy of the data provider, VivoSensMedical GmbH (Leipzig, Germany).
|
||||
|
||||
@@ -17,8 +17,8 @@ In~\citeyear{wallach_prediction_1980}, \citeauthor{wallach_prediction_1980} iden
|
||||
including salivary ferning and viscosity, serum levels of progesterone and estrogen,
|
||||
and urinary luteinizing hormone (LH) concentrations~\cite{wallach_prediction_1980}.
|
||||
These indicators showed strong correlation with ovulation timing as measured via transvaginal ultrasound.
|
||||
\citeauthor{noauthor_monitoring_1987} later expanded on this work by focusing specifically on LH and estradiol,
|
||||
confirming that LH surges reliably indicate an imminent ovulation event.
|
||||
\citeauthor{vermesh_monitoring_1987} later expanded on this work by focusing specifically on LH and estradiol,
|
||||
confirming that LH surges reliably indicate an imminent ovulation event~\cite{vermesh_monitoring_1987}.
|
||||
|
||||
Despite their diagnostic value, many of these biomarkers are difficult to measure continuously and reliably in everyday settings,
|
||||
limiting their practicality for real-time or large-scale applications.
|
||||
@@ -36,7 +36,7 @@ However, several studies have raised concerns about its reliability as a predict
|
||||
high susceptibility to external confounders, recommending caution in its clinical or research use~\cite{bauman_basal_1981}.
|
||||
Similarly, \citeauthor{moghissi_accuracy_1976} emphasized its limited accuracy, particularly in cycles with irregularities~\cite{moghissi_accuracy_1976}.
|
||||
|
||||
However, such conclusions were largely based on the standard BBT method, which relies on a single-point measurement taken
|
||||
Such conclusions were largely based on the standard BBT method, which relies on a single-point measurement taken
|
||||
immediately upon waking—typically reflecting the body's lowest resting temperature.
|
||||
In contrast, this study, along with several recent works, leverages continuous or high-resolution temperature data collected during sleep or throughout the day.
|
||||
This richer signal provides a more robust foundation for detecting ovulatory patterns and addresses many of the limitations historically associated with BBT-based methods.
|
||||
@@ -78,10 +78,27 @@ For menstruation prediction, the model detected 70.70\% of menstruation days in
|
||||
|
||||
These results indicate that the model performed well in regular cycles but struggled with irregularity, particularly in detecting the fertile window.
|
||||
|
||||
Complementing academic efforts, several commercial products have adopted temperature-based tracking,
|
||||
such as \textit{Ava}~\cite{sl_ava_nodate}, \textit{Daysy}~\cite{electronics_zykluscomputer_nodate}, \textit{Trackle}~\cite{noauthor_trackle_nodate}
|
||||
or \textit{Natural Cycles}~\cite{noauthor_natural_nodate}.
|
||||
However, these products typically rely on proprietary algorithms, and no peer-reviewed publications are available detailing their methodology or performance.
|
||||
In~\citeyear{kilungeja_machine_2025},~\citeauthor{kilungeja_machine_2025} trained a set of classification models
|
||||
to predict the cycle phase a day based on skin temperature, electrodermal activity, interbeat interval and heart rate.
|
||||
The measurements were automatic and did not require manual participant input~\cite{kilungeja_machine_2025}.
|
||||
The classification was either into three or four targets: period, ovulation, luteal phase, and follicular phase for the four-class models.
|
||||
Their dataset included 65 cycles across 18 subjects.
|
||||
They trained a decision tree, random forest ensemble, logistic regression and support vector machine to enable
|
||||
an architectural comparison.
|
||||
Results show an edge for the random forest model with a reported 87\% accuracy and AUC-ROC (area under the receiver operating characteristic curve)
|
||||
of 0.96 for the three class approach.
|
||||
The four class approach significantly reduced accuracy to 68\% and AUC-ROC of 0.77.
|
||||
There was no separation into cycle groups and all cycles were in a regular group, with a mean lengths of 28 days (SD: 1.65).
|
||||
|
||||
There are some additional studies based on commercial products, such as \emph{Oura Ring}\cite{thigpen_oura_2025}
|
||||
or \emph{Natural Cycles}\cite{bull_real-world_2019} that work with temperature data as a base.
