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Alex Blank
2025-08-25 11:38:26 +00:00
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thesis/main.tex
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@@ -14,6 +14,7 @@
\usepackage{pdflscape}
\usepackage{adjustbox}
\usepackage{multirow}
\usepackage{subcaption}
\usepackage{blindtext}
\usepackage[a4paper, margin=1in]{geometry}
\usepackage[toc,page]{appendix}
thesis/sections/discussion.tex
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@@ -42,7 +42,7 @@ 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.
It is clearly visible, that the predictions improve with each cycle, until they almost exactly match the targets.
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}.
@@ -63,6 +63,16 @@ 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.
It is not uncommon for women to have a clear temperature rise without an ovulation and vice versa,
to have an ovulation but no clear temperature rise.
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.
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{resources/figures/discussion/temperature_drop_fertility}
@@ -86,7 +96,7 @@ to be able to differentiate between ovulation-related and unrelated temperature
\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 fertility-probability prediction. (Values are scaled features)
incorrect prediction. (Values are scaled features)
}
\label{fig:discussion_unclear_temperature_drop}
\end{figure}
@@ -102,6 +112,25 @@ This is likely information indicating some form of regularity, which the models
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.
%
%In general, we expect the transformer based model to outperform the LSTM basd models, as they have proven to be
thesis/sections/results.tex
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@@ -582,24 +582,6 @@ Each evaluation used a test set of 100 users (100 user-years) and was repeated f
we report means and 95\% confidence intervals (CIs).
\subsubsection{Contraception Use-Case Results}\label{subsubsec:use_case_contraception_results}
\begin{table}
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Denials & Incorrect Denials \\
\midrule
Convolutional LSTM & 1154 (1149-1158) & 34.9 (34.1-35.7) & 1615 (1611-1620) & 4963 (4954-4971) \\
Transformer & 3200 (3194-3207) & 4.4 (4.1-4.7) & 1817 (1812-1822) & 2717 (2710-2724) \\
Convolutional Transformer & 1156 (1151-1160) & 34.3 (33.5-35.0) & 1613 (1608-1619) & 4974 (4965-4983) \\
LSTM & 3206 (3199-3213) & 4.6 (4.3-4.9) & 1832 (1827-1838) & 2711 (2705-2717) \\
Last-Cycle Baseline & 6066 (6057-6075) & 127.5 (125.9-129.1) & 918 (915-922) & 762 (759-766) \\
Population-Mean Baseline & 5874 (5865-5883) & 153.7 (151.9-155.5) & 749 (746-752) & 1121 (1116-1125) \\
User-Mean Baseline & 5933 (5924-5942) & 105.8 (104.4-107.2) & 1030 (1026-1034) & 776 (772-779) \\
\bottomrule
\end{tabularx}
\caption{Contraception metrics at threshold \textbf{0.01} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.}
\label{tab:results_contraception_use_case_0_01}
\end{table}
\paragraph{Threshold 0.01 (Table~\ref{tab:results_contraception_use_case_0_01}).}
At the strictest threshold of 0.01, Transformer and LSTM models achieve the lowest pregnancy rates, only 4.4 to 4.6
@@ -611,10 +593,36 @@ leading to roughly 34–35 pregnancies, or about 30 per 1,000 events—far less
All baseline models perform substantially worse, with pregnancy counts exceeding 100 in all cases, confirming the value of personalized predictions.
\begin{table}
\centering
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Denials & Incorrect Denials \\
Model & No. of Intercourse Events & Pregnancies & Correct Denials & Incorrect Denials \\
\midrule
Convolutional LSTM & 1154 (1149-1158) & 34.9 (34.1-35.7) & 1615 (1611-1620) & 4963 (4954-4971) \\
Transformer & 3200 (3194-3207) & 4.4 (4.1-4.7) & 1817 (1812-1822) & 2717 (2710-2724) \\
Convolutional Transformer & 1156 (1151-1160) & 34.3 (33.5-35.0) & 1613 (1608-1619) & 4974 (4965-4983) \\
LSTM & 3206 (3199-3213) & 4.6 (4.3-4.9) & 1832 (1827-1838) & 2711 (2705-2717) \\
Last-Cycle Baseline & 6066 (6057-6075) & 127.5 (125.9-129.1) & 918 (915-922) & 762 (759-766) \\
Population-Mean Baseline & 5874 (5865-5883) & 153.7 (151.9-155.5) & 749 (746-752) & 1121 (1116-1125) \\
User-Mean Baseline & 5933 (5924-5942) & 105.8 (104.4-107.2) & 1030 (1026-1034) & 776 (772-779) \\
\bottomrule
\end{tabularx}
\caption{Contraception metrics at threshold \textbf{0.01} for all models.}
\label{tab:results_contraception_use_case_0_01}
\end{subtable}
\vspace{1.5em}
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Intercourse Events & Pregnancies & Correct Denials & Incorrect Denials \\
\midrule
Convolutional LSTM & 2509 (2502-2515) & 55.0 (54.0-56.0) & 1448 (1444-1452) & 3768 (3760-3775) \\
Transformer & 3801 (3793-3810) & 8.2 (7.8-8.6) & 1768 (1763-1773) & 2162 (2157-2168) \\
@@ -625,24 +633,18 @@ All baseline models perform substantially worse, with pregnancy counts exceeding
User-Mean Baseline & 5988 (5978-5997) & 108.8 (107.3-110.3) & 998 (994-1002) & 764 (761-768) \\
\bottomrule
\end{tabularx}
\caption{Contraception metrics at threshold \textbf{0.05} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.}
\caption{Contraception metrics at threshold \textbf{0.05} for all models.}
\label{tab:results_contraception_use_case_0_05}
\end{table}
\end{subtable}
\paragraph{Threshold 0.05 (Table~\ref{tab:results_contraception_use_case_0_05}).}
Increasing the threshold to 0.05 improves access: Transformer and LSTM models now permit approximately 3,800 intercourse
events while still limiting pregnancies to around 8.2 (2.2 per 1,000).
