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\section{Discussion}\label{sec:discussion}
\subsection{RQ1: Model Architecture Evuation an Optimization}\label{subsec:discussion_rq1_model_evaluation}
The first research objective considered different model architectures and how they perform
under various hyperparameter configurations, with respect to the optimization goals of this study.
We found that non-convolutional models performed best with medium resolutions and longer input windows,
where they also outperformed their convolutional counterparts.
This suggests that including more historical context improves prediction accuracy.
However, there appears to be a trade-off:
while more information can improve predictions, it also introduces additional noise, which the models struggle to handle effectively.
The strong performance at medium resolutions indicates a possible sweet spot—balancing information richness with model capacity and generalization.
The convolutional variants performed best with medium-length input windows, which was somewhat surprising.
One would expect convolutional downsampling to enable more efficient data representation,
allowing the model to extract relevant patterns from high-resolution data and to perform better on longer sequences.
However, this was not observed in our experiments.
Instead, convolutional models performed worse than non-convolutional models on longer input windows,
suggesting that the benefits of downsampling may be offset by limitations in capturing long-range dependencies.
For medium and short input windows, however, convolutional models did outperform the non-convolutional
variants—indicating that the convolution itself provides an advantage when input length is limited.
To our knowledge, no prior studies have compared different deep learning architectures for real-time fertility prediction.
This highlights both the novelty and the exploratory nature of our approach.
All these results must be interpreted with caution, as they are based on single-shot experiments and are not statistically robust.
A more rigorous evaluation would involve training all models multiple times to minimize the
impact of random initialization and other stochastic processes in training.
For most metrics, differences in performance were small, often less than 1\%, and could easily be attributed to such variability.
We are also aware of potential losses in predictive quality due to class imbalance in the labels.
Especially in long cycles, the targets are mostly zero, except for a narrow window around ovulation
(for the fertility-probability target) or the area after ovulation (for the ov-over target).
Positive-to-negative target ratios can reach 10–20:1 in long cycles, meaning for each non-zero target day,
there are 10 to 20 days with all-zero targets.
This imbalance may introduce instability during training and reduce predictive performance.
Future iterations of this study could incorporate class-weighting or loss-balancing mechanisms to address this issue.
Future work should include a more thorough parameter search and statistically more robust evaluation methodology.
A more sophisticated hyperparameter search may be necessary to identify globally optimal configurations for each model architecture.
Time and resource constraints could be alleviated using more efficient search algorithms such as Bayesian Optimization,
Genetic Algorithms, or Neural Architecture Search (NAS) to better explore the joint parameter space.
Additionally, we only focused on basic models—LSTMs and Transformers, with convolutional hybrids.
A closer look into alternative architectures, or tailoring architectures more specifically
to the characteristics of menstrual cycle data, could significantly improve predictions.
Recent Transformer variants for time series modeling, such as \emph{TimeXer}~\cite{wang_timexer_2024}
or \emph{MAMBA}~\cite{wang_is_2024}, may offer better performance.
Alternatively, a custom architecture could be developed to reflect the domain-specific structure of biological temperature data more closely.
This could be combined with a more sophisticated convolutional setup or preprocessing strategy
to handle high-resolution inputs more efficiently.
Such preprocessing might help overcome computational bottlenecks that raw LSTMs and Transformers encounter when dealing with large input sequences.
Moreover, a more statistically grounded approach to feature selection could further improve predictive performance.
Both raw and engineered features could be evaluated for their impact on model output.
Especially promising are intermediate features such as cycle-level aggregates,
temperature accumulation over time or space, and static user-level characteristics.
The database used in this study also contains an extensive set of user-logged marker events, such as intercourse,
intermediate bleeding, or illnesses, which could help the models learn correlations between these events and temperature fluctuations.
Finally, exploring alternative prediction targets may help address some of the core challenges of fertility prediction.