|
||||
However, they all focus on retrospective ovulation-detection and often complement this with advice to remain
|
||||
abstinent during the first cycle phase until the ovulation was reliably detected.
|
||||
This way they can offer a contraceptive product option, without needing to create a predictive model or algorithm.
|
||||
|
||||
Complementing academic efforts, several other commercial products have also adopted temperature-based tracking,
|
||||
such as \textit{Ava}~\cite{sl_ava_nodate}, \textit{Daysy}~\cite{electronics_zykluscomputer_nodate} or \textit{Trackle}~\cite{noauthor_trackle_nodate}.
|
||||
However, these products rely on proprietary algorithms, and no peer-reviewed publications are available detailing their methodology or performance.
|
||||
This lack of transparency limits their scientific evaluation and comparability.
|
||||
In contrast, the present study provides an open and data-driven approach to ovulation prediction based on continuous temperature data, aiming to contribute reproducible evidence to the field.
|
||||
|
||||
|
||||
+28
-211
@@ -6,11 +6,14 @@
|
||||
|
||||
% find introduction
|
||||
|
||||
\subsection{RQ1: Comparative Study of Model Architectures}\label{subsec:rq1_temp_predictive_value}
|
||||
\subsection{Objective 1: Comparative Study of Model Architectures}\label{subsec:rq1_temp_predictive_value}
|
||||
|
||||
We systematically evaluated multiple model architectures to assess their performance in
|
||||
predicting the targets.
|
||||
We report results for two targets: (i) fertility probability and (ii) an indicator that ovulation has already occurred (OV-Over).
|
||||
We mainly report results for the fertility probability target.
|
||||
Results for the second target, an indicator that ovulation has already occurred (OV-Over),
|
||||
can be found in Appendix~\ref{sec:appendix_ov_over_results}
|
||||
|
||||
Each architecture was tested across a range of input window lengths, temporal resolutions, and model capacities.
|
||||
The best-performing configurations for each architecture were selected for downstream analyses.
|
||||
Unless stated otherwise, \textbf{MSE} is the primary metric (equivalent to the Brier score for probabilistic targets),
|
||||
@@ -178,148 +181,6 @@ with full results in Appendix Tables~\ref{tab:fertility_results_by_model_paramet
|
||||
\label{tab:fertility_params_compact_mse}
|
||||
\end{table}
|
||||
|
||||
\subsubsection{Ovulation-Over Prediction}\label{subsubsec:ov_over_prediction}
|
||||
|
||||
We evaluate prediction of a binary indicator denoting whether ovulation has already occurred.
|
||||
We examine the influence of input window length, input resolution, and model capacity.
|
||||
|
||||
\paragraph{Impact of input window length.}
|
||||
For predicting whether ovulation has occurred (OV-over),
|
||||
optimal window lengths again vary by architecture and target phase (pre- vs post-ovulation).
|
||||
|
||||
The \textbf{Transformer} yields the lowest overall (0.0533) and post-ovulation MSE (0.0520) at 40 days.
|
||||
The \textbf{LSTM} performs best before ovulation (MSE 0.0212 at 20 days), while its overall MSE improves with longer context (160 days).
|
||||
|
||||
The \textbf{Convolutional LSTM} favors short windows, with the best overall MSE (0.0699), before-OV (0.0389),
|
||||
and after-OV (0.0833) all occurring at 20 days.
|
||||
The \textbf{Convolutional Transformer} performs best overall at 40 days and best before ovulation at 160 days (MSE 0.0286).
|
||||
See Table~\ref{tab:ovover_windows_compact_mse} for a summary.
|
||||
|
||||
\begin{table}[t]
|
||||
\small
|
||||
\renewcommand{\arraystretch}{1.15}
|
||||
\setlength{\tabcolsep}{6pt}
|
||||
\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
|
||||
\toprule
|
||||
\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
|
||||
\cmidrule(r){2-4}
|
||||
& \shortstack[c]{Overall best\\(days / MSE)}
|
||||
& \shortstack[c]{Before-OV best\\(days / MSE)}
|
||||
& \shortstack[c]{After-OV best\\(days / MSE)} \\
|
||||
\midrule
|
||||
LSTM
|
||||
& 160 / 0.0557
|
||||
& \textbf{20 / 0.0212}
|
||||
& 160 / 0.0580 \\
|
||||
Transformer
|
||||
& \textbf{40 / 0.0533}
|
||||
& 20 / 0.0255
|
||||
& \textbf{40 / 0.0520} \\
|
||||
Convolutional LSTM
|
||||
& 20 / 0.0699
|
||||
& 20 / 0.0389
|
||||
& 20 / 0.0833 \\
|
||||
Convolutional Transformer
|
||||
& 40 / 0.0709
|
||||
& 160 / 0.0286
|
||||
& 40 / 0.0820 \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{OV-Over: best input window per architecture (MSE only) at a fixed input resolution of 12 values/day.
