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WIP: Thesis update

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Radu C. Martin 2021-06-21 22:32:43 +02:00
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50_Choice_of_Hyperparameters.tex
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@ -348,6 +348,8 @@ being cheaper from a computational perspective. In order to make a more informed
choice for the best hyperparamerers, the performance of all three combinations
has been analysed.
\clearpage
\begin{table}[ht]
%\vspace{-8pt}
\centering
@ -384,25 +386,22 @@ therefore been chosen as the model for the full year simulations.
% TODO: [Hyperparameters] Validation of hyperparameters
The validation of model parameters has the dual purpose of
The validation step has the purpose of testing the fiability of the trained
models. If choosing a model according to loss function values on a new dataset
is a way of minimizing the possibility of overfitting the model to the training
data, validating the model by analyzing its multi-step prediction performance
ensures the model was able to learn the correct dynamics and is useful in
simulation scenarios.
The following subsections analyze the performance of the trained \arcshort{gp}
and \acrshort{svgp} models over 20-step ahead predictions. For the \acrshort{gp}
model the final choice of parameters is made according to the simulation
performance. The simulation performance of the \acrshort{svgp} model is compared
to that of the classical models while speculating on the possible reasons for
the discrepancies.
\subsubsection{Conventional Gaussian Process}
\begin{figure}[ht]
\centering
\includegraphics[width = \textwidth]{Plots/GP_113_training_performance.pdf}
\caption{}
\label{fig:GP_train_validation}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width = \textwidth]{Plots/GP_113_test_performance.pdf}
\caption{}
\label{fig:GP_test_validation}
\end{figure}
\begin{figure}[ht]
\centering
@ -412,23 +411,39 @@ The validation of model parameters has the dual purpose of
\label{fig:GP_multistep_validation}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width =
\textwidth]{Plots/GP_213_-1pts_test_prediction_20_steps.pdf}
\caption{}
\label{fig:GP_213_multistep_validation}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width =
\textwidth]{Plots/GP_313_-1pts_test_prediction_20_steps.pdf}
\caption{}
\label{fig:GP_313_multistep_validation}
\end{figure}
\clearpage
\subsubsection{Sparse and Variational Gaussian Process}
\begin{figure}[ht]
\centering
\includegraphics[width = \textwidth]{Plots/SVGP_123_training_performance.pdf}
\caption{}
\label{fig:SVGP_train_validation}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width = \textwidth]{Plots/SVGP_123_test_performance.pdf}
\caption{}
\label{fig:SVGP_test_validation}
\end{figure}
%\begin{figure}[ht]
% \centering
% \includegraphics[width = \textwidth]{Plots/SVGP_123_training_performance.pdf}
% \caption{}
% \label{fig:SVGP_train_validation}
%\end{figure}
%
%\begin{figure}[ht]
% \centering
% \includegraphics[width = \textwidth]{Plots/SVGP_123_test_performance.pdf}
% \caption{}
% \label{fig:SVGP_test_validation}
%\end{figure}
\begin{figure}[ht]
\centering