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temperature-based-fertility…/thesis/sections/results.tex
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Alex Blank f9b1b63a12 fixes
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%! Author = alex
%! Date = 3/6/25
\section{Results}\label{sec:results}
%
%We begin by comparing the overall performance of all trained models and baselines using four key evaluation metrics:
%mean absolute error (MAE) and mean squared error (MSE), as well as the metrics for their respective sub-intervals.
%
%Overall, transformer-based models consistently outperformed LSTM variants and baseline methods across most evaluation criteria.
%Among the baselines, [e.g., "the rule-based method"] showed the weakest performance,
%while the [e.g., "windowed logistic regression"] performed competitively in certain contexts.
%Differences across models were most pronounced in MSE and \(R^2\),
%indicating that advanced architectures better captured higher-order dynamics and reduced large prediction errors.
%
%The previous section detailed the design and implementation of our fertility prediction pipeline,
%including data preprocessing, feature engineering, input encoding, and the development of several deep learning architectures.
%We now present the results of our evaluation, focusing on the predictive accuracy of the proposed models across different temporal resolutions,
%cycle types and use cases.
%Model performance is assessed using both overall metrics and biologically targeted subintervals,
%allowing for a nuanced comparison of approaches and their practical relevance to real-time fertility forecasting.
%Additionally, model performance is compared to the three baseline models introduced.
%
% provide information about the training behaviour and statistic of the different models??
\subsection{Overall Model Performance Across Architectures}\label{subsec:overall_model_performance_across_architectures}
\subsection{Fertility Probability Prediction Accuracy}\label{subsec:fertility_probability_precition_accuracy}
% show why I selected the individual input configs for model config training
% selected by best mse fertility, use 2nd best, as it provides basically the same performance, but more input data for more complex model configs
\subsubsection{Fertility Probability Prediction}\label{subsubsec:fertility_probability_prediction}
\subsubsection{Impact of Input Window Length}\label{subsubsec:fert_impact_of_historical_context}
\begin{landscape}
\begin{table}
\small
\begin{tabularx}{\linewidth}{l*{6}{X}}
\toprule
\multirow{2}{*}{Input-Length in Days} & \multicolumn{3}{c}{MAE} & \multicolumn{3}{c}{MSE} \\
\cmidrule(r){2-4} \cmidrule(r){5-7}
& Fertility Overall & Fertile Days & Non-Fertile Days & Fertility Overall & Fertile Days & Non-Fertile Days \\
\midrule
\multicolumn{7}{c}{\textbf{LSTM}} \\ \midrule
10 & 0.0399 & 0.0857 & 0.0212 & 0.0045 & 0.0105 & 0.0021 \\
20 & 0.0421 & 0.0994 & 0.0180 & 0.0052 & 0.0144 & \underline{\textbf{0.0013}} \\
40 & 0.0406 & 0.0938 & 0.0184 & 0.0049 & 0.0128 & 0.0016 \\
80 & 0.0420 & 0.1006 & \underline{\textbf{0.0176}} & 0.0053 & 0.0147 & 0.0014 \\
160 & \underline{0.0378} & \underline{\textbf{0.0834}} & 0.0192 & \underline{0.0043} & \underline{\textbf{0.0102}} & 0.0019 \\
\midrule
\multicolumn{7}{c}{\textbf{Transformer}} \\ \midrule
10 & 0.0443 & 0.0868 & 0.0273 & 0.0046 & 0.0110 & 0.0021 \\
20 & 0.0472 & 0.0949 & 0.0274 & 0.0051 & 0.0133 & 0.0018 \\
40 & 0.0413 & 0.0861 & 0.0233 & \underline{0.0044} & 0.0111 & 0.0017 \\
80 & 0.0437 & \underline{0.0859} & 0.0269 & 0.0045 & \underline{0.0108} & 0.0021 \\
160 & \underline{0.0411} & 0.0882 & \underline{0.0218} & 0.0045 & 0.0116 & \underline{0.0016} \\
