further work on results
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@@ -136,10 +136,10 @@ For women aiming to avoid pregnancy, minimizing false-negative predictions is cr
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Although false-positives may lead to unnecessary abstinence, this outcome is generally considered less severe.
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Consequently, prediction algorithms should be conservative, erring on the side of higher fertility estimates to prioritize safety.
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Conversely, for women aiming to conceive, false-positive predictions could misdirect efforts toward incorrect cycle days,
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causing frustration or delays.
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False-negatives have fewer negative consequences.
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Therefore, algorithms for this group should prefer cautious fertility estimates, reducing the risk of misdirected effort.
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For women aiming to conceive, incorrect predictions are less severe, as they might, at worst, result in misdirected
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pregnancy effort, causing frustration or delays, but no potential dangers to the health of a woman.
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Therefore, algorithms for this group don't need to be as conservative.
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It remains to be seen, where the middle ground lies and how different algorithms perform for different use cases.
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\subsubsection{Physiological Signs of Ovulation}\label{subsubsec:physiological_signs}
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Several physiological signs correlate with ovulation and can be used for prediction.
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@@ -500,6 +500,9 @@ To identify suitable configurations for each model architecture, model-specific
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The selected value ranges were intentionally broad to explore the trade-off between model complexity and generalization.
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This allowed assessment of whether increased architectural depth and capacity contribute meaningfully to performance,
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or whether simpler models are sufficient for the task.
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Due to resource and time limitations, not all configuration permutations can be tested.
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Thus, the parameters will be tested on the input configuration with the best MSE on the fertile days for each model,
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as this is the metric that represents the use cases and overall intention the best.
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\begin{table}[htbp]
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\centering
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@@ -539,6 +542,9 @@ Tables~\ref{tab:lstm_model_hyperparameters} and~\ref{tab:transformer_model_hyper
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for the LSTM-based and Transformer-based models, respectively.
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Note that the same settings were used for the hybrid models, as their architecture beyond the convolutional front end is structurally identical.
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Based on the results of the model parameter search, a best parameter set will be selected for each model architecture,
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based on the MSE of the fertility-probability target during the fertile days.
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These model configurations will then be used for further evaluations.
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\vspace{0.5em}
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We acknowledge that interactions between input and model parameters may influence final model performance,
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+170
-58
@@ -25,12 +25,11 @@
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\subsection{Overall Model Performance Across Architectures}\label{subsec:overall_model_performance_across_architectures}
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\subsection{Fertility Probability Prediction Accuracy}\label{subsec:fertility_probability_precition_accuracy}
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% show why I selected the individual input configs for model config training
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% selected by best mse fertility, use 2nd best, as it provides basically the same performance, but more input data for more complex model configs
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\subsubsection{Fertility Probability Prediction}\label{subsubsec:fertility_probability_prediction}
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\subsection{Fertility Probability Prediction}\label{subsec:fertility_probability_prediction}
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\subsubsection{Impact of Input Window Length}\label{subsubsec:fert_impact_of_historical_context}
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\begin{landscape}
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@@ -78,34 +77,31 @@
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\end{table}
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\end{landscape}
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Table~\ref{tab:fertility_results_by_window_length} presents the performance of different model architectures across various metrics and input window lengths.
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Table~\ref{tab:fertility_results_by_window_length} summarises performance across metrics and input window lengths for the fertility-probability target.
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It is evident that for both the LSTM and Transformer models, \textbf{longer input windows generally yield better performance}.
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Specifically, the LSTM achieves the best results for four out of six metrics with the 160-day window.
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The only exception is the error metrics for non-fertile days, where shorter input windows perform better.
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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.
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For both the LSTM and Transformer, longer input windows generally yield better results.
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The LSTM achieves the top scores in four of six metrics with the 160-day window, including the global best for MAE and MSE on both fertile and non-fertile days.
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The only exception is non-fertile day errors, where shorter windows perform better.
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For the Transformer model, the best performance is observed with the 160-day input window in three out of six metrics.
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However, for non-fertile day metrics, performance improves with shorter input windows.
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It is consistently outperformed by the LSTM model.
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The Transformer peaks at the 160-day window in three of six metrics but improves on non-fertile days with shorter inputs.
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Across all window lengths, it is consistently outperformed by the LSTM\@.
