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Appendix.tex
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\section{Herleitung: Gradient for Logistic Regression}%
\label{sec:Herleitung: Gradient for Logistic Regression}
\includegraphics[page=64,width=\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\includegraphics[page=64,width=.8\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\section{Herleitung: Multiclass Classification: Data log-likelihood}%
\label{sec:Herleitung: Multiclass Classification: Data log-likelihood}
\includegraphics[page=68,width=\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\includegraphics[page=68,width=.8\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\section{Herleitung: CART: Classification Tree}%
\label{sec:Herleitung: CART: Classification Tree}
\includegraphics[page=32,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=33,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=34,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=35,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=36,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=32,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=33,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=34,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=35,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=36,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\section{Herleitung: CART: Regression Tree}%
\label{sec:Herleitung: CART: Regression Tree}
\includegraphics[page=24,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=25,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=26,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=27,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=28,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=29,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=30,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=31,width=\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\includegraphics[page=24,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=25,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=26,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=27,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=28,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=29,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=30,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}\\
\includegraphics[page=31,width=.8\textwidth]{Vorlesungen/04_TreesAndForests.pdf}
\section{Herleitung: Soft Max-Margin: Hinge Loss}%
\label{sec:Herleitung: Soft Max-Margin: Hinge Loss}
\includegraphics[page=21,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=21,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}
\section{Anwendungsbeispiele: \glstopshortpl{SVM}}%
\label{sec:Anwendungsbeispiele: SVMs}
\includegraphics[page=34,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=35,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=36,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=37,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=38,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=39,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=40,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=34,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=35,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=36,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=37,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=38,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=39,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=40,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}
\section{Herleitung: SVMs with Kernels}%
\label{sec:Herleitung: SVMs with Kernels}
\includegraphics[page=52,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=53,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=54,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=55,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=56,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=52,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=53,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=54,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=55,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=56,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}
\section{Beispiele: SVM: Model Selection}%
\label{sec:Beispiele: SVM: Model Selection}
\includegraphics[page=57,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=58,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=59,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=60,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=62,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=63,width=\textwidth]{Vorlesungen/06_SVMs.pdf}
\includegraphics[page=57,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=58,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=59,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=60,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=62,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}\\
\includegraphics[page=63,width=.8\textwidth]{Vorlesungen/06_SVMs.pdf}
\section{Anwendungsbeispiel: Bayesian Learning: Regression}%
\label{sec:Anwendungsbeispiel: Bayesian Learning: Regression}
\includegraphics[page=18,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=19,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=20,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=18,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=19,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=20,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Beweis: Gaussian Processes ist eine kernelized Bayesian Linear Regression}%
\label{sec:Beweis: Gaussian Processes ist eine kernelized Bayesian Linear Regression}
\includegraphics[page=41,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=42,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=43,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=44,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=45,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=41,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=42,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=43,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=44,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=45,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Herleitung: Gaussian Processes: Posterior}%
\label{sec:Herleitung: Gaussian Processes: Posterior}
\includegraphics[page=38,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=38,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Herleitung: Gaussian Processes: \nomsym{mean} und \nomsym{variance}}%
\label{sec:Herleitung: Gaussian Processes: mean and variance}
\includegraphics[page=39,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=39,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Beispiel: Neural Network: XOR}%
\label{sec:Beispiel: Neural Network: XOR}
\includegraphics[page=25,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=26,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=25,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}\\
\includegraphics[page=26,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\section{Beispiel: Neural Networks: Feature Learning}%
\label{sec:Beispiel: Neural Networks: Feature Learning}
\includegraphics[page=35,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=35,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\section{Herleitung: Backpropagation in Matrix-Form}%
\label{sec:Herleitung: Backpropagation in Matrix-Form}
\includegraphics[page=52,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=53,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=52,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}\\
\includegraphics[page=53,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\section{Zusätzliche Informationen: Second Order Optimization}%
\label{sec:Zusaetzliche Informationen: Second Order Optimization}
\includegraphics[page=74,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=75,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=76,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=74,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}\\
\includegraphics[page=75,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}\\