\midrule
\multicolumn{7}{c}{\textbf{Convolution-LSTM}} \\ \midrule
10 & 0.0435 & 0.0954 & 0.0224 & 0.0050 & 0.0133 & 0.0017 \\
20 & 0.0414 & 0.0996 & \underline{0.0179} & 0.0050 & 0.0145 & \underline{\textbf{0.0013}} \\
40 & \underline{0.0394} & \underline{0.0911} & 0.0184 & \underline{0.0045} & \underline{0.0122} & 0.0014 \\
80 & 0.0481 & 0.1005 & 0.0278 & 0.0054 & 0.0146 & 0.0019 \\
160 & 0.0505 & 0.1067 & 0.0290 & 0.0060 & 0.0166 & 0.0020 \\
\midrule
\multicolumn{7}{c}{\textbf{Convolution-Transformer}} \\ \midrule
10 & 0.0459 & 0.0962 & 0.0256 & 0.0049 & 0.0136 & \underline{0.0015} \\
20 & 0.0423 & \underline{0.0848} & 0.0257 & 0.0045 & \underline{\textbf{0.0102}} & 0.0022 \\
40 & \underline{\textbf{0.0376}} & 0.0854 & \underline{0.0186} & \underline{\textbf{0.0041}} & 0.0108 & \underline{0.0015} \\
80 & 0.0414 & 0.0932 & 0.0210 & 0.0048 & 0.0128 & 0.0018 \\
160 & 0.0523 & 0.1018 & 0.0337 & 0.0059 & 0.0148 & 0.0026 \\
\bottomrule
\end{tabularx}
\caption{Evaluation Metrics for the Fertility-Probability Target across Different Model Architectures and Input Lengths on a fixed Input Resolution of 12 Values per Day.
\underline{Underlined} values represent the best value for each metric within a model.
\textbf{\underline{Bold + Underlined}} values represent the global best values across all models for a given metric.}
\label{tab:fertility_results_by_window_length}
\end{table}
\end{landscape}
Table~\ref{tab:fertility_results_by_window_length} presents the performance of different model architectures across various metrics and input window lengths.
It is evident that for both the LSTM and Transformer models, \textbf{longer input windows generally yield better performance}.
Specifically, the LSTM achieves the best results for four out of six metrics with the 160-day window.
The only exception is the error metrics for non-fertile days, where shorter input windows perform better.
Notably, the LSTM achieves the \textbf{global best performance} for four out of six metrics, including MAE and MSE on non-fertile and fertile days.
For the Transformer model, the best performance is observed with the 160-day input window in three out of six metrics.
However, for non-fertile day metrics, performance improves with shorter input windows.
It is consistently outperformed by the LSTM model.
The \textbf{convolutional models} tend to perform best with \textbf{medium-length input windows} (20 to 40 days).
The \textbf{convolutional LSTM} shows its best performance with a 40-day window for most metrics,
except for non-fertile day errors, where the 20-day window yields smaller errors.
It also achieves the \textbf{global best performance} for non-fertile day MSE with the 20-day window.
Similarly, the \textbf{convolutional Transformer} excels with 40-day windows for the overall and non-fertile-day metrics,
while the best fertile-day metrics are seen with 20-day windows.
The \textbf{convolutional Transformer} also achieves the \textbf{global best performance} for 40-day windows in both MAE and MSE\@.
In all but non-fertile day metrics, the \textbf{convolutional Transformer} outperforms the LSTM variant.
\subsubsection{Impact of Input Resolution}\label{subsubsec:fert_impact_of_input_resolution}
Figure~\ref{fig:results_performance_lstm_fertility_input_resolution} presents the results for different input resolutions used in the LSTM models,
alongside the corresponding mean squared error (MSE) metrics.
The plot shows the MSE values for three target categories: non-fertile days, overall MSE, and fertile days MSE\@.
Notably, the MSE for non-fertile days appears to behave inversely in relation to the other two metrics.