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The \textbf{convolutional models} tend to perform best with \textbf{medium-length input windows} (20 to 40 days).
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The \textbf{convolutional LSTM} shows its best performance with a 40-day window for most metrics,
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except for non-fertile day errors, where the 20-day window yields smaller errors.
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It also achieves the \textbf{global best performance} for non-fertile day MSE with the 20-day window.
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Similarly, the \textbf{convolutional Transformer} excels with 40-day windows for the overall and non-fertile-day metrics,
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while the best fertile-day metrics are seen with 20-day windows.
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The \textbf{convolutional Transformer} also achieves the \textbf{global best performance} for 40-day windows in both MAE and MSE\@.
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In all but non-fertile day metrics, the \textbf{convolutional Transformer} outperforms the LSTM variant.
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Convolutional models perform best with medium-length windows (20--40 days).
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The convolutional LSTM reaches its lowest errors for most metrics at 40 days, except for non-fertile MSE, where 20 days is optimal---also a global best.
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The convolutional Transformer similarly favours 40 days for overall and non-fertile-day metrics, while fertile-day metrics perform best with 20-day inputs.
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It achieves global best scores for 40-day MAE and MSE, and outperforms the convolutional LSTM in all but non-fertile day metrics.
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\subsubsection{Impact of Input Resolution}\label{subsubsec:fert_impact_of_input_resolution}
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Shifting focus from temporal span to sampling density, Table~\ref{tab:fertility_results_by_window_resolution} reports performance for the fertility-probability target across varying input resolutions.
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Convolutional models are omitted, as their convolution layers inherently perform learnable resampling.
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Figure~\ref{fig:results_performance_lstm_fertility_input_resolution} presents the results for different input resolutions used in the LSTM models,
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alongside the corresponding mean squared error (MSE) metrics.
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The plot shows the MSE values for three target categories: non-fertile days, overall MSE, and fertile days MSE\@.
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The LSTM outperforms the Transformer at all resolutions, with best-performing metrics scattered across the medium-to-high range (4--288 values/day) and no single optimum.
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Fertile-day errors are lowest at 288 values/day, while non-fertile day errors peak at 12 values/day.
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Overall MAE and MSE minima occur at 48 and 4 values/day, respectively.
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The Transformer shows a clearer trend towards higher-resolution inputs.
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Its fertile-day metrics are best at 4 values/day, whereas non-fertile day, overall MAE, and overall MSE scores peak between 48 and 288 values/day.
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Notably, the MSE for non-fertile days appears to behave inversely in relation to the other two metrics.
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However, there is no consistent upward or downward trend when changing the input window length with a fixed input resolution.
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\begin{landscape}
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\begin{table}
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@@ -145,29 +141,80 @@ However, there is no consistent upward or downward trend when changing the input
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\label{tab:fertility_results_by_window_resolution}
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\end{table}
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\end{landscape}
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\begin{figure}
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\centering
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\includegraphics[width=1.0\textwidth]{resources/figures/results/transformer_fertility_results_by_input_resolution}
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\caption{Performance of transformer models with different input window lengths and fixes input resolutions for the fertility probability target}
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\label{fig:results_performance_transformer_fertility_input_resolution}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=1.00\textwidth]{resources/figures/results/lstm_fertility_results_by_input_resolution}
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\caption{Performance of LSTM models with different input resolutions and fixes input window lengths for the fertility probability target}
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\label{fig:results_performance_lstm_fertility_input_resolution}
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\end{figure}
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\subsubsection{Impact of Model Parameters}\label{subsubsec:fert_impaoct_of_model_parameters}
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\begin{landscape}
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\begin{table}
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\scriptsize
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\begin{tabularx}{\linewidth}{l*{8}{X}}
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\toprule
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\multirow{2}{*}{Hidden Layer Size} &
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\multirow{2}{*}{\# LSTM Layers} &
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\multicolumn{3}{c}{MAE} &
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\multicolumn{3}{c}{MSE} \\
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\cmidrule(lr){3-5} \cmidrule(lr){6-8}
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& & Fert Overall & Fert Days & Non-Fert Days & Fert Overall & Fert Days & Non-Fert Days \\
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\midrule
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16 & 1 & 0.0485 & 0.1050 & 0.0252 & 0.0059 & 0.0161 & 0.0016 \\
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32 & 1 & 0.0477 & 0.1029 & 0.0248 & 0.0057 & 0.0155 & 0.0016 \\
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32 & 2 & 0.0458 & 0.0922 & 0.0269 & 0.0052 & \textbf{0.0122} & 0.0024 \\
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64 & 2 & 0.0447 & 0.0925 & 0.0250 & 0.0051 & 0.0123 & 0.0021 \\
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128 & 2 & 0.0424 & 0.0951 & 0.0201 & 0.0051 & 0.0131 & 0.0018 \\
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128 & 4 & 0.0427 & 0.0989 & 0.0191 & 0.0053 & 0.0145 & 0.0014 \\
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256 & 4 & 0.0433 & 0.1050 & \textbf{0.0175} & 0.0055 & 0.0161 & \textbf{0.0011} \\
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512 & 4 & \textbf{0.0399} & \textbf{0.0911} & 0.0189 & \textbf{0.0047} & \textbf{0.0122} & 0.0016 \\
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\bottomrule
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\end{tabularx}
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\caption{Evaluation Metrics for the Fertility-Probability Target across Different Model Parameters for the LSTM model with
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a fixed input window length of 160 days and an input resolution of 12 values per day.