\includegraphics[page=76,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\section{Zusätzliche Informationen: MNIST Datensatz}%
\label{sec:Zusaetzliche Informationen: MNIST Datensatz}
\includegraphics[page=82,width=\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\includegraphics[page=82,width=.8\textwidth]{Vorlesungen/08_NeuralNets.pdf}
\section{Anwendungsbeispiele für CNNs}%
\label{sec:Anwendungsbeispiele fuer CNNs}
\includegraphics[page=3,width=\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\includegraphics[page=4,width=\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\includegraphics[page=3,width=.8\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}\\
\includegraphics[page=4,width=.8\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\section{Beispiel: Convolutional Layer: Stride and Padding}%
\label{sec:Beispiel: Convolutional Layer: Stride and Padding}
\includegraphics[page=14,width=\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\includegraphics[page=15,width=\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\includegraphics[page=14,width=.8\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}\\
\includegraphics[page=15,width=.8\textwidth]{Vorlesungen/09_CNNs+RNNs.pdf}
\section{Herleitung: Dimensionality Reduction: Minimizing the Error}%
\label{sec:Herleitung: Dimensionality Reduction: Minimizing the Error}
\includegraphics[page=16,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=16,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\section{Herleitung: PCA: Maximierungsproblem in Matrix-Schreibweise}%
\label{sec:Herleitung: PCA: Maximierungsproblem in Matrix-Schreibweise}
\includegraphics[page=19,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=19,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\section{Anwendungsbeispiele: PCA}%
\label{sec:Anwendungsbeispiele: PCA}
\includegraphics[page=27,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=28,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=29,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=30,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=31,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=32,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=33,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=27,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=28,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=29,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=30,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=31,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=32,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}\\
\includegraphics[page=33,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\section{Beweis: K-Means Konvergenz}%
\label{sec:Beweis: K-Means Konvergenz}
\includegraphics[page=49,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=49,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\section{Formale Definition: Histrograms}%
\label{sec:Formale Definition: Histrograms}
\includegraphics[page=64,width=\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\includegraphics[page=64,width=.8\textwidth]{Vorlesungen/10_DimensionalityReductionClustering.pdf}
\section{Herleitung: Differenzierung des \glstopshortpl{GMM}}%
\label{sec:Herleitung: Differenzierung des GMMs}
\includegraphics[page=7,width=\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\includegraphics[page=7,width=.8\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\section{Herleitung: \glstopshort{EM}-Decomposition}%
\label{sec:Herleitung: EM-Decomposition}
\includegraphics[page=24,width=\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\includegraphics[page=24,width=.8\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\section{Herleitung: EM for GMMs: Maximization"~Step}%
\label{sec:Herleitung: EM for GMMs: Maximization-Step}
\includegraphics[page=16,width=\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\includegraphics[page=16,width=.8\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\section{Herleitung: EM for Dimensionality Reduction: Maximization"~Step}%
\label{sec:Herleitung: EM for Dimensionality Reduction: Maximization-Step}
\includegraphics[page=38,width=\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\includegraphics[page=38,width=.8\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\section{Herleitung: EM for Dimensionality Reduction: Maximization"~Step: Monte-Carlo Esitmation}%
\label{sec:Herleitung: EM for Dimensionality Reduction: Maximization-Step: Monte-Carlo Esitmation}
\includegraphics[page=40,width=\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\includegraphics[page=40,width=.8\textwidth]{Vorlesungen/11 - ExpectationMaximization.pdf}
\section{Herleitung: Variational Bayes: Maximierung des Marginal Log"~Likelihood}%
\label{sec:Herleitung: Variational Bayes: Maximierung des Marginal Log-Likelihood}
\includegraphics[page=13,width=\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\includegraphics[page=14,width=\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\includegraphics[page=13,width=.8\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}\\
\includegraphics[page=14,width=.8\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\section{Reparameterization Trick}%
\label{sec:Reparameterization Trick}
\includegraphics[page=19,width=\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\includegraphics[page=20,width=\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\includegraphics[page=19,width=.8\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}\\
\includegraphics[page=20,width=.8\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\section{Zusätzliche Informationen: Optimization over the variational distribution}%
\label{sec:Zusaetzliche Informationen: Optimization over the variational distribution}
\includegraphics[page=21,width=\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\includegraphics[page=21,width=.8\textwidth]{Vorlesungen/12 - VaraitionalAutoEncoders.pdf}
\section{Zusätzliche Informationen: MLE: conditional log-likelihood}%
\label{sec:Zusaetzliche Informationen: MLE: conditional log-likelihood}
\includegraphics[page=21,width=\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\includegraphics[page=22,width=\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\includegraphics[page=21,width=.8\textwidth]{Vorlesungen/02_LinearClassification.pdf}\\
\includegraphics[page=22,width=.8\textwidth]{Vorlesungen/02_LinearClassification.pdf}
\section{Beweis für die positive Definitheit des Gaussian Kernels}%
\label{sec:Beweis fuer die positive Definitheit des Gaussian Kernels}
\includegraphics[page=14,width=\textwidth]{Vorlesungen/05_KernelMethods.pdf}
\includegraphics[page=15,width=\textwidth]{Vorlesungen/05_KernelMethods.pdf}
\includegraphics[page=14,width=.8\textwidth]{Vorlesungen/05_KernelMethods.pdf}\\
\includegraphics[page=15,width=.8\textwidth]{Vorlesungen/05_KernelMethods.pdf}
\section{Beispiele für die Optimierung von Hyper-Parametern eines Gaussian Kernels}%
\label{sec:Beispiele fuer die Optimierung von Hyper-Parametern eines Gaussian Kernels}
\includegraphics[page=53,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=54,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=55,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=56,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=57,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=53,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=54,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=55,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=56,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=57,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Herleitung: Gaussian Bayes Rules}%
\label{sec:Herleitung: Gaussian Bayes Rules}
\includegraphics[page=26,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=27,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=26,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}\\
\includegraphics[page=27,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\section{Herleitung: Gaussian Propagation}%
\label{sec:Herleitung: Gaussian Propagation}
\includegraphics[page=29,width=\textwidth]{Vorlesungen/07_BayesianLearning.pdf}
\includegraphics[page=29,width=.8\textwidth]{Vorlesungen/07_BayesianLearning.pdf}

