Updated results, hebrew, abstract, intro, etc.

content/related_work/related_work.tex

@@ -62,9 +62,9 @@ where $x_1 \sim \mathcal{D}_1$ and $x_0 \sim \mathcal{D}_0$ are drawn independen
 
 \subsection{AUC as a metric of model performance}
 
-The AUC is a direct representation of the performance of a classifier, as opposed to a loss. There are instances where the loss may be minimized, yet seperation might be minimal. These two metrics might correlate, but do not necessarily correspond.
+The AUC is a direct representation of the performance of a classifier, as opposed to a loss. There are instances where the loss may be minimized, yet separation might be minimal. These two metrics might correlate, but do not necessarily correspond.
 
-An example of this is a result for which all true samples receive a score of $0.51$ and all false samples receie a score of $0.49$. Using many losses, including BCE, this would result in a relatively high loss value. On this score however, the AUC is $1$. The model perfectly seperates the samples, so further training is not necessary.
+An example of this is a result for which all true samples receive a score of $0.51$ and all false samples receive a score of $0.49$. Using many losses, including BCE, this would result in a relatively high loss value. On this score however, the AUC is $1$. The model perfectly separates the samples, so further training is not necessary.
 
 Direct AUC optimization can be ideal with optimizing for imbalanced datasets. With most losses such as BCE or focal, the loss is calculated per-sample and then summed (or averaged). In order to properly train for both true and false populations, the scores are weighted, so that equal weight falls on both the true and the false populations. With direct AUC optimization, the imbalance does not affect the calculation, and the reweighting can be forgone.
 
@@ -72,9 +72,9 @@ The noise-robustness properties of ranking-based objectives are discussed in \Cr
 
 \subsection{AUC optimization in literature}
 
-While AUC as a metric for model performance has existed for a while, methods to optimize for it directly are relatively recent. At it's core, it is a non-trivial problem to solve. Existing efforts to directly optimize AUC have been based on the Wilcoxon-Mann-Whitney interpretation of AUC. However, directly calculating the afformentioned probability of a random positive score behing higher than a negative one introduces two complications. The first is that one must iterate over $n^2$ pairs to cover every posible pair. Additionally, the pairwise function one must evaluate ( $\mathbb{P}(f(x_1) > f(x_0))$ ) is a non-contiguous stepwise function, and is therefor on-differentiable.
+While AUC as a metric for model performance has existed for a while, methods to optimize for it directly are relatively recent. At it's core, it is a non-trivial problem to solve. Existing efforts to directly optimize AUC have been based on the Wilcoxon-Mann-Whitney interpretation of AUC. However, directly calculating the aforementioned probability of a random positive score being higher than a negative one introduces two complications. The first is that one must iterate over $n^2$ pairs to cover every possible pair. Additionally, the pairwise function one must evaluate ($\mathbb{P}(f(x_1) > f(x_0))$) is a discontinuous stepwise function, and is therefore non-differentiable.
 
-The non-contiguous stepwise nature of the evaluated pairwise function is generally fixed by using a surrogate, either sigmoid-like or hinge functions are applied to the score difference~\cite{cortes2003auc}.
+The discontinuous stepwise nature of the evaluated pairwise function is generally addressed by using a surrogate, either sigmoid-like or hinge functions are applied to the score difference~\cite{cortes2003auc}.
 \citet{yuan2021auc} proposed a compositional stochastic gradient framework that reformulates AUC maximization as a min-max saddle-point problem, enabling mini-batch training without maintaining all pairwise scores in memory. Their PESG optimizer and the LibAUC library are the primary practical tools for deep AUC maximization and serve as the main AUC baseline in this thesis.
 
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@@ -182,7 +182,11 @@ Intermediate values therefore trade noise tolerance for faster convergence.
 We evaluate GCE at $q = 0.7$ as a baseline in the Experiments chapter.
 \citet{zhou2021asymmetric} extend the theoretical framework to asymmetric noise, introducing
 the \emph{asymmetry ratio} to quantify how noise tolerance degrades when flip rates differ
-between classes.
+between classes, and propose an asymmetric loss that applies distinct focusing parameters to
+positive and negative samples: easy negatives are downweighted more aggressively than positives,
+counteracting both gradient dominance from numerous easy negatives in imbalanced settings and
+the increased noise sensitivity that comes with symmetric focusing.
+This asymmetric loss is evaluated as a baseline (\textbf{Asym.}) in \Cref{chapter:experiments}.
 \citet{feng2020can} confirm that standard cross-entropy cannot be made noise-tolerant
 through simple modification, establishing robust losses as a genuinely distinct family
 rather than a patch on existing objectives.
@@ -265,13 +269,13 @@ This gives the KDE cumulative distribution function a closed form as well:
 It is rare for a dataset to have an equal amount of true and false samples. Class imbalance
 is something that must be taken into account during training on most datasets.
 Extreme imbalance exacerbates this issue further - for a dataset with an imbalance ratio of $100$,
-a \emph{constant} classifier (outputting only the most probable class) acheives a very good result.
+a \emph{constant} classifier (outputting only the most probable class) achieves a very good result.
 Without correction, many learning methods will find a local minima in a relatively trivial solution, such
 as constant output, and have a hard time adjusting. Even if not in this local minima, less emphasis is put
 on the rare class during training, as it contributes less to the loss metric, and the model tends to
 generalize on the rare class poorly.
 
-Dealing with this depends on the loss used. For most losses, for which the loss for each sample is calculated seperately,
+Dealing with this depends on the loss used. For most losses, for which the loss for each sample is calculated separately,
 the solution is to simply weight the losses for each class differently,
 by multiplying the loss for the rare class
 so that it contributes equally. Other approaches using pairwise losses, such as those implemented in LibAUC \cite{yuan2021auc}, naturally weight positive and negative contributions to learning through their implementation.
@@ -323,7 +327,7 @@ The NP lemma provides the theoretically optimal solution but assumes the class-c
 $p(\mathbf{x} \mid y=0)$ and $p(\mathbf{x} \mid y=1)$ are known.
 In practice these densities must be estimated from data.
 A model must be fit to the data in order to estimate these probabilities, meaning that
-there is no gaurantee on optimality.
+there is no guarantee on optimality.
 
 Further work regarding \emph{Neyman-Pearson classification} adapts the NP
 principle to the finite-sample setting using nonparametric methods