%! Author = alex
%! Date = 3/6/25


\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.
Below we discuss the findings in relation to these objectives, their implications, and limitations.

\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.

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.

\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.

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.

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.



%\section{Discussion}\label{sec:discussion}

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

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.

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.

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.

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