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ML_Zusammenfassung.tex
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@ -128,5 +128,7 @@
\bibliographystyle{IEEEtran-de}
\bibliography{Bibliography.bib}
\pagenumbering{arabic}
\renewcommand*{\thepage}{A-\arabic{page}}
\include{Appendix.tex}
\end{document}

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Readme.md
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@ -5,8 +5,8 @@
- [x] für alle \nameref prüfen, ob eine richtige Referenz nachfolgen sollte.
- [x] Folien aus der Vorlesung, auf die in der Zusammenfassung verwiesen werden einfach in den Anhang packen
- [x] babel shortcuts fixen
- [ ] Teilnummer in Anhang entfernen
- [ ] Seitenumbrüche optimieren
- [x] Teilnummer in Anhang entfernen
- [x] Seitenumbrüche optimieren
## Notice
Requires you to enable [--shell escape](https://tex.stackexchange.com/questions/516604/how-to-enable-shell-escape-or-write18-visual-studio-code-latex-workshop)

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Style.tex
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@ -10,7 +10,7 @@
\pagestyle{fancy}
\fancyhf{}
\chead{\textbf{Zusammenfassung \MODULE \\\vspace{1mm}}}
\lhead{\partname~\thepart}
\lhead{}
\rhead{\leftmark}
\lfoot{\AUTHOR~|~\DATE}
\rfoot{\thepage}