|
||||
Bold entries are bests within a column.}
|
||||
\label{tab:ovover_windows_compact_mse}
|
||||
\end{table}
|
||||
|
||||
\paragraph{Impact of input resolution.}
|
||||
Fixing the input window to 20 days, we compare input resolutions for LSTM and Transformer models.
|
||||
|
||||
For the \textbf{LSTM}, the lowest overall MSE (0.0633) occurs at 24/day,
|
||||
with best before-OV and after-OV MSEs at 12/day (0.0212) and 48/day (0.0550), respectively.
|
||||
|
||||
The \textbf{Transformer} performs best overall at 72/day (0.0585),
|
||||
with lowest before-OV MSE at 12/day (0.0255) and after-OV MSE at 288/day (0.0578).
|
||||
|
||||
Results are summarized in Table~\ref{tab:ovover_resolution_compact_mse};
|
||||
full resolution grids are in Appendix Table~\ref{tab:ov_over_results_by_resolution}.
|
||||
|
||||
\begin{table}[t]
|
||||
\small
|
||||
\renewcommand{\arraystretch}{1.15}
|
||||
\setlength{\tabcolsep}{6pt}
|
||||
\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
|
||||
\toprule
|
||||
\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
|
||||
\cmidrule(r){2-4}
|
||||
& \shortstack[c]{Overall best\\(values/day / MSE)}
|
||||
& \shortstack[c]{Before-OV best\\(values/day / MSE)}
|
||||
& \shortstack[c]{After-OV best\\(values/day / MSE)} \\
|
||||
\midrule
|
||||
LSTM
|
||||
& 24 / 0.0633
|
||||
& \textbf{12 / 0.0212}
|
||||
& \textbf{48 / 0.0550} \\
|
||||
Transformer
|
||||
& \textbf{72 / 0.0585}
|
||||
& 12 / 0.0255
|
||||
& 288 / 0.0578 \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{OV-Over: best input resolution per architecture (MSE only) at a fixed input-window length of 20\,days.
|
||||
Bold entries are bests within a column. Convolutional models are excluded (they consume 288 values/day internally).}
|
||||
\label{tab:ovover_resolution_compact_mse}
|
||||
\end{table}
|
||||
|
||||
\paragraph{Impact of model parameters.}
|
||||
Using fixed input settings (160 days at 12/day for LSTM/Transformer; 40 days for convolutional models), we evaluate model scaling.
|
||||
|
||||
The \textbf{Transformer} achieves the lowest overall (0.0543) and after-ovulation MSE (0.0410) at a large configuration (512×8×8).
|
||||
Before-OV MSE is lowest at 256×4×4 (0.0293).
|
||||
|
||||
For the \textbf{LSTM}, the best overall and after-OV performance is at 512×4,
|
||||
while the best before-OV MSE occurs at 128×2 (0.0274).
|
||||
The \textbf{Convolutional LSTM} performs best overall and after-OV at 256×4, with the best before-OV MSE at 128×2.
|
||||
|
||||
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.
|
||||
|
||||
Table~\ref{tab:ovover_params_compact_mse} summarizes these parameter-dependent results;
|
||||
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}.
