further work on discussion

thesis/sections/background.tex

@@ -11,11 +11,12 @@ The menstrual cycle consists of physiological changes preparing the female body
 typically spanning around 28 days but varying considerably among individuals.
 It includes two main phases: the follicular phase, beginning with menstruation, and the luteal phase, following ovulation.
 
-During the follicular phase, ovarian follicles mature under the influence of rising estradiol levels, thickening the uterine lining (endometrium).
+During the follicular phase (Figure~\ref{fig:background_menstrual_cycle_physiology} until day 14),
+ovarian follicles mature under the influence of rising estradiol levels, thickening the uterine lining (endometrium).
 Around mid-cycle, a surge of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), triggered by peak estradiol,
 induces ovulation—the release of a mature egg into the fallopian tube.
 
-After ovulation, the luteal phase begins.
+After ovulation, the luteal phase begins (Figure~\ref{fig:background_menstrual_cycle_physiology} day 14 to 28).
 Progesterone increases substantially, maintaining endometrial thickness for potential embryo implantation.
 In parallel, a subtle rise in body temperature (~0.5°C) occurs due to progesterone elevation.
 If fertilization does not happen, progesterone and temperature decline back to baseline levels, resulting in menstruation and initiating a new cycle.
@@ -55,13 +56,17 @@ The luteal phase begins at the ovulation and continues until the next menstruati
 
 
 While many cycles exhibit a characteristic biphasic pattern, deviations from this norm are common.
-Some remain monophasic, which might be an indication for an anovulatory cycle, which is a menstrual cycle, where no ovulation occurs.
+Some do not show the typical temperature surge, which might be an indication for an anovulatory cycle.
+Anovulatory cycles don't have an ovulation, and thus cannot result in a pregnancy.
 Anovulation can have various causes, including hormonal imbalances, stress, or underlying health conditions~\cite{rosenfield_adolescent_2013}.
-Monophasic cycles with a confirmed ovulation event have been observed, so there seems to be no clear indication that it is a direct cause of anovulation~\cite{moghissi_accuracy_1976}.
+Monophasic cycles with a confirmed ovulation event have also been observed, so there seems to be no clear indication that it is a direct cause of anovulation~\cite{moghissi_accuracy_1976}.
 Thus, distinguishing between ovulatory and anovulatory cycles is challenging, as the only definitive confirmation of
 successful ovulation in a clinical sense is a pregnancy.
 Even ultrasound imaging can only confirm that an egg was released from its follicle—not whether it was successfully implanted or fertilized.
-Figure~\ref{fig:background_anovulation} shows a cycle with a monophasic temperature pattern.
+
+Figure~\ref{fig:background_labeled_cycle} shows a cycle with a typical biphasic temperature pattern.
+In contrast, Figure~\ref{fig:background_anovulation} shows a cycle with a monophasic temperature pattern.
+Over time, the temperature does not show any significant or longer lasting temperature changes.
 
 To illustrate the diversity of real-world menstrual cycles, Figures~\ref{fig:background_long_cycle} and~\ref{fig:background_short_cycle}
 show examples of cycles that are significantly longer or shorter than a normative 28-day cycle.
@@ -107,6 +112,7 @@ Fertility varies throughout the menstrual cycle, centered around the ovulation e
 An egg remains viable for about 24 hours post-ovulation, while sperm can survive up to 6 days in a woman's reproductive tract,
 thus the fertile period extends to approximately five days prior to ovulation~\cite{dunson_day-specific_1999}.
 Consequently, the whole fertile window generally spans six days: five days preceding ovulation and one day after.
+The distribution of fertility probability is not dependent on the length of the cycle.
 
 \begin{figure}[htbp]
     \centering
@@ -116,7 +122,8 @@ Consequently, the whole fertile window generally spans six days: five days prece
     \label{fig:background_pregnancy_chance}
 \end{figure}
 
-Figure~\ref{fig:background_pregnancy_chance} demonstrates the probability of fertilization peaking one day before ovulation, emphasizing the critical timing for fertility prediction.
+Figure~\ref{fig:background_pregnancy_chance} demonstrates the probability of fertilization peaking one day before ovulation,
+emphasizing the critical timing for fertility prediction.
 
 Fertility prediction fundamentally depends on accurate ovulation timing.
 However, since the goal is to identify the fertile window before ovulation occurs, detection must be early and precise.
@@ -141,6 +148,11 @@ pregnancy effort, causing frustration or delays, but no potential dangers to the
 Therefore, algorithms for this group don't need to be as conservative.
 It remains to be seen, where the middle ground lies and how different algorithms perform for different use cases.
 