Beyond the fertility-probability and ov-over indicators used in this study,
targets such as the number of days to the next ovulation (or since the last), or the ovulation day
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}
Our second research objective focused on identifying potential factors and patterns in the data
that influence fertility prediction.
To our knowledge, no prior work has explicitly analyzed the relationship between temperature patterns
and ovulation—including the corresponding fertile window—in a way that could directly inform machine learning models.
This underscores the exploratory nature of this analysis.
We identified a consistent pre-ovulatory temperature dip that aligned closely with the ground-truth fertility curve.
This drop was particularly pronounced in short and regular cycles.
In contrast, irregular cycles often exhibited too much variability and noise in the follicular phase
for the models to reliably detect this temperature drop, or to associate it meaningfully with increased fertility probability.
Interestingly, the magnitude of the temperature dip was strongly correlated with the predicted fertility probability:
larger dips tended to produce higher model confidence.
This observed correlation may be coincidental, or it may indicate a meaningful biological marker
for fertility and successful ovulation.
We hypothesize that there is a real association between the magnitude of the pre-ovulatory temperature dip and the likelihood of ovulation.
However, our method has a critical limitation: the ground-truth labels used were not based on clinically confirmed ovulation events.
This limitation may result not only in fertility-probability curves that are arbitrarily offset from their true value,
but also in the inclusion of cycles labeled as ovulatory that in fact were anovulatory.
As shown in Section~\ref{subsubsec:physiological_signs}, the only reliable indicator
of ovulation is daily transvaginal ultrasound, which was not feasible given the scale of our dataset.
Future studies could apply the current model to a smaller subset of cycles with clinically
confirmed ovulation and/or cycles exhibiting a clear temperature rise, to test the hypothesis
that a significant pre-ovulatory temperature drop is either necessary for ovulation or strongly correlated with fertility.
This approach may also help clarify the role of temperature anomalies in fertility prediction,
for example, the sharp spike shown in Figure~\ref{fig:results_rq2_anomaly_in_temperature_drop}.
Anomalies like this, which may be due to illness with fever symptoms, likely affect both
the menstrual cycle and the model's ability to detect pre-ovulatory fertility.
This case highlights that body temperature is highly sensitive to external physiological factors
that cannot be inferred from the temperature curve alone.
It is likely that many additional patterns or confounding factors in
the temperature data directly or indirectly affect model predictions.
Future research could explore this further, ideally in collaboration with experts in reproductive health.
This could lead to a more biologically grounded interpretation of the patterns uncovered by the models.
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}
The third research objective of this study was to compare model performance across subsets of users
with regular and irregular menstrual cycles.
We found that predictive performance is clearly sensitive to cycle irregularity.
Both overall accuracy and the improvement in performance over a growing user history
were substantially better for regular cycles compared to irregular ones.
This suggests that past cycles contain valuable information that helps the models
predict the current cycle more reliably, especially when those past cycles follow consistent patterns.
Some of this improvement can also be attributed to static features, several of which are
derived from aggregated past cycles, such as average cycle length or average ovulation day.
These features appear to be more informative and stable in the regular cycle group.
Based on the clear difference in performance, we hypothesize, that all models rely more on those static features
than on patterns identified in the temperature curves, since if that were the case, the difference would be smaller
or non-existent.
There might be additional factors that differentiate regular from irregular cycles, that might explain the results,
which have not been identified yet.
This could also point out, that it is hard or even impossible to reliably predict fertility based on temperature alone,
but this hypothesis needs to be investigated in further research.
\citeauthor{yu_tracking_2022} also report a significant drop in performance for irregular cycles
in their study~\cite{yu_tracking_2022}, particularly in terms of sensitivity.
While we cannot directly compare results due to methodological differences, especially since
our models do not perform explicit binary classification into fertile vs.\ non-fertile days, a similar trend is observable.
In our case, the models tend to overestimate fertility probability when faced with uncertainty, particularly in irregular cycles
(see Figure~\ref{fig:results_rq2_irregular_cycle_predictions_example}).