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\textbf{Bold} values represent the best value for each metric within a model.}
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\label{tab:fertility_results_by_model_parameters_lstm}
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\end{table}
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\begin{table}
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\scriptsize
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\begin{tabularx}{\linewidth}{l*{8}{X}}
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\toprule
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\multirow{2}{*}{Size of Embedding} &
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\multirow{2}{*}{\# Encoder Layers} &
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\multirow{2}{*}{\# Attention Heads} &
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\multicolumn{3}{c}{MAE} &
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\multicolumn{3}{c}{MSE} \\
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\cmidrule(lr){4-6} \cmidrule(lr){7-9}
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& & & Fert Overall & Fert Days & Non-Fert Days & Fert Overall & Fert Days & Non-Fert Days \\
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\midrule
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16 & 1 & 1 & 0.0708 & 0.1262 & 0.0475 & 0.0084 & 0.0227 & 0.0024 \\
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32 & 1 & 1 & 0.0599 & 0.1163 & 0.0378 & 0.0070 & 0.0196 & 0.0019 \\
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64 & 1 & 1 & 0.0601 & 0.1178 & 0.0373 & 0.0071 & 0.0200 & 0.0020 \\
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64 & 2 & 2 & 0.0477 & 0.0908 & 0.0301 & 0.0049 & 0.0121 & 0.0020 \\
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128 & 2 & 2 & 0.0449 & 0.0904 & 0.0263 & 0.0047 & 0.0119 & 0.0017 \\
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128 & 4 & 4 & 0.0461 & 0.0979 & 0.0247 & 0.0050 & 0.0143 & 0.0013 \\
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256 & 4 & 4 & 0.0475 & 0.0919 & 0.0293 & 0.0048 & 0.0125 & 0.0017 \\
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512 & 4 & 4 & 0.0403 & \textbf{0.0831} & 0.0229 & \textbf{0.0043} & \textbf{0.0103} & 0.0018 \\
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512 & 8 & 8 & \textbf{0.0395} & 0.0967 & \textbf{0.0159} & 0.0048 & 0.0139 & \textbf{0.0011} \\
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\bottomrule
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\end{tabularx}
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\caption{Evaluation Metrics for the Fertility-Probability Target across Different Model Parameters for the Transformer model with
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a fixed input window length of 160 days and an input resolution of 12 values per day.
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\textbf{Bold} values represent the best value for each metric within a model.}
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\label{tab:fertility_results_by_model_parameters_transformer}
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\end{table}
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\end{landscape}
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\subsubsection{Comparison with Baselines}\label{subsubsec:fert_comparison_with_baselines}
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\subsection{Ovulation-Over Prediction}\label{subsubsec:ov_over_prediction}
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\subsubsection{Performance around Ovulation}\label{subsubsec:ov_over_performance_around_ovulation}
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\subsubsection{Impact of Input Window Length}\label{subsubsec:ov_over_impact_of_historical_context}
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Table~\ref{tab:ov_over_results_by_window_length} presents performance across metrics and input window lengths for the ovulation-over target.