However, there is no consistent upward or downward trend when changing the input window length with a fixed input resolution.
\begin{landscape}
\begin{table}
\small
\begin{tabularx}{\linewidth}{l*{6}{X}}
\toprule
\multirow{2}{*}{Values Per Day} & \multicolumn{3}{c}{MAE} & \multicolumn{3}{c}{MSE} \\
\cmidrule(r){2-4} \cmidrule(r){5-7}
& Fertility Overall & Fertile Days & Non-Fertile Days & Fertility Overall & Fertile Days & Non-Fertile Days \\
\midrule
\multicolumn{7}{c}{\textbf{LSTM}} \\
\midrule
1 & 0.0471 & 0.0987 & 0.0220 & 0.0062 & 0.0145 & 0.0022 \\
2 & 0.0457 & 0.0962 & 0.0231 & 0.0052 & 0.0133 & 0.0016 \\
4 & 0.0421 & 0.0898 & 0.0223 & \underline{\textbf{0.0046}}& 0.0116 & 0.0018 \\
12 & 0.0421 & 0.0994 & \underline{\textbf{0.0180}}& 0.0052 & 0.0144 & \underline{\textbf{0.0013}}\\
24 & 0.0419 & 0.0949 & 0.0201 & 0.0050 & 0.0132 & 0.0017 \\
48 & \underline{\textbf{0.0402}}& 0.0929 & 0.0182 & 0.0049 & 0.0126 & 0.0018 \\
72 & 0.0433 & 0.0972 & 0.0216 & 0.0052 & 0.0137 & 0.0018 \\
288 & 0.0410 & \underline{\textbf{0.0872}}& 0.0223 & 0.0049 & \underline{\textbf{0.0110}}& 0.0025 \\
\midrule
\multicolumn{7}{c}{\textbf{Transformer}} \\
\midrule
1 & 0.0541 & 0.1015 & 0.0313 & 0.0063 & 0.0146 & 0.0023 \\
2 & 0.0468 & 0.0946 & 0.0259 & 0.0054 & 0.0128 & 0.0021 \\
4 & 0.0456 & \underline{0.0891}& 0.0277 & 0.0050 & \underline{0.0115}& 0.0023 \\
12 & 0.0472 & 0.0949 & 0.0274 & 0.0051 & 0.0133 & 0.0018 \\
24 & 0.0502 & 0.0960 & 0.0323 & 0.0052 & 0.0133 & 0.0021 \\
48 & 0.0447 & 0.0912 & \underline{0.0254}& \underline{0.0048}& 0.0122 & 0.0017 \\
72 & 0.0468 & 0.0975 & 0.0257 & 0.0051 & 0.0140 & \underline{0.0014} \\
288 & \underline{0.0449}& 0.0937 & 0.0257 & \underline{0.0048}& 0.0128 & 0.0017 \\
\bottomrule
\end{tabularx}
\caption{Evaluation Metrics for the Fertility-Probability Target across Different Model Architectures and Input Resolutions on a fixed Input-Window-Length of 20 Days.
\underline{Underlined} values represent the best value for each metric within a model.