As a result, we do not report specificity or sensitivity values.
However, the use-case scenarios in the next section offer a more binary evaluation framework.
A promising direction for future work would be to further investigate the causes of
performance degradation in irregular cycle groups.
One potential experiment could involve removing static features derived from past cycles to evaluate whether the models
are genuinely using the temperature patterns from previous cycles that fall within
the current input window, or relying mainly on those engineered features.
It may also be valuable to explore the effect of increasing the input window length further.
Ideally, the model would have access to the entire cycle history of a user for training and decision-making.
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}
% -------------------------------------------------------------------------------------
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.
@@ -12,21 +171,24 @@ Below we discuss the findings in relation to these objectives, their implication
\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.
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.
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
%[continue here: bring in your figure-based examples of temperature drops, anomalies, and unclear cases, with interpretation rather than description.]
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.
%[continue here: bring in your figure-based examples of temperature drops, anomalies, and unclear cases, with interpretation rather than description.]
\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.
@@ -49,44 +211,6 @@ For pregnancy planning, results were less directly comparable, reflecting the mu
Nonetheless, the analysis illustrates how probabilistic outputs could be adapted to individual risk preferences,
highlighting the flexibility of machine learning approaches over fixed rules.
%[continue here: expand with more detail on threshold effects, how different models fared in contraception vs. pregnancy contexts, and the implications for user-facing tools.]
\subsection{Comparison to Rule-Based Baselines}
Compared with simple heuristic baselines, all machine learning models demonstrated superior predictive performance,
particularly in irregular cycles where rule-based approaches break down.
This highlights the advantage of data-driven methods, which can learn subtle patterns and adapt to user-specific variability
that static rules cannot capture.
Nevertheless, rule-based methods retain value for their simplicity and interpretability,
and could complement machine learning models in hybrid approaches where transparency is essential.
%[continue here: connect this explicitly to natural family planning methods in the literature, and comment on where ML truly adds value.]
\subsection{Limitations}
Several limitations constrain interpretation.
First, results were reported on aggregate test sets without uncertainty quantification;
per-user predictions were not retained, preventing bootstrap confidence intervals or paired statistical testing.
Second, labels were generated by a retrospective algorithm trained on expert annotations.
Any inaccuracies in this algorithm propagate directly into the training data and may bias model learning.
Third, reliance on temperature alone leaves the models vulnerable to anomalies caused by illness, lifestyle, or measurement error.
Finally, resource constraints limited the scope of hyperparameter optimization and the exploration of more advanced architectures.
%[continue here: add dataset-specific limitations such as age range, long-cycle imbalance, and lack of prospective evaluation.]
\subsection{Future Work}
Future extensions of this work should pursue several directions.
Incorporating additional user-entered markers—such as bleeding, stress, illness,
or intercourse—may provide critical context to disambiguate temperature anomalies.
Alternative target formulations, such as predicting the day of ovulation or the time-to-ovulation,
could reduce class imbalance and better reflect clinical needs.
Training separate models for fertility and ovulation-over tasks may also improve performance by reducing task interference.
From a methodological perspective, exploring architectures tailored for time-series forecasting—such as
TimeXer or MAMBA—alongside principled hyperparameter optimization techniques (e.g., Bayesian optimization, NAS) could yield further gains.
Most importantly, future studies should evaluate these approaches prospectively,
with clinically validated ovulation labels and diverse populations,
to establish their real-world utility in natural family planning and contraception.
%[continue here: add your own vision for clinical applications, e.g. integration into fertility apps, medical oversight, or regulatory implications.]
%\section{Discussion}\label{sec:discussion}
@@ -126,16 +250,6 @@ 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.
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/discussion/regular_cycle_fertility_prediction}
\caption{
Temperature rolling average and fertility-probability prediction for a user with a regular cycle pattern. (Values are scaled features)
}
\label{fig:discussion_regular_cycle_fertility_prediction}
\end{figure}
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.
