feat: rearrange sections

reports/Content/main-summary.tex

@@ -48,6 +48,12 @@ \section{Results}
 
 We derive from exhaustive robustness tests, that performance is stable across multiple subsets. Outperformance is strongest for in-the-money options, options with a long maturity, as well as options traded at the quotes.
 
+For an evaluation of feature importances, that suffices for a cross-model comparison, we use \gls{SAGE} \autocite{covertUnderstandingGlobalFeature2020}. It is a global feature importance measure based on Shapley values and is capable of handling complex feature interactions, such as highly correlated quotes and prices. We estimate \gls{SAGE} values in terms of improvement in zero-one loss per feature set, complementing our accuracy-based evaluation.
+
+As evident from \cref{fig:sage-importances} we find, that all models attain the largest improvement in loss from quoted prices and if provided from the quoted sizes. The contribution of the \gls{NBBO} to performance is roughly equal for all models, suggesting that even simple heuristics effectively exploit the data. For \gls{ML}-based predictors, quotes at the exchange level hold equal importance in classification. This contrasts with \gls{GSU} methods, which rely less on exchange-level quotes.  The performance improvements from the trade size and quoted size, are slightly lower for rule-based methods compared to \gls{ML}-based methods. Transformers and \glspl{GBRT} slightly benefit from the addition of option features, i.e., moneyness and time to maturity. 
+
+Regardless of the method used, changes in trade price, central to the tick test, are irrelevant for classification and can even harm performance. This result aligns with earlier studies of \textcites{savickasInferringDirectionOption2003}{grauerOptionTradeClassification2022}.
+
 \section{Disucssion}
 
 Advancements in classical trade classification have been fueled by relying more complex decision boundaries, e.g., by fragmenting the spread \autocites{ellisAccuracyTradeClassification2000}{chakrabartyTradeClassificationAlgorithms2007} or by assembling multiple heuristics \autocite{grauerOptionTradeClassification2022}. It is thus likely, that the outperformance of our \gls{ML} estimators is due to the more complex, learned decision boundaries.
@@ -58,12 +64,6 @@ \section{Disucssion}
 
 Self-training with \glspl{GBRT} as a base learner generally performs worse than \glspl{GBRT} trained on labeled trades. With the pseudo labels derived from high-confident predictions, the success of self-training hinges on the reliability of the predicted class probabilities. In an analysis of the \gls{GBRT}, we observe that the validation loss in terms of sample-wise loss stagnates due to a growing number of overconfident but erroneous predictions. It is conceivable, that the increased number of confident yet incorrect predictions, affects the generated pseudo labels. Given these observations, we recommend using \glspl{GBRT} for supervised trade classification only. 
 
-For an evaluation of feature importances, that suffices for a cross-model comparison, we use \gls{SAGE} \autocite{covertUnderstandingGlobalFeature2020}. It is a global feature importance measure based on Shapley values and is capable of handling complex feature interactions, such as highly correlated quotes and prices. We estimate \gls{SAGE} values in terms of improvement in zero-one loss per feature set, complementing our accuracy-based evaluation.
-
-As evident from \cref{fig:sage-importances} we find, that all models attain the largest improvement in loss from quoted prices and if provided from the quoted sizes. The contribution of the \gls{NBBO} to performance is roughly equal for all models, suggesting that even simple heuristics effectively exploit the data. For \gls{ML}-based predictors, quotes at the exchange level hold equal importance in classification. This contrasts with \gls{GSU} methods, which rely less on exchange-level quotes.  The performance improvements from the trade size and quoted size, are slightly lower for rule-based methods compared to \gls{ML}-based methods. Transformers and \glspl{GBRT} slightly benefit from the addition of option features, i.e., moneyness and time to maturity. 
-
-Regardless of the method used, changes in trade price, central to the tick test, are irrelevant for classification and can even harm performance. This result aligns with earlier studies of \textcites{savickasInferringDirectionOption2003}{grauerOptionTradeClassification2022}.
-
 \section{Conclusion}
 
 In conclusion, our study showcases the efficacy of machine learning as a viable alternative to existing trade signing algorithms for classifying option trades, if partially-labeled or labeled trades are available for training. Compared to existing approaches, our classifiers also improve robustness, which together reduces noise and bias in option research dependent on reliable trade initiator estimates.