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The LSTM and Transformer both outperform their convolutional counterparts.
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The LSTM benefits from longer windows (160 days) except for the before-ovulation metric, where 20 days is optimal---also the \textbf{global best} across models.
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The Transformer performs best with mid-length windows (40 days) for most metrics, with exceptions in after-ovulation performance (MAE: 80 days, MSE: 20 days).
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Among convolutional models, the convolutional LSTM peaks at mid-length windows, reaching lowest MAE at 40 days and lowest MSE at 20 days.
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The convolutional Transformer also favours 40 days overall, but before-ovulation performance benefits from longer inputs (160 days).
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\begin{landscape}
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\begin{table}
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\small
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@@ -179,36 +226,37 @@ However, there is no consistent upward or downward trend when changing the input
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\midrule
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\multicolumn{7}{c}{\textbf{LSTM}} \\
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\midrule
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10 & 0.1218 & 0.1044 & 0.1223 & \underline{0.0612} & 0.0289 & 0.0711 \\
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20 & 0.1153 & \underline{\textbf{0.0745}} & 0.1312 & 0.0641 & \underline{\textbf{0.0212}} & 0.0822 \\
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40 & 0.1066 & 0.0820 & 0.1128 & 0.0616 & 0.0281 & 0.0740 \\
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80 & 0.1173 & 0.0842 & 0.1291 & 0.0647 & 0.0263 & 0.0801 \\
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160 & \underline{0.1039} & 0.1139 & \underline{0.0973} & 0.0557 & 0.0462 & \underline{0.0580} \\
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10 & 0.1218 & 0.1044 & 0.1223 & 0.0612 & 0.0289 & 0.0711 \\
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20 & 0.1153 & \underline{\textbf{0.0745}} & 0.1312 & 0.0641 & \underline{\textbf{0.0212}} & 0.0822 \\
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40 & 0.1066 & 0.0820 & 0.1128 & 0.0616 & 0.0281 & 0.0740 \\
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80 & 0.1173 & 0.0842 & 0.1291 & 0.0647 & 0.0263 & 0.0801 \\
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160 & \underline{0.1039} & 0.1139 & \underline{0.0973} & \underline{0.0557} & 0.0462 & \underline{0.0580} \\
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\midrule
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\multicolumn{7}{c}{\textbf{Transformer}} \\
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\midrule
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10 & 0.1137 & 0.1006 & 0.1186 & 0.0618 & 0.0336 & 0.0740 \\
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20 & 0.1204 & 0.0771 & 0.1366 & 0.0690 & \underline{0.0255} & 0.0864 \\
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40 & \underline{\textbf{0.1017}} & 0.1409 & \underline{\textbf{0.0883}} & \underline{\textbf{0.0533}} & 0.0621 & \underline{\textbf{0.0520}} \\
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80 & 0.1138 & \underline{0.0897} & 0.1234 & 0.0654 & 0.0356 & 0.0788 \\
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160 & 0.1076 & 0.0959 & 0.1141 & 0.0606 & 0.0379 & 0.0714 \\
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10 & 0.1137 & 0.1006 & 0.1186 & 0.0618 & 0.0336 & 0.0740 \\
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20 & 0.1204 & 0.0771 & 0.1366 & 0.0690 & \underline{0.0255} & 0.0864 \\
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40 & \underline{\textbf{0.1017}} & 0.1409 & \underline{\textbf{0.0883}} & \underline{\textbf{0.0533}} & 0.0621 & \underline{\textbf{0.0520}} \\
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80 & 0.1138 & \underline{0.0897} & 0.1234 & 0.0654 & 0.0356 & 0.0788 \\
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160 & 0.1076 & 0.0959 & 0.1141 & 0.0606 & 0.0379 & 0.0714 \\
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\midrule