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chapters/Classical_Supervised_Learning/Linear_Classification.tex
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@ -212,13 +212,13 @@ Dies stellt eine Approximation des tatsächlich erwarteten Verlustes nach dem Pr
\subsection{\texorpdfstring{\glsxtrfull{SDG}}{\glsfmtfull{SDG}}}%
\label{sub:SDG}
\begin{wrapfigure}{r}{.5\textwidth}
\begin{wrapfigure}{r}{.4\textwidth}
\vspace*{-15mm}
\centering
\includegraphics[width=0.8\linewidth]{batch_vs_stochastic_gradient_descent.png}
\caption{Batch vs. Stochastic Gradient Descent}
\label{fig:batch_vs_stochastic_gradient_descent}
\vspace*{-20mm}
\vspace*{-10mm}
\end{wrapfigure}
Um die Loss Function nicht für alle Datenpunkte evaluieren zu müssen wird beim \gls{SDG} lediglich der Verlust an einem einzelnen, zufällig gewählten Punkt ermittelt
\begin{equation} \label{eq:stochastic_gradient_descent}

1
chapters/Classical_Supervised_Learning/Trees_and_Forests.tex
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@ -82,6 +82,7 @@ welchen Anteil die Klasse $k$ auf der linken Seite des Splits hat.
\label{ssub:Classification Tree}
\includegraphics[width=.6\textwidth]{classification_tree.png}\\
(Herleitung: \cref{sec:Herleitung: CART: Classification Tree})
\clearpage
\subsubsection{Regression Tree}%
\label{ssub:Regression Tree}

2
chapters/Mathematische_Grundlagen/Constraint_Optimization.tex
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@ -33,6 +33,8 @@ Man spricht hierbei dann von einem Dual Optimization Problem
\bm\lambda^*=\argmax_{\bm\lambda} g(\bm\lambda), g(\bm\lambda)= \min_{\bm x}L(\bm x,\bm\lambda)
\end{equation}
Hieraus ergibt sich der folgende Ablauf für die Lagrangian Optimization
\pagebreak
\begin{mybox}
\textbf{\large Lagrangian Optimization}\\
\begin{enumerate}

2
chapters/Mathematische_Grundlagen/Gaussian_Identities.tex
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@ -73,7 +73,7 @@ Gegeben: Marginal (\cref{eq:marginal_gaussian_distribution}) und Conditional (\c
\section{Gaussian Propagation}%
\label{sec:Gaussian Propagation}
Mit den Marginal und Conditional aus \cref{eq:marginal_gaussian_distribution} und \cref{eq:conditional_gaussian_distribution} ist es möglich den Conditional $p(\bm y)$ zu ermitteln:\\
({\color{red}Herleitung Vorlesung 07 Folie 31})
(Herleitung: \cref{sec:Herleitung: Gaussian Propagation})
\begin{itemize}
\item Mean: \tabto{2.2cm}$\bm\mu_{\bm y} = \bm F\bm\mu_{\bm x}$
\item Covariance:\tabto{2.2cm} $\nomeq{covariance}_{\bm y} = \sigma_{\bm y}^2\nomeq{identity_matrix} + \bm F\nomeq{covariance}_{\bm x}\bm F^T$

2
chapters/Mathematische_Grundlagen/Kernel_Basics.tex
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@ -75,7 +75,7 @@ und ist die am häufigsten genutzte Kernel Methode
\begin{equation} \label{eq:gaussian_kernel}
\nomeq{kernel_function}(\bm x,\bm y) = \exp\left(-\frac{\|\bm x - \bm y\|^2}{2\nomeq{variance}}\right)
\end{equation}
{\color{red}Beweis für die positive Definitheit in Vorlesung 04 Seite 14 f.}
(Beweis für die positive Definitheit in \cref{sec:Beweis fuer die positive Definitheit des Gaussian Kernels})
\section{Kernel Trick}%
\label{sec:Kernel Trick}

