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\section{Conclusion and Outlook}\label{sec:conclusion-and-outlook}
\subsection{Conclusion}\label{subsec:conclusion}
\subsection{Outlook}\label{subsec:outlook}

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\section{Experimental Results}

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\section{Implementation}\label{sec:implementation}
The model is defined as $g(\pmb{x};\pmb{w})$ where $\pmb{w}$ are the model weights and $\pmb{x}$ the input samples.
We define two hyperparameters, the batch size $\mathcal{B}$ and the sample size $\mathcal{S}$ where $\mathcal{B} < \mathcal{S}$.
In every active learning loop iteration we sample $\mathcal{S}$ random samples from our total unlabeled sample set $\mathcal{X}_S \subset\mathcal{X}_U \subset \mathcal{X}$
\begin{equation}\label{eq:equation2}
z = g(\mathcal{X}_S;\pmb{w})
\end{equation}
\begin{align}
S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; \arg\max_j \sigma(\mathbf{z})
\end{align}
\cite{activelearning}

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\section{Introduction}\label{sec:introduction}
\subsection{Motivation}\label{subsec:motivation}
For most supervised learning tasks lots of training samples are essential.
With too less training data the model will not generalize well and not fit a real world task.
Labeling datasets is commonly seen as an expensive task and wants to be avoided as much as possible.
That's why there is a machine-learning field called active learning.
The general approach is to train a model that predicts within every iteration a ranking metric or Pseudo-Labels which then can be used to rank the importance of samples to be labeled.
The goal of this practical work is to test active learning within a simple classification task and evaluate its performance.
\subsection{Research Questions}\label{subsec:research-questions}
\subsubsection{Does Active-Learning benefit the learning process?}
Should Active-learning be used for classification tasks to improve learning performance?
Furthermore, how does the sample-selection process impact the learning?
\subsubsection{Is Dagster and Label-Studio a proper tooling to build an AL Loop?}
Is combining Dagster with Label-Studio a good match for building scalable and reliable Active-Learning loops?
\subsubsection{Does balancing the learning samples improve performance?}
The sample-selection metric might select samples just from one class by chance.
Does balancing this distribution help the model performance?
\subsection{Outline}\label{subsec:outline}

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%% This command processes the author and affiliation and title %% This command processes the author and affiliation and title
%% information and builds the first part of the formatted document. %% information and builds the first part of the formatted document.
\maketitle \maketitle
\input{introduction}
\section{Introduction}\label{sec:introduction} \input{materialandmethods}
\subsection{Motivation} \input{implementation}
For most supervised learning tasks lots of training samples are essential. \input{experimentalresults}
With too less training data the model will not generalize well and not fit a real world task. \input{conclusionandoutlook}
Labeling datasets is commonly seen as an expensive task and wants to be avoided as much as possible.
That's why there is a machine-learning field called active learning.
The general approach is to train a model that predicts within every iteration a ranking metric or Pseudo-Labels which then can be used to rank the importance of samples to be labeled.
The goal of this practical work is to test active learning within a simple classification task and evaluate its performance.
\subsection{Research Questions}
\subsubsection{Does Active-Learning benefit the learning process?}
Should Active-learning be used for classification tasks to improve learning performance?
Furthermore, how does the sample-selection process impact the learning?
\subsubsection{Is Dagster and Label-Studio a proper tooling to build an AL Loop?}
Is combining Dagster with Label-Studio a good match for building scalable and reliable Active-Learning loops?
\subsubsection{Does balancing the learning samples improve performance?}
The sample-selection metric might select samples just from one class by chance.
Does balancing this distribution help the model performance?
\subsection{Outline}
\section{Material and Methods}
\subsection{Material}
\subsubsection{Dagster}
\subsubsection{Label-Studio}
\subsubsection{Pytorch}
\subsection{Methods}
\subsubsection{Active-Learning}
\subsubsection{ROC}
\subsubsection{RESNet}
\section{Implementation}
Model is defined as $g(\pmb{x};\pmb{w})$ where $\pmb{w}$ are the model weights and $\pmb{x}$ the input samples.
We define two hyperparameters, the batch size $\mathcal{B}$ and the sample size $\mathcal{S}$ where $\mathcal{B} < \mathcal{S}$.
In every active learning loop iteration we sample $\mathcal{S}$ random samples from our total unlabeled sample set $\mathcal{X}_S \subset\mathcal{X}_U \subset \mathcal{X}$
\begin{equation}
z = g(\mathcal{X}_S;\pmb{w})
\end{equation}
To get a class distribution summing up to one we apply a softmax to the result values.
\begin{equation}
\sigma(\mathbf{z})_j = \frac{e^{z_j}}{\sum_{k=1}^K e^{z_k}} \; for j\coloneqq\{0,1\}\label{eq:equation}
\end{equation}
\begin{align}
S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; \arg\max_j \sigma(\mathbf{z})
\end{align}
\cite{activelearning}
\section{Semi-Supervised learning}\label{sec:semi-supervised-learning} \section{Semi-Supervised learning}\label{sec:semi-supervised-learning}
In traditional supervised learning we have a labeled dataset. In traditional supervised learning we have a labeled dataset.

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\section{Material and Methods}\label{sec:material-and-methods}
\subsection{Material}\label{subsec:material}
\subsubsection{Dagster}
\subsubsection{Label-Studio}
\subsubsection{Pytorch}
\subsubsection{NVTec}
\subsubsection{Imagenet}
\subsection{Methods}\label{subsec:methods}
\subsubsection{Active-Learning}
\subsubsection{ROC and AUC}
\subsubsection{RESNet}
\subsubsection{CNN}
\subsubsection{Softmax}
The Softmax function converts $n$ numbers of a vector into a probability distribution.
Its a generalization of the Sigmoid function and often used as an Activation Layer in neural networks.
\begin{equation}\label{eq:softmax}
\sigma(\mathbf{z})_j = \frac{e^{z_j}}{\sum_{k=1}^K e^{z_k}} \; for j\coloneqq\{1,\dots,K\}
\end{equation}