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\multicolumn{7}{c}{\textbf{Convolution-LSTM}} \\
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\midrule
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10 & 0.1847 & 0.1878 & 0.1840 & 0.0819 & 0.0581 & 0.0949 \\
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20 & 0.1493 & 0.1274 & 0.1562 & \underline{0.0699} & \underline{0.0389} & \underline{0.0833} \\
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40 & \underline{0.1455} & \underline{0.1089} & \underline{0.1561} & 0.0722 & 0.0358 & 0.0852 \\
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80 & 0.2327 & 0.1796 & 0.2507 & 0.1168 & 0.0686 & 0.1327 \\
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160 & 0.2518 & 0.2040 & 0.2757 & 0.1293 & 0.0878 & 0.1503 \\
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10 & 0.1847 & 0.1878 & 0.1840 & 0.0819 & 0.0581 & 0.0949 \\
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20 & 0.1493 & 0.1274 & 0.1562 & \underline{0.0699} & \underline{0.0389} & \underline{0.0833} \\
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40 & \underline{0.1455} & \underline{0.1089} & \underline{0.1561} & 0.0722 & 0.0358 & 0.0852 \\
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80 & 0.2327 & 0.1796 & 0.2507 & 0.1168 & 0.0686 & 0.1327 \\
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160 & 0.2518 & 0.2040 & 0.2757 & 0.1293 & 0.0878 & 0.1503 \\
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\midrule
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\multicolumn{7}{c}{\textbf{Convolution-Transformer}} \\
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\midrule
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10 & 0.1472 & 0.1053 & 0.1651 & 0.0768 & 0.0317 & 0.0966 \\
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20 & 0.1530 & 0.1307 & 0.1637 & 0.0745 & 0.0443 & 0.0886 \\
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40 & \underline{0.1448} & 0.1228 & \underline{0.1514} & \underline{0.0709} & 0.0435 & \underline{0.0820} \\
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80 & 0.1685 & 0.1164 & 0.1889 & 0.0865 & 0.0345 & 0.1089 \\
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160 & 0.2440 & \underline{0.1051} & 0.3117 & 0.1403 & \underline{0.0286} & 0.1946 \\
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10 & 0.1472 & 0.1053 & 0.1651 & 0.0768 & 0.0317 & 0.0966 \\
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20 & 0.1530 & 0.1307 & 0.1637 & 0.0745 & 0.0443 & 0.0886 \\
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40 & \underline{0.1448} & 0.1228 & \underline{0.1514} & \underline{0.0709} & 0.0435 & \underline{0.0820} \\
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80 & 0.1685 & 0.1164 & 0.1889 & 0.0865 & 0.0345 & 0.1089 \\
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160 & 0.2440 & \underline{0.1051} & 0.3117 & 0.1403 & \underline{0.0286} & 0.1946 \\
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\bottomrule
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||||
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\end{tabularx}
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\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.
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\underline{Underlined} values represent the best value for each metric within a model.
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@@ -219,6 +267,12 @@ However, there is no consistent upward or downward trend when changing the input
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\subsubsection{Impact of Input Resolution}\label{subsubsec:ov_over_impact_of_input_resolution}
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Table~\ref{tab:ov_over_results_by_resolution} shows results for the ovulation-over target across different resolutions.
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Convolutional models are excluded, as their convolution layers inherently perform resampling.
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The LSTM generally performs best at medium resolutions (12--48 values/day), except for the after-ovulation metric, where higher resolutions yield better results.
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The Transformer prefers higher resolutions, with optimal performance for all but the before-ovulation metric at 72 or 288 values/day.
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Before-ovulation performance peaks at a medium resolution of 12 values/day.
