Many changes to results and conclusions and such

content/related_work/related_work.tex

@@ -74,7 +74,7 @@ The noise-robustness properties of ranking-based objectives are discussed in \Cr
 
 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.
 
-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.
+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}.
 \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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@@ -220,7 +220,7 @@ Some data, such as adult heights, follows a Gaussian-like distribution; the occu
 events or car arrivals at an intersection follows a Poisson distribution. For arbitrary real-world data,
 however, no such assumption can be made safely.
 
-This motivates Kernel Density Estimation (KDE). Rather than assuming a parametric form, KDE uses the
+This motivates Kernel Density Estimation (KDE)~\cite{parzen1962estimation}. Rather than assuming a parametric form, KDE uses the
 empirical sample itself as the model: each observed point $x_i$ contributes a smooth bump, a
 \emph{kernel}, to the estimated density. The assumption is that nearby points are plausibly likely,
 so probability mass is spread locally around each sample. Summing all kernels and normalizing yields a