This represents a ~19\% increase in events over threshold 0.01, at the cost of a modest rise in pregnancies (+3.8 absolute, +86\% relative).
\vspace{1.5em}
Convolutional models also allow more events (~2,510) but continue to produce significantly more pregnancies (~55),
yielding a less favorable risk-benefit profile.
Baselines remain underperforming.
\begin{table}
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Denials & Incorrect Denials \\
Model & No. of Intercourse Events & Pregnancies & Correct Denials & Incorrect Denials \\
\midrule
Convolutional LSTM & 3596 (3588-3603) & 75.2 (74.0-76.4) & 1292 (1288-1297) & 2847 (2840-2853) \\
Transformer & 4226 (4217-4234) & 13.3 (12.8-13.7) & 1692 (1687-1696) & 1822 (1817-1827) \\
@@ -653,10 +655,23 @@ Baselines remain underperforming.
User-Mean Baseline & 6014 (6005-6022) & 111.8 (110.3-113.3) & 969 (965-973) & 758 (755-762) \\
\bottomrule
\end{tabularx}
\caption{Contraception metrics at threshold \textbf{0.10} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.}
\caption{Contraception metrics at threshold \textbf{0.10} for all models.}
\label{tab:results_contraception_use_case_0_10}
\end{subtable}
\caption{grouped contraception metrics at thresholds 0.01, 0.05, and 0.10. values are means over 200 iterations; 95\% confidence intervals in parentheses.}
\label{tab:results_contraception_grouped}
\end{table}
\paragraph{Threshold 0.05 (Table~\ref{tab:results_contraception_use_case_0_05}).}
Increasing the threshold to 0.05 improves access: Transformer and LSTM models now permit approximately 3,800 intercourse
events while still limiting pregnancies to around 8.2 (2.2 per 1,000).
This represents a ~19\% increase in events over threshold 0.01, at the cost of a modest rise in pregnancies (+3.8 absolute, +86\% relative).
Convolutional models also allow more events (~2,510) but continue to produce significantly more pregnancies (~55),
yielding a less favorable risk-benefit profile.
Baselines remain underperforming.
\paragraph{Threshold 0.10 (Table~\ref{tab:results_contraception_use_case_0_10}).}
A further increase to 0.10 raises Transformer/LSTM events to ~4,220, but also raises pregnancies to ~13.3 (3.1 per 1,000).
This is a ~11\% gain in access compared to 0.05, but the pregnancy count increases by ~62\%.
@@ -669,11 +684,16 @@ Transformer and LSTM models perform best, allowing a relatively high number of i
This threshold offers the best compromise and is selected as the most promising setting for contraceptive use.
\subsubsection{Pregnancy Use-Case Results}\label{subsubsec:use_case_pregnancy_results}
\begin{table}
\centering
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
Model & No. of Intercourse Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
\midrule
Convolutional LSTM & 4899 (4890-4908) & 216.9 (214.8-219.1) & 10038 & 1734 \\
Transformer & 3685 (3678-3692) & 264.9 (262.7-267.0) & 17489 & 350 \\
@@ -684,23 +704,18 @@ This threshold offers the best compromise and is selected as the most promising
User-Mean Baseline & 1652 (1647-1656) & 158.4 (156.8-160.0) & 24528 & 3523 \\
\bottomrule
\end{tabularx}
\caption{Pregnancy metrics at threshold \textbf{0.01} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.