|
||||
|
||||
\begin{table}[t]
|
||||
\scriptsize
|
||||
\renewcommand{\arraystretch}{1.15}
|
||||
\setlength{\tabcolsep}{6pt}
|
||||
\begin{tabularx}{\linewidth}{l*{3}{>{\centering\arraybackslash}X}}
|
||||
\toprule
|
||||
\textbf{Architecture} & \multicolumn{3}{c}{\textbf{MSE}} \\
|
||||
\cmidrule(r){2-4}
|
||||
& \shortstack[c]{Overall best\\(params / MSE)}
|
||||
& \shortstack[c]{Before-OV best\\(params / MSE)}
|
||||
& \shortstack[c]{After-OV best\\(params / MSE)} \\
|
||||
\midrule
|
||||
LSTM
|
||||
& \(512\times4\) / 0.0616
|
||||
& \textbf{\(128\times2\) / 0.0274}
|
||||
& \(512\times4\) / 0.0613 \\
|
||||
Transformer
|
||||
& \textbf{\(512\times8\times8\) / 0.0543}
|
||||
& \(256\times4\times4\) / 0.0293
|
||||
& \textbf{\(512\times8\times8\) / 0.0410} \\
|
||||
Convolutional LSTM
|
||||
& \(256\times4\) / 0.0687
|
||||
& \(128\times2\) / 0.0357
|
||||
& \(256\times4\) / 0.0715 \\
|
||||
Convolutional Transformer
|
||||
& \(512\times4\times4\) / 0.0703
|
||||
& \(512\times8\times8\) / 0.0339
|
||||
& \(512\times4\times4\) / 0.0814 \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{OV-Over: best parameter settings per architecture (MSE only).
|
||||
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).
|
||||
Bold values indicate bests within a column. Fixed input settings: 160\,days with 12 values/day for LSTM/Transformer; 40\,days for convolutional models.}
|
||||
\label{tab:ovover_params_compact_mse}
|
||||
\end{table}
|
||||
|
||||
\subsubsection{Best Model Configuration Selection}\label{subsubsec:results_best_model_config_selection}
|
||||
|
||||
To identify the best configuration for each model architecture, we followed the procedure described in Section~\ref{subsubsec:methodology_best_model_config_selection}.
|
||||
@@ -408,7 +269,7 @@ confirming the advantage of personalized and temporally-aware modeling.
|
||||
|
||||
% -------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
\subsection{RQ2: Factors and Patterns that Influence Predictions}\label{subsec:rq2_factors_and_patterns}
|
||||
\subsection{Objective 2: Factors and Patterns that Influence Predictions}\label{subsec:rq2_factors_and_patterns}
|
||||
|
||||
\subsubsection{Representative predictions}\label{subsubsec:rq2_examples}
|
||||
|
||||
@@ -517,7 +378,7 @@ but show greater scatter for users with longer data records.
|
||||
|
||||
% -------------------------------------------------------------
|
||||
|
||||
\subsection{RQ3: Performance across Regular and Irregular Cycles}\label{subsec:rq3_regular_vs_irregular}
|
||||
\subsection{Objective 3: Performance across Regular and Irregular Cycles}\label{subsec:rq3_regular_vs_irregular}
|
||||
|
||||
\begin{table}[htbp]
|
||||
\centering
|
||||
@@ -568,59 +429,6 @@ Baselines degrade more sharply in this group.
|
||||
|
||||
The full table with MSE and MAE for all models can be found in the appendix, Table~\ref{tab:regular_vs_irregular_fertility_results}.
|
||||
|
||||
\vspace{1em}
|
||||
|
||||
\begin{table}[htbp]
|
||||
\centering
|
||||
\small
|
||||
\begin{tabularx}{\linewidth}{l*{3}{X}}
|
||||
\toprule
|
||||
\multirow{2}{*}{Model} & \multicolumn{3}{c}{MSE} \\
|
||||
\cmidrule(r){2-4}
|
||||
& OV-Over Overall & OV-Over Before OV & OV-Over After OV \\
|
||||
\midrule
|
||||
\multicolumn{4}{c}{\textbf{Regular Cycle Group}} \\
|
||||
\midrule
|
||||
LSTM & \textbf{0.028519} & 0.031695 & \textbf{0.026116} \\
|
||||
Transformer & 0.032929 & \textbf{0.024774} & 0.033411 \\
|
||||
Convolutional LSTM & 0.034224 & 0.028962 & 0.033929 \\
|
||||
Convolutional Transformer & 0.033333 & 0.039045 & 0.029329 \\
|
||||
Last-Cycle Baseline & 0.087916 & 0.093465 & 0.074191 \\
|
||||
Population Mean Baseline & 0.285887 & 0.008876 & 0.418879 \\
|
||||
User Mean Baseline & 0.069245 & 0.069152 & 0.055724 \\
|
||||
\midrule
|
||||
\multicolumn{4}{c}{\textbf{Irregular Cycle Group}} \\
|
||||
\midrule
|
||||
LSTM & \textbf{0.051747} & \textbf{0.016777} & 0.070419 \\
|
||||
Transformer & 0.055990 & 0.026159 & 0.067520 \\
|
||||
Convolutional LSTM & 0.054523 & 0.030092 & \textbf{0.066643} \\
|
||||
Convolutional Transformer & 0.056075 & 0.029638 & 0.067965 \\
|
||||
Last-Cycle Baseline & 0.222906 & 0.134945 & 0.258047 \\
|
||||
Population Mean Baseline & 0.171368 & 0.130366 & 0.140363 \\
|
||||
User Mean Baseline & 0.180702 & 0.088884 & 0.217144 \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{MSEs for ovulation-over target across different model architectures for regular and irregular cycle groups. Bold values denote the best scores per column.}
|
||||
\label{tab:ov_over_mse_regular_irregular}
|
||||
\end{table}
|
||||
|
||||
\noindent
|
||||
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.