\textbf{\underline{Bold + Underlined}} values represent the global best values across all models for a given metric.}
\label{tab:fertility_results_by_window_resolution}
\end{table}
\end{landscape}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/results/transformer_fertility_results_by_input_resolution}
\caption{Performance of transformer models with different input window lengths and fixes input resolutions for the fertility probability target}
\label{fig:results_performance_transformer_fertility_input_resolution}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.00\textwidth]{resources/figures/results/lstm_fertility_results_by_input_resolution}
\caption{Performance of LSTM models with different input resolutions and fixes input window lengths for the fertility probability target}
\label{fig:results_performance_lstm_fertility_input_resolution}
\end{figure}
\subsubsection{Comparison with Baselines}\label{subsubsec:fert_comparison_with_baselines}
\subsection{Ovulation-Over Prediction}\label{subsubsec:ov_over_prediction}
\subsubsection{Performance around Ovulation}\label{subsubsec:ov_over_performance_around_ovulation}
\subsubsection{Impact of Input Window Length}\label{subsubsec:ov_over_impact_of_historical_context}
\begin{landscape}
\begin{table}
\small
\begin{tabularx}{\linewidth}{l*{6}{X}}
\toprule
\multirow{2}{*}{Input-Length in Days} & \multicolumn{3}{c}{MAE} & \multicolumn{3}{c}{MSE} \\
\cmidrule(r){2-4} \cmidrule(r){5-7}
& OV-Over Overall & OV-Over Before OV & OV-Over After OV & OV-Over Overall & OV-Over Before OV & OV-Over After OV \\
\midrule
\multicolumn{7}{c}{\textbf{LSTM}} \\
\midrule
10 & 0.1218 & 0.1044 & 0.1223 & \underline{0.0612} & 0.0289 & 0.0711 \\
20 & 0.1153 & \underline{\textbf{0.0745}} & 0.1312 & 0.0641 & \underline{\textbf{0.0212}} & 0.0822 \\
40 & 0.1066 & 0.0820 & 0.1128 & 0.0616 & 0.0281 & 0.0740 \\
80 & 0.1173 & 0.0842 & 0.1291 & 0.0647 & 0.0263 & 0.0801 \\
160 & \underline{0.1039} & 0.1139 & \underline{0.0973} & 0.0557 & 0.0462 & \underline{0.0580} \\
\midrule
\multicolumn{7}{c}{\textbf{Transformer}} \\
\midrule
10 & 0.1137 & 0.1006 & 0.1186 & 0.0618 & 0.0336 & 0.0740 \\
20 & 0.1204 & 0.0771 & 0.1366 & 0.0690 & \underline{0.0255} & 0.0864 \\
40 & \underline{\textbf{0.1017}} & 0.1409 & \underline{\textbf{0.0883}} & \underline{\textbf{0.0533}} & 0.0621 & \underline{\textbf{0.0520}} \\
80 & 0.1138 & \underline{0.0897} & 0.1234 & 0.0654 & 0.0356 & 0.0788 \\
160 & 0.1076 & 0.0959 & 0.1141 & 0.0606 & 0.0379 & 0.0714 \\
\midrule
\multicolumn{7}{c}{\textbf{Convolution-LSTM}} \\
\midrule
10 & 0.1847 & 0.1878 & 0.1840 & 0.0819 & 0.0581 & 0.0949 \\
20 & 0.1493 & 0.1274 & 0.1562 & \underline{0.0699} & \underline{0.0389} & \underline{0.0833} \\
40 & \underline{0.1455} & \underline{0.1089} & \underline{0.1561} & 0.0722 & 0.0358 & 0.0852 \\
80 & 0.2327 & 0.1796 & 0.2507 & 0.1168 & 0.0686 & 0.1327 \\
160 & 0.2518 & 0.2040 & 0.2757 & 0.1293 & 0.0878 & 0.1503 \\
\midrule
\multicolumn{7}{c}{\textbf{Convolution-Transformer}} \\
\midrule
10 & 0.1472 & 0.1053 & 0.1651 & 0.0768 & 0.0317 & 0.0966 \\
20 & 0.1530 & 0.1307 & 0.1637 & 0.0745 & 0.0443 & 0.0886 \\
40 & \underline{0.1448} & 0.1228 & \underline{0.1514} & \underline{0.0709} & 0.0435 & \underline{0.0820} \\
80 & 0.1685 & 0.1164 & 0.1889 & 0.0865 & 0.0345 & 0.1089 \\
160 & 0.2440 & \underline{0.1051} & 0.3117 & 0.1403 & \underline{0.0286} & 0.1946 \\
\bottomrule
\end{tabularx}
\caption{Evaluation Metrics for the Ovulation-Over Target across Different Model Architectures and Input Lengths on a fixed Input Resolution of 12 Values per Day.
\underline{Underlined} values represent the best value for each metric within a model.