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\begin{landscape}
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\begin{table}
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@@ -259,6 +313,64 @@ However, there is no consistent upward or downward trend when changing the input
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\end{table}
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\end{landscape}
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\subsubsection{Impact of Model Parameters}\label{subsubsec:ov_over_impaoct_of_model_parameters}
|
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\begin{landscape}
|
||||
\begin{table}
|
||||
\scriptsize
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||||
\begin{tabularx}{\linewidth}{l*{8}{X}}
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||||
\toprule
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||||
\multirow{2}{*}{Hidden Layer Size} &
|
||||
\multirow{2}{*}{\# LSTM Layers} &
|
||||
\multicolumn{3}{c}{MAE} &
|
||||
\multicolumn{3}{c}{MSE} \\
|
||||
\cmidrule(lr){3-5} \cmidrule(lr){6-8}
|
||||
& & Fert Overall & Fert Days & Non-Fert Days & Fert Overall & Fert Days & Non-Fert Days \\
|
||||
\midrule
|
||||
16 & 1 & 0.2253 & 0.1353 & 0.2735 & 0.1196 & 0.0397 & 0.1621 \\
|
||||
32 & 1 & 0.1746 & 0.1255 & 0.2005 & 0.0860 & 0.0404 & 0.1109 \\
|
||||
32 & 2 & 0.1349 & 0.1240 & 0.1399 & 0.0674 & 0.0396 & 0.0786 \\
|
||||
64 & 2 & 0.1270 & 0.0943 & 0.1365 & 0.0645 & 0.0292 & 0.0772 \\
|
||||
128 & 2 & 0.1151 & \textbf{0.0861} & 0.1243 & 0.0626 & \textbf{0.0274} & 0.0755 \\
|
||||
128 & 4 & 0.1326 & 0.1064 & 0.1407 & 0.0658 & 0.0291 & 0.0811 \\
|
||||
256 & 4 & 0.1353 & 0.1111 & 0.1407 & 0.0662 & 0.0360 & 0.0765 \\
|
||||
512 & 4 & \textbf{0.1120} & 0.1358 & \textbf{0.0983} & \textbf{0.0616} & 0.0603 & \textbf{0.0613} \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{Evaluation Metrics for the Ovulation-Over Target across Different Model Parameters for the LSTM model with
|
||||
a fixed input window length of 160 days and an input resolution of 12 values per day.
|
||||
\textbf{Bold} values represent the best value for each metric within a model.}
|
||||
\label{tab:ov_over_results_by_model_parameters_lstm}
|
||||
\end{table}
|
||||
\begin{table}
|
||||
\scriptsize
|
||||
\begin{tabularx}{\linewidth}{l*{8}{X}}
|
||||
\toprule
|
||||
\multirow{2}{*}{Size of Embedding} &
|
||||
\multirow{2}{*}{\# Encoder Layers} &
|
||||
\multirow{2}{*}{\# Attention Heads} &
|
||||
\multicolumn{3}{c}{MAE} &
|
||||
\multicolumn{3}{c}{MSE} \\
|
||||
\cmidrule(lr){4-6} \cmidrule(lr){7-9}
|
||||
& & & Fert Overall & Fert Days & Non-Fert Days & Fert Overall & Fert Days & Non-Fert Days \\
|
||||
\midrule
|
||||
16 & 1 & 1 & 0.4792 & 0.5280 & 0.4675 & 0.2336 & 0.2820 & 0.2220 \\
|
||||
32 & 1 & 1 & 0.4406 & 0.4572 & 0.4417 & 0.2046 & 0.2179 & 0.2068 \\
|
||||
64 & 1 & 1 & 0.3614 & 0.3411 & 0.3796 & 0.1696 & 0.1604 & 0.1800 \\
|
||||
64 & 2 & 2 & 0.1532 & \textbf{0.0810} & 0.1913 & 0.0904 & 0.0302 & 0.1214 \\
|
||||
128 & 2 & 2 & 0.1476 & 0.0979 & 0.1739 & 0.0816 & 0.0332 & 0.1064 \\
|
||||
128 & 4 & 4 & \textbf{0.1114} & 0.0887 & 0.1236 & 0.0668 & 0.0368 & 0.0821 \\
|
||||
256 & 4 & 4 & 0.1310 & 0.0920 & 0.1433 & 0.0722 & \textbf{0.0293} & 0.0876 \\
|
||||
512 & 4 & 4 & 0.1222 & 0.1047 & 0.1261 & 0.0610 & 0.0321 & 0.0708 \\
|
||||
512 & 8 & 8 & 0.1126 & 0.1965 & \textbf{0.0753} & \textbf{0.0543} & 0.0868 & \textbf{0.0410} \\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\caption{Evaluation Metrics for the Ovulation-Over Target across Different Model Parameters for the Transformer model with
|
||||
a fixed input window length of 160 days and an input resolution of 12 values per day.
|
||||
\textbf{Bold} values represent the best value for each metric within a model.}
|
||||
\label{tab:ov_over_results_by_model_parameters_transformer}
|
||||
\end{table}
|
||||
\end{landscape}
|
||||
|
||||
\subsubsection{Comparison with Baselines}\label{subsubsec:ov_over_comparison_with_baselines}
|
||||
|
||||
\subsection{Stratified Analysis}\label{subsec:stratified_analysis}
|
||||
|
||||
Reference in New Issue
Block a user