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content/introduction/introduction.tex

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-Some references \cite{demaine2007jigsaw, altman1989solving}.
+\section{Problem Statement}
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+Real-world data is hardly ever perfect. Many real-world datasets suffer a myriad of problems. One such common problem is improper labeling. While we would like our models to learn based off of an exact ground truth, often the labels with which we train our classifiers have errors themselves. Label-noise plagues many datasets for a variety of reasons. In datasets such as CIFAR-10N, a benchmark of natural images across 10 object classes, labels were collected from crowdworker annotators, who are prone to mistakes. In ChestX-ray14, a dataset of medical chest X-rays, labels were given by a natural language processing algorithm, since labelling each image by hand was deemed impractical. Such automatic labeling gave way to relatively high label error rates.
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+Gradient based learning methods, like those used to train neural networks, have trouble dealing with such datasets. Standard, per-sample losses (BCE, focal-loss), are confused easily by mislabeled points, as they produce a very large gradient which throws off training. Current attempts at noise-robust losses (GCE, MAE) help smooth these large gradients, yet still optimize on a per-sample basis, targeting per-sample accuracy rather than ranking quality --- leaving them misaligned with AUC even when they do reduce noise sensitivity. 
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+In this field, optimizing directly for our desired metric (AUC) proves to be useful in dealing with noise. Per-sample losses help optimize each sample on their own, while AUC losses optimize the sample ranking amongst the whole. This helps them make smart tradeoffs while training, and accepting errors.
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+\section{Contribution}
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+In this work we introduce the \textsc{ROLL} framework for ROC curve related losses and \textsc{ROLL}-AoC, a noise-robust loss that optimizes AUC \emph{directly}. We show that the loss is more robust to label noise than other methods, and how it handles class-imbalance naturally.
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+\section{Roadmap}
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+In this work, we will first review AUC optimization, KDE, imbalanced classification, label noise and existing methods for dealing with it in datasets. We then introduce \textsc{ROLL} and \textsc{ROLL}-AoC, formulate it using KDE distribution approximation, and offer derivations for use in gradient-based learning. Then, we show performance on real world data. Finally, we discuss advantages and disadvantages with regards to other methods, as well as offer avenues for future research.
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