|
||||
For this target, performance patterns differ more distinctly across phases.
|
||||
In the regular group, the LSTM performs best overall and after ovulation, while the Transformer performs best before ovulation.
|
||||
Convolutional models perform slightly worse than their recurrent and transformer-based counterparts across all phases.
|
||||
The population mean baseline shows a spurious low MSE before ovulation, but this is not consistent across phases, suggesting it is not reliable.
|
||||
In general, baselines are notably weaker than learned models across all splits.
|
||||
|
||||
For irregular cycles, all model performances deteriorate relative to regular cycles.
|
||||
The LSTM remains the most robust, achieving the best MSEs both overall and before ovulation.
|
||||
Convolutional LSTM performs best after ovulation.
|
||||
Transformer-based models perform less consistently in this group, suggesting decreased robustness to cycle irregularity.
|
||||
As before, all learned models outperform the baselines by a wide margin.
|
||||
|
||||
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}.
|
||||
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.8\textwidth]{resources/figures/results/model_results_on_regular_cycles}
|
||||
@@ -645,7 +453,7 @@ visualize performance improvements with increasing numbers of past cycles.
|
||||
For regular cycles, all models except the population-mean baseline benefit from more historical data, showing consistent MSE reductions for both targets.
|
||||
Interestingly, the population-mean baseline performs worse as more cycles are added.
|
||||
The largest improvement can be seen for the last-cycle baseline and user-mean baseline models.
|
||||
The outliers in the last-cycle and user-mean baseline are MSE values of 0.0, which result in these vertical lines.
|
||||
The outliers in the last-cycle and user-mean baseline are MSE values of 0.0, which result in vertical lines based on the logarithmic scaling of the axis.
|
||||
|
||||
In contrast, irregular cycles exhibit more variability and less performance gain with more cycles available.
|
||||
All trained models improve on both targets with more context.
|
||||
@@ -662,7 +470,7 @@ as indicated by the wider deviations from the trend lines.
|
||||
|
||||
% -------------------------------------------------------------
|
||||
|
||||
\subsection{RQ4: Use-Case Evaluations}\label{subsec:rq4_use_case_evaluations}
|
||||
\subsection{Objective 4: Evaluating Use-Case Scenarios}\label{subsec:rq4_use_case_evaluations}
|
||||
|
||||
We evaluated the use-case scenarios described in Section~\ref{subsubsec:practical_use_cases} using the algorithms
|
||||
in Section~\ref{subsubsec:use_case_evaluation} across multiple fertility thresholds.
|
||||
@@ -687,7 +495,7 @@ The four evaluated metrics are: number of pregnancies, number of intercourse eve
|
||||
number of correct denials (i.e., appropriately flagged fertile days),
|
||||
and number of incorrect denials (i.e., fertile days incorrectly flagged as infertile).
|
||||
|
||||
\paragraph{Pregnancies.}
|
||||
\paragraph{Potential Pregnancies.}
|
||||
All trained models start with very low pregnancy rates (Transformer: 0, LSTM: 4)
|
||||
and then increase roughly linearly with the threshold,
|
||||
reaching between 99 (Convolutional Transformer) and 122 (Transformer) at the highest setting.
|
||||
@@ -696,12 +504,16 @@ The Transformer starts with the lowest pregnancy rate but rises steeply,
|
||||
ending with the highest number of pregnancies at threshold 0.1.