Under our simulation at a fixed threshold, correct/incorrect deferrals are deterministic; CIs are therefore omitted for these columns.}
\caption{Pregnancy metrics at threshold \textbf{0.01} for all models. }
\label{tab:results_pregnancy_use_case_0_01}
\end{table}
\end{subtable}
\paragraph{Threshold 0.01 (Table~\ref{tab:results_pregnancy_use_case_0_01}).}
In the conception use-case, Transformer and LSTM models generate the highest pregnancy counts (~265–267) at ~3,685 intercourse events (72 per 1,000).
Convolutional models yield fewer pregnancies (~214–217) but allow ~4,900 intercourse events, resulting in ~44 pregnancies per 1,000.
\vspace{1.5em}
Baselines underperform on both metrics, allowing fewer events and achieving lower pregnancy counts, suggesting they are
overly conservative without yielding benefits in effectiveness.
\begin{table}
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
Model & No. of Intercourse Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
\midrule
Convolutional LSTM & 6174 (6164-6184) & 236.1 (234.1-238.2) & 4332 & 1076 \\
Transformer & 4253 (4245-4261) & 270.9 (268.6-273.1) & 14825 & 190 \\
@@ -711,24 +726,18 @@ overly conservative without yielding benefits in effectiveness.
User-Mean Baseline & 1695 (1690-1701) & 158.3 (156.6-160.1) & 24271 & 3567 \\
\bottomrule
\end{tabularx}
\caption{Pregnancy metrics at threshold \textbf{0.05} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.}
\caption{Pregnancy metrics at threshold \textbf{0.05} for all models.}
\label{tab:results_pregnancy_use_case_0_05}
\end{table}
\end{subtable}
\paragraph{Threshold 0.05 (Table~\ref{tab:results_pregnancy_use_case_0_05}).}
At threshold 0.05, Transformer/LSTM models slightly increase intercourse access (~4,250 events) with pregnancies rising to ~271–273 (64 per 1,000).
Notably, these models also achieve very low incorrect deferral counts (~190), indicating they rarely block opportunities for conception when they shouldn’t.
\vspace{1.5em}
Convolutional models allow substantially more intercourse (~6,170) with lower pregnancy counts (~236),
but at the cost of higher incorrect deferrals (~1,076).
This suggests they are more permissive but less selective.
\begin{table}
\begin{subtable}{\textwidth}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{l*{5}{X}}
\toprule
Model & No. of Inter. Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
Model & No. of Intercourse Events & Pregnancies & Correct Deferrals & Incorrect Deferrals \\
\midrule
Convolutional LSTM & 3887 (3880-3895) & 198.0 (196.1-199.9) & 14544 & 2296 \\
Transformer & 3291 (3284-3298) & 260.7 (258.6-262.7) & 19261 & 551 \\
@@ -739,10 +748,30 @@ This suggests they are more permissive but less selective.
User-Mean Baseline & 1619 (1614-1624) & 154.0 (152.4-155.6) & 24717 & 3501 \\
\bottomrule
\end{tabularx}
\caption{Pregnancy metrics at threshold \textbf{0.10} for all models. Values are means over 200 iterations; 95\% CIs in parentheses.}
\caption{Pregnancy metrics at threshold \textbf{0.10} for all models.}
\label{tab:results_pregnancy_use_case_0_10}
\end{subtable}
\caption{grouped pregnancy metrics at thresholds 0.01, 0.05, and 0.10. values are means over 200 iterations; 95\% confidence intervals in parentheses.
Under our simulation at a fixed threshold, correct/incorrect deferrals are deterministic; CIs are therefore omitted for these columns.}
\label{tab:results_pregnancy_grouped}
\end{table}
\paragraph{Threshold 0.01 (Table~\ref{tab:results_pregnancy_use_case_0_01}).}
In the conception use-case, Transformer and LSTM models generate the highest pregnancy counts (~265–267) at ~3,685 intercourse events (72 per 1,000).
Convolutional models yield fewer pregnancies (~214–217) but allow ~4,900 intercourse events, resulting in ~44 pregnancies per 1,000.
Baselines underperform on both metrics, allowing fewer events and achieving lower pregnancy counts, suggesting they are
overly conservative without yielding benefits in effectiveness.
\paragraph{Threshold 0.05 (Table~\ref{tab:results_pregnancy_use_case_0_05}).}
At threshold 0.05, Transformer/LSTM models slightly increase intercourse access (~4,250 events) with pregnancies rising to ~271–273 (64 per 1,000).
Notably, these models also achieve very low incorrect deferral counts (~190), indicating they rarely block opportunities for conception when they shouldn’t.
Convolutional models allow substantially more intercourse (~6,170) with lower pregnancy counts (~236),
but at the cost of higher incorrect deferrals (~1,076).
This suggests they are more permissive but less selective.
\paragraph{Threshold 0.10 (Table~\ref{tab:results_pregnancy_use_case_0_10}).}
At the highest threshold, Transformer/LSTM models see a drop in access (~3,290 events) and in pregnancies (~261),
but with an increase in incorrect deferrals (~551).