+In this study, we'll focus on fertility prediction, which incorporates both use cases, and thus we will not train
+different models for each use-case.
+However, we will test the thresholds used for decision-making to find use-case dependent optimums.
+Section~\ref{subsubsec:use_case_evaluation} will introduce the methodology in more detail.
+
 \subsubsection{Physiological Signs of Ovulation}\label{subsubsec:physiological_signs}
 Several physiological signs correlate with ovulation and can be used for prediction.
 As shown in Figure~\ref{fig:background_menstrual_cycle_physiology}, these include hormonal fluctuations (LH and FSH surges) and
@@ -177,7 +189,7 @@ Thanks to a battery life of at least six months, the device supports continuous
 
 A known limitation of manual cycle annotations is the potential for misalignment.
 Intermediate bleeding events unrelated to menstruation (e.g., ovulatory spotting or irregular shedding) or missing menstruation entries can lead to ambiguous cycle definitions.
-Therefore, all user-entered cycle starts undergo manual review to reduce annotation errors.
+Manual review of all user-entered cycle starts would improve the quality of the annotations, but is currently not done.
 
 \begin{figure}[htbp]
     \centering
@@ -198,7 +210,7 @@ contained hardware-related anomalies, or fell outside a reasonable cycle length
 
 Cycles shorter than 10 days typically result from incorrect cycle start entries or premature termination of temperature recordings.
 Long cycles, longer than 150 days, are often due to data entry errors or pregnancy-related recordings,
-where the sensor was worn continuously throughout gestation—sometimes producing sequences up to nine months long.
+where the sensor was worn continuously throughout gestation, sometimes producing sequences up to nine months long.
 
 While such cases may still contain useful information, they were excluded from this analysis to avoid complications in preprocessing and labeling.
 In most instances, only a small portion of these extended cycles contributes meaningfully to the study objectives.
@@ -207,8 +219,10 @@ The cutoff values for cycle length are 10 and 150 days, respectively.
 The cleaned dataset has 40{,}266 menstrual cycles from 6{,}245 users.
 The median number of cycles per user is 4 (IQR: 2--8) and the median cycle length is 28 days (IQR: 26--32).
 
-The average data density—defined as the fraction of available measurements out of the theoretical maximum of 288 measurements per day—is 0.90.
+The average data density, defined as the fraction of available measurements out of the theoretical maximum of 288 measurements per day, is 0.90.
 This corresponds to an average data availability of 90\% per cycle, with an average loss of 10\%.
+Data loss is usually caused by users not wearing the sensor for a longer time, or an erroneous sensor that needed replacement,
+but was not immediately delivered.
 
 37934 cycles (94\%) were classified as biphasic and 2333 (6\%) as monophasic.
 
@@ -217,7 +231,7 @@ Users had a median age of 32 years (IQR: 29–36), median weight of 65 kg (IQR:
 \subsubsection{Irregularities and Confounding Factors}
 Despite careful data collection, real-world measurements are subject to physiological and behavioral noise.
 Especially core body temperature is influenced by various factors unrelated to the menstrual cycle.
-Illnesses—especially those involving fever—can significantly affect temperature patterns.
+Illnesses, especially those involving fever, can significantly affect temperature patterns.
 This poses a challenge for any analysis relying on temperature data, as one of the key physiological indicators of ovulation is a post-ovulatory temperature rise (see Section~\ref{subsubsec:physiological_signs}).
 
 Figure~\ref{fig:background_fever_cycle} shows an example of a cycle where an illness caused a marked increase in temperature.
@@ -403,10 +417,9 @@ In the case of machine translation, this input would be a sentence in the source
 
 
 The input tokens are first mapped to dense continuous vector representations (embeddings).
-Since the attention mechanism permutation-invariant---that is, it does not inherently encode the order of tokens in the sequence---
+Since the attention mechanism permutation-invariant, that is, it does not inherently encode the order of tokens in the sequence,
 \emph{positional encodings} are added to the token embeddings to provide information about the token positions in the sequence.
 
-
 Without positional encoding, repeated tokens such as `The` would be indistinguishable
 to the model regardless of their location, even if they play different syntactic or semantic roles.
 Positional encodings, often based on sinusoidal functions, inject a unique position-dependent signal
@@ -419,6 +432,7 @@ In this work, we use sine and cosine functions of different frequencies:
 \end{align}
 where \(i\) is the dimension of the input and \(pos\) is the position in the sequence,
 as in the original paper~\cite{vaswani_attention_2017}.
+Positional encodings are added to the embedded inputs through simple addition.
 
 \begin{figure}[htbp]
     \centering
@@ -562,6 +576,8 @@ These techniques reduce the computational load while maintaining salient informa
 
 Figure~\ref{fig:background_convolution_example} illustrates a simple one-dimensional convolution applied to a sequence using a filter of size 3.
 The stride determines how far the filter moves at each step, affecting both the resolution and length of the resulting feature map.
+As a recap, resolution in this context means, how many of the daily measurements (initially 288) are retained for the input of the models.
+The sequence length is the overall number of measurements available.
 
 \begin{figure}[htbp]
     \centering
@@ -571,6 +587,6 @@ The stride determines how far the filter moves at each step, affecting both the
 \end{figure}
 
 In summary, time-series modeling offers a range of approaches, each with specific trade-offs.
-RNNs and LSTMs provide explicit sequential modeling but suffer from training inefficiencies.
+RNNs and LSTMs provide explicit sequential modeling but suffer from vanishing gradients, especially for longer sequences.
 Transformers excel at long-range context capture but demand more memory and parallelization.
-Convolutional layers offer efficient local feature extraction and often serve as useful pre-processing stages for both model families.
+Convolutional layers might offer efficient local feature extraction and might mitigate the shortcomings of both architecture types.