diff --git a/Appendix.tex b/Appendix.tex index 364fc47..68b8d39 100644 --- a/Appendix.tex +++ b/Appendix.tex @@ -5,203 +5,203 @@ \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} diff --git a/ML_Zusammenfassung.tex b/ML_Zusammenfassung.tex index d886037..95ba831 100644 --- a/ML_Zusammenfassung.tex +++ b/ML_Zusammenfassung.tex @@ -128,5 +128,7 @@ \bibliographystyle{IEEEtran-de} \bibliography{Bibliography.bib} + \pagenumbering{arabic} + \renewcommand*{\thepage}{A-\arabic{page}} \include{Appendix.tex} \end{document} diff --git a/Readme.md b/Readme.md index b7df512..7546b12 100644 --- a/Readme.md +++ b/Readme.md @@ -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) diff --git a/Style.tex b/Style.tex index 16a51fc..43133a9 100644 --- a/Style.tex +++ b/Style.tex @@ -10,7 +10,7 @@ \pagestyle{fancy} \fancyhf{} \chead{\textbf{Zusammenfassung \MODULE \\\vspace{1mm}}} -\lhead{\partname~\thepart} +\lhead{} \rhead{\leftmark} \lfoot{\AUTHOR~|~\DATE} \rfoot{\thepage} diff --git a/chapters/Classical_Supervised_Learning/Linear_Classification.tex b/chapters/Classical_Supervised_Learning/Linear_Classification.tex index 417972e..15e05f2 100644 --- a/chapters/Classical_Supervised_Learning/Linear_Classification.tex +++ b/chapters/Classical_Supervised_Learning/Linear_Classification.tex @@ -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} diff --git a/chapters/Classical_Supervised_Learning/Trees_and_Forests.tex b/chapters/Classical_Supervised_Learning/Trees_and_Forests.tex index ccfa2eb..8cd7fe0 100644 --- a/chapters/Classical_Supervised_Learning/Trees_and_Forests.tex +++ b/chapters/Classical_Supervised_Learning/Trees_and_Forests.tex @@ -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} diff --git a/chapters/Mathematische_Grundlagen/Constraint_Optimization.tex b/chapters/Mathematische_Grundlagen/Constraint_Optimization.tex index 74ce145..84dc2f8 100644 --- a/chapters/Mathematische_Grundlagen/Constraint_Optimization.tex +++ b/chapters/Mathematische_Grundlagen/Constraint_Optimization.tex @@ -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} diff --git a/chapters/Mathematische_Grundlagen/Gaussian_Identities.tex b/chapters/Mathematische_Grundlagen/Gaussian_Identities.tex index 54de320..4800692 100644 --- a/chapters/Mathematische_Grundlagen/Gaussian_Identities.tex +++ b/chapters/Mathematische_Grundlagen/Gaussian_Identities.tex @@ -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} $\nomeq{covariance}_{\bm y} = \sigma_{\bm y}^2\nomeq{identity_matrix} + \bm F\nomeq{covariance}_{\bm x}\bm F^T$ diff --git a/chapters/Mathematische_Grundlagen/Kernel_Basics.tex b/chapters/Mathematische_Grundlagen/Kernel_Basics.tex index fa93fb0..a8c655c 100644 --- a/chapters/Mathematische_Grundlagen/Kernel_Basics.tex +++ b/chapters/Mathematische_Grundlagen/Kernel_Basics.tex @@ -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} diff --git a/chapters/Neural_Networks/Basics.tex b/chapters/Neural_Networks/Basics.tex index 1839bca..580646a 100644 --- a/chapters/Neural_Networks/Basics.tex +++ b/chapters/Neural_Networks/Basics.tex @@ -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}% diff --git a/chapters/Neural_Networks/Gradient_Descent.tex b/chapters/Neural_Networks/Gradient_Descent.tex index 102c06f..8581951 100644 --- a/chapters/Neural_Networks/Gradient_Descent.tex +++ b/chapters/Neural_Networks/Gradient_Descent.tex @@ -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}