@@ -166,33 +280,6 @@ The identified temperature drop and the fertility that seems to come with it cou
with more accurate ovulation labeling.
It might be an indicator for a successful upcoming ovulation.
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_drop_fertility}
\caption{
Temperature rolling average and fertility-probability prediction with a clear correlation between the temperature drop
pre-ovulation and the fertility. (Values are scaled features)
}
\label{fig:discussion_temperature_drop_fertility_prediction}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_spike_in_temperature_dop}
\caption{
Temperature rolling average and fertility-probability prediction with a disruptive temperature spike during the pre-ovulatory phase,
leading to an early end of the predicted fertile window.
}
\label{fig:discussion_spike_in_temperature_drop}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_unclear_temperature_drop}
\caption{
Temperature rolling average and fertility-probability prediction with no clear temperature drop and a resulting
incorrect prediction. (Values are scaled features)
}
\label{fig:discussion_unclear_temperature_drop}
\end{figure}
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.
@@ -240,53 +327,6 @@ While the results themselves can give a clear indication of both the fertility p
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.
\subsection{Limitations}\label{subsec:limiations}
This analysis reports aggregate test-set metrics without uncertainty quantification.
Because we did not retain per-user predictions, we cannot compute user-level bootstrap confidence intervals or perform paired significance testing.
As a result, apparent performance differences, especially small ones, may reflect sampling variability.
Future re-evaluation that stores per-user predictions will enable user-level bootstrapping, calibration assessment, and formal comparisons.
\subsection{Future Work}\label{sec:future_work}
There are several directions in which this study could be extended,
most of which were omitted due to time and resource constraints but represent valuable areas for future exploration.
One major area is feature selection.
The dataset used includes additional user-entered markers such as physiological signs (e.g., bleeding, illness, stress)
and external events (e.g., intercourse, pregnancy tests).
These markers were not included in the present analysis but may carry predictive value and could meaningfully improve model performance.
Similarly, the introduction of engineered or intermediate features, derived from raw inputs, may help models better
capture relevant patterns and temporal dependencies.
Additionally, the target features could be modelled in a better way, as, especially for long cycles,
there is a large imbalance of value distribution.
If a cycle has a length of 100 days with an ovulation at day 90, only 10\% of the ovulation-over targets are one.
The same applies to the fertility target, which will be zero throughout almost the whole sequence,
which will make it harder for the models to learn useful information.
Alternative target formulations could also be explored to better reflect the structure of the fertile window and ovulation.
For example, instead of predicting a daily fertility probability, models could aim to identify the absolute day of ovulation,
or estimate the time until the next (or since the last) ovulation event.
Additionally, multiple models could be trained individually for each target, to avoid confusing the models
on two different prediction tasks.
While the fertility-probability and the timing of the ovulation have an inherent causal relationship,
there might be anomalies in the data that confuse one or both targets, and independent predictions might perform better.
As noted in Section~\ref{subsubsec:data_labeling}, ovulation labels were assigned using a
retrospective algorithm trained on expert-annotated data.
Any inaccuracies in this algorithm propagate directly to the supervised learning labels.
Thus, improving prediction quality may require a newly labeled dataset—ideally combining expert review with algorithmic assistance.
Finally, while the models used in this study (LSTMs and Transformers) are well-established for time-series analysis,
they were not extensively customized.
Future work could involve tailoring architectures more specifically to the characteristics of menstrual cycle data.
Recent transformer variants designed for time series, such as \emph{TimeXer}~\cite{wang_timexer_2024} or \emph{MAMBA}~\cite{wang_is_2024},
may offer improved performance.
Alternatively, a custom architecture could be developed to better reflect the domain-specific structure of biological temperature data.
Future work may incorporate more advanced hyperparameter optimization techniques,
such as Bayesian Optimization, Genetic Algorithms, or Neural Architecture Search (NAS),
to better explore the joint parameter space in a more efficient and principled manner.
% 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.