|
||||
By comparison, the baselines show much higher pregnancy rates throughout,
|
||||
starting between 103 (user-mean) and 150 (population-mean) and increasing by about 50 pregnancies over the range of thresholds.
|
||||
The control group, which does not use any predictions shows very high potential pregnancy rates at 274 for 100 user years.
|
||||
Note, that the thresholds do not alter the control group, as intercourse can happen on any day by design.
|
||||
|
||||
\paragraph{Intercourse Events.}
|
||||
All trained models except the LSTM begin with low values of about 1000 intercourse events.
|
||||
The LSTM starts much higher, around 3000, and increases sharply, converging toward approximately 6100.
|
||||
All trained model variants show curved growth resembling logarithmic convergence, approaching the same upper range.
|
||||
In contrast, the baselines start near 6000 events and converge toward the same levels as the trained models at higher thresholds.
|
||||
Here, the control group allows for 7610 intercourse events, which is also the maximum for 100 user years by design,
|
||||
since no denials happen.
|
||||
|
||||
\paragraph{Correct Denials.}
|
||||
The number of correct denials decreases by about half across the tested thresholds.
|
||||
@@ -732,6 +544,7 @@ and the number of pregnancies per 1000 intercourse events.
|
||||
|
||||
Here, the difference between the models becomes clearer.
|
||||
The baselines start at 62 to 73 pregnancies per 100 users and become linearly worse over the threshold range.
|
||||
The control group results in 90 pregnant users of 100 for a year.
|
||||
|
||||
The LSTM performs worse than all other trained models, except for the upper end of the threshold interval.
|
||||
The Transformer, while being the best model for small thresholds, becomes worse over growing values until being on par with
|
||||
@@ -764,18 +577,20 @@ and number of incorrect deferrals (i.e., fertile days incorrectly flagged as inf
|
||||
The overall pattern mirrors the contraception use-case, but the optimization goal is reversed:
|
||||
here, a higher number of pregnancies is desirable.
|
||||
|
||||
\paragraph{Pregnancies.}
|
||||
\paragraph{Potential Pregnancies.}
|
||||
Trained models achieve substantially higher pregnancy rates than the baselines.
|
||||
They begin at around 275 pregnancies for low thresholds and decline linearly to between 157 and 176 at higher thresholds.
|
||||
By contrast, the baselines start much lower (user-mean: 159, last-cycle: 139, population-mean: 117) and also decrease linearly,
|
||||
reaching 119, 102, and 71 pregnancies, respectively.
|
||||
This places all trained models well above baseline performance across the full threshold range.
|
||||
The control group results in 261 potential pregnancies for 100 user years.
|
||||
|
||||
\paragraph{Intercourse Events.}
|
||||
Trained models start with high numbers of intercourse events, near 7000, except for the LSTM which begins lower at 4252.
|
||||
All decline sublinearly and converge toward approximately 1500 at the highest thresholds.
|
||||
In contrast, the baselines start far lower, between 1700 and 1900, and decrease linearly to about 1300.
|
||||
Thus, the improved pregnancy rates of trained models come at the cost of substantially higher intercourse event counts.
|
||||
Here, the control group allows for 7258 intercourse events, which is again the maximum possible for that interval by design.
|
||||
|
||||
\paragraph{Correct Deferrals.}
|
||||
The baselines initially show higher numbers of correct deferrals, with values that increase linearly as thresholds rise.
|
||||
@@ -804,9 +619,11 @@ To facilitate comparison here as well, Figure~\ref{fig:results_pregnancy_use_cas
|
||||
normalized pregnancy metrics across fertility thresholds: the number of pregnancies per 100 users per year,
|
||||
and the number of pregnancies per 1000 intercourse events.
|
||||
|
||||
All trained models clearly result in more pregnancies per 100 users overall.
|
||||
All trained models clearly result in more pregnancies per 100 users than the baselines.
|
||||
However, for lower fertility thresholds, there are fewer pregnancies per 1000 intercourse events for the trained models
|
||||
compared to the baselines.
|
||||
The control group attains 90 pregnant users per 100 for a year, which is on par with the trained models for low thresholds.
|
||||
The efficiency is much lower than both trained and baseline models with 36 pregnancies per 1000 intercourse events.