\textbf{\underline{Bold + Underlined}} values represent the global best values across all models for a given metric.}
\label{tab:ov_over_results_by_window_length}
\end{table}
\end{landscape}
\subsubsection{Impact of Input Resolution}\label{subsubsec:ov_over_impact_of_input_resolution}
\begin{landscape}
\begin{table}
\small
\begin{tabularx}{\linewidth}{l*{6}{X}}
\toprule
\multirow{2}{*}{Values Per Day} & \multicolumn{3}{c}{MAE} & \multicolumn{3}{c}{MSE} \\
\cmidrule(r){2-4} \cmidrule(r){5-7}
& OV-Over Overall & OV-Over Before OV & OV-Over After OV & OV-Over Overall & OV-Over Before OV & OV-Over After OV \\
\midrule
\multicolumn{7}{c}{\textbf{LSTM}} \\
\midrule
1 & 0.1691 & 0.1280 & 0.1819 & 0.0914 & 0.0411 & 0.1099 \\
2 & 0.1431 & 0.1239 & 0.1471 & 0.0747 & 0.0442 & 0.0849 \\
4 & 0.1344 & 0.1130 & 0.1417 & 0.0680 & 0.0371 & 0.0807 \\
12 & \underline{0.1153} & \underline{\textbf{0.0745}} & 0.1312 & 0.0641 & \underline{\textbf{0.0212}} & 0.0822 \\
24 & 0.1192 & 0.0975 & 0.1240 & \underline{0.0633} & 0.0288 & 0.0755 \\
48 & 0.1463 & 0.2493 & \underline{0.0973} & 0.0768 & 0.1203 & \underline{\textbf{0.0550}} \\
72 & 0.1587 & 0.1113 & 0.1844 & 0.0857 & 0.0341 & 0.1126 \\
288 & 0.1353 & 0.1801 & 0.1169 & 0.0726 & 0.0799 & 0.0713 \\
\midrule
\multicolumn{7}{c}{\textbf{Transformer}} \\
\midrule
1 & 0.1687 & 0.1582 & 0.1709 & 0.0883 & 0.0578 & 0.0996 \\
2 & 0.1469 & 0.0895 & 0.1676 & 0.0823 & 0.0260 & 0.1044 \\
4 & 0.1282 & 0.0999 & 0.1393 & 0.0704 & 0.0329 & 0.0862 \\
12 & 0.1204 & \underline{0.0771}& 0.1366 & 0.0690 & \underline{0.0255}& 0.0864 \\
24 & 0.1952 & 0.1649 & 0.2102 & 0.0904 & 0.0638 & 0.1040 \\
48 & 0.1137 & 0.1159 & 0.1073 & 0.0610 & 0.0480 & 0.0629 \\
72 & \underline{\textbf{0.1041}}& 0.1180 & \underline{\textbf{0.0947}}& \underline{\textbf{0.0585}}& 0.0538 & 0.0581 \\
288 & 0.1319 & 0.1879 & 0.1097 & 0.0617 & 0.0769 & \underline{0.0578}\\
\bottomrule
\end{tabularx}
\caption{Evaluation Metrics for the Ovulation-Over Target across Different Model Architectures and Input Resolutions on a fixed Input-Window-Length of 20 Days.
\underline{Underlined} values represent the best value for each metric within a model.
\textbf{\underline{Bold + Underlined}} values represent the global best values across all models for a given metric.}
\label{tab:ov_over_results_by_resolution}
\end{table}
\end{landscape}
\subsubsection{Comparison with Baselines}\label{subsubsec:ov_over_comparison_with_baselines}
\subsection{Stratified Analysis}\label{subsec:stratified_analysis}
\subsubsection{Regular vs Irregular Cycles}\label{subsubsec:regular_vs_irregular_cycles}
\subsubsection{Influence of User History Depth}\label{subsubsec:influence_of_past_user_data}
\subsection{Use-Case Evaluation Results}\label{subsec:use_case_evaluation_results}
\subsubsection{Contraception Use-Case Results}\label{subsubsec:use_case_contraception_results}
\subsubsection{Pregnancy Use-Case Results}\label{subsubsec:use_case_pregnancy_results}
\subsection{Summary of Key Findings}\label{subsec:summary_of_key_findings}
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