11
chapters/Neural_Networks/Basics.tex
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@ -57,7 +57,6 @@ ergibt sich durch:
\bm y = \nomeq{activation_function}(\bm W\bm x + \bm b)
\end{equation}
\begin{wrapfigure}{r}{.3\textwidth}
\vspace*{-8mm}
\centering
\includegraphics[width=0.8\linewidth]{feedforward_neural_network_composition.png}
\caption{Feedforward Neural Network mit Funktionen}
@ -92,15 +91,15 @@ ab welchem Schwellwert das Produkt aus Eingangswerten und Gewichten zu relevante
In den meisten Fällen wird die \glsxtrshort{ReLU} \noms{activation_function} verwendet,
wobei es sich auch lohnt, die Leaky \glsxtrshort{ReLU} oder \glsxtrshort{ELU} auszubrobieren.
Die Sigmoid Funktion (\cref{ssub:Logistic sigmoid function}) sollte ausschließlich als \noms{activation_function} in Klassifikationsproblemen verwendet werden.\\
\includegraphics[scale=.7]{sigmoid_activation_function.png}\\
\includegraphics[scale=.6]{sigmoid_activation_function.png}\\
\hrule{\textwidth,1mm}
\includegraphics[scale=.7]{tanh_activation_function.png}\\
\includegraphics[scale=.6]{tanh_activation_function.png}\\
\hrule{\textwidth,1mm}
\includegraphics[scale=.7]{ReLU_activation_function.png}\\
\includegraphics[scale=.6]{ReLU_activation_function.png}\\
\hrule{\textwidth,1mm}
\includegraphics[scale=.7]{Leaky_ReLU_activation_function.png}\\
\includegraphics[scale=.6]{Leaky_ReLU_activation_function.png}\\
\hrule{\textwidth,1mm}
\includegraphics[scale=.7]{exponential_linear_units_activation_function.png}\\
\includegraphics[scale=.6]{exponential_linear_units_activation_function.png}\\
\section{Optimization}%

11
chapters/Neural_Networks/Gradient_Descent.tex
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@ -39,6 +39,7 @@ Hier berechnet sich der Loss durch
\mathcal L &= \frac{1}{2}(y-t)^2
\end{align}
Für dieses Neural Network ist die Backpropagation dann
\begin{alignat}{5} \label{eq:backward_pass}
\frac{\partial \mathcal L}{\partial y} &= y - t &&
&&=\overline{y}\\
@ -163,17 +164,17 @@ bei denen die Lernrate abhängig von der Anzahl der Durchläufe des \nameref{cha
\begin{tabularx}{\textwidth}{X|Y|Y}
\bfseries\centering Verfahren & \bfseries Learning Rate & \bfseries Training Loss\\
\hline
\textbf{Step:} Lernrate verändert sich nach einer bestimmten Anzahl von Algorithmus-Durchläufen & & \includegraphics[width=\linewidth,align=c]{learning_rate_decay_step.png}\\
\textbf{Step:} Lernrate verändert sich nach einer bestimmten Anzahl von Algorithmus-Durchläufen & & \includegraphics[width=.8\linewidth,align=c]{learning_rate_decay_step.png}\\
\hline
\textbf{Cosine:}$\alpha_t = \frac{1}{2}\alpha_0(1+\cos(\frac{t\pi}{T}))$ &
\includegraphics[width=\linewidth,align=c]{learning_rate_decay_cosine_learning_rate.png} &
\includegraphics[width=\linewidth,align=c]{learning_rate_decay_cosine_training_loss.png} \\
\includegraphics[width=.8\linewidth,align=c]{learning_rate_decay_cosine_learning_rate.png} &
\includegraphics[width=.8\linewidth,align=c]{learning_rate_decay_cosine_training_loss.png} \\
\hline
\textbf{Linear:}$\alpha_t = \alpha_0(1-\frac{t}{T})$ &
\includegraphics[width=\linewidth,align=c]{learning_rate_decay_linear_learning_rate.png} & \\
\includegraphics[width=.8\linewidth,align=c]{learning_rate_decay_linear_learning_rate.png} & \\
\hline
\textbf{Inverse sqrt:}$\alpha_t = \frac{\alpha_0}{\sqrt{t}}$ &
\includegraphics[width=\linewidth,align=c]{learning_rate_decay_inverse_sqrt.png} & \\
\includegraphics[width=.8\linewidth,align=c]{learning_rate_decay_inverse_sqrt.png} & \\
\end{tabularx}
($\alpha_0$: inital learning rate, $\alpha_t$: learning rate at epoch $t$, $T$: total number of epochs)
\end{table}