|
||||
|
||||
\paragraph{Summary.}
|
||||
In the pregnancy use-case, trained models clearly outperform baselines in terms of pregnancy rates,
|
||||
@@ -820,7 +637,7 @@ There is an edge for the non-convolutional models for smaller thresholds that sw
|
||||
|
||||
% -------------------------------------------------------------
|
||||
|
||||
\subsection{Summary of key results}\label{subsec:key_results}
|
||||
\subsection{Summary of Key Results}\label{subsec:key_results}
|
||||
% Keep this as a tight bulleted list mirroring RQs; strictly findings, no causes/interpretations.
|
||||
|
||||
%\begin{itemize}[leftmargin=*]
|
||||
@@ -832,10 +649,10 @@ There is an edge for the non-convolutional models for smaller thresholds that sw
|
||||
% the largest margins occur on post-ovulation metrics.
|
||||
%\end{itemize}
|
||||
|
||||
\noindent\textbf{RQ1 (Architectures, context, and capacity).}
|
||||
\noindent\textbf{Objective 1: Architectures, context, and capacity.}
|
||||
\begin{itemize}
|
||||
\item \emph{Architectures.} All learned models beat baselines by a wide margin.
|
||||
The \textbf{LSTM} is the most reliable overall and post-ovulation; the \textbf{Transformer} is strongest on fertile days.
|
||||
The LSTM is the most reliable overall and post-ovulation; the Transformer is strongest on fertile days.
|
||||
Convolutional variants are competitive but rarely best.
|
||||
|
||||
\item \emph{Temporal context.} Performance depends on window length and differs by model.
|
||||
@@ -855,10 +672,10 @@ There is an edge for the non-convolutional models for smaller thresholds that sw
|
||||
\item LSTM is best \emph{overall}: fertility MSE \(0.0036\) (best overall; best non-fertile \(0.0008\)) and OV-over overall \(0.0437\)
|
||||
(best; best after-OV \(0.0492\)). Transformer is best on fertile days (MSE \(0.0089\)).
|
||||
|
||||
\item Versus the strongest baseline (User-Mean), LSTM cuts fertility MSE by \(\sim 44\%\) and post-ovulatory MSE by \(\sim 59\%\).
|
||||
\item Versus the strongest baseline (User-Mean), LSTM cuts fertility MSE by \(\sim 44\%\) and ov-over MSE by \(\sim 59\%\).
|
||||
\end{itemize}
|
||||
|
||||
\noindent\textbf{RQ2 (Factors and Patterns).}
|
||||
\noindent\textbf{Objective 2: Factors and Patterns.}
|
||||
\begin{itemize}
|
||||
\item Models consistently key on the \emph{pre-ovulatory temperature drop}; larger drops yield higher predicted fertility.
|
||||
This pattern weakens in irregular cycles with noisier temperature traces (Figures~\ref{fig:results_rq2_regular_cycle_predictions_example}–\ref{fig:results_rq2_irregular_cycle_predictions_example}, \ref{fig:results_temperature_drop_pattern}).
|
||||
@@ -867,7 +684,7 @@ There is an edge for the non-convolutional models for smaller thresholds that sw
|
||||
Baselines do not: Last-Cycle and Population-Mean often degrade with more history (Figure~\ref{fig:results_performance_on_different_historical_context}).
|
||||
\end{itemize}
|
||||
|
||||
\noindent\textbf{RQ3 (Regular vs.\ Irregular).}
|
||||
\noindent\textbf{Objective 3: Regular vs.\ Irregular.}
|
||||
\begin{itemize}
|
||||
\item All models are better on \emph{regular} cycles.
|
||||
For fertility, Transformer leads overall and on fertile days; LSTM leads on non-fertile days.
|
||||
@@ -879,7 +696,7 @@ There is an edge for the non-convolutional models for smaller thresholds that sw
|
||||
\item Variance of predictions grow with longer context lengths.
|
||||
\end{itemize}
|
||||
|
||||
\noindent\textbf{RQ4 (Use-case Evaluations).}
|
||||
\noindent\textbf{Objective 4: Use-case Evaluations.}
|
||||
\begin{itemize}
|
||||
\item \emph{Contraception:} Trained models cut pregnancies sharply vs baselines,
|
||||
at the cost of more denials and fewer intercourse opportunities.
|
||||
|
||||
Reference in New Issue
Block a user