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Victor Mylle
2024-05-10 00:29:12 +02:00
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Reports/Thesis/sections/results/models/comparison.tex
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@@ -38,3 +38,43 @@ After training the different models and experimenting with various hyperparamete
A first recurring conclusion that can be made is that the \ac{NAQR} models have higher \ac{MSE} and \ac{MAE} errors but higher \ac{CRPS}. The reason for this behavior is not immediately clear. One reason for this could be the way the autoregressive quantile regression works. Autoregressive models use the previous predicted value as input to predict the next value. The autoregressive model does not know that it will be used to predict multiple values in the future. In the case of NRV modeling, a value is sampled as input for the next day. The sampling introduces an error which the model is not trained for. Because of this, the NRV distribution outputted by the model will be further away from the expected distribution. This error propagates further in the full-day NRV samples which results in a higher CRPS. The non-autoregressive models do not have this problem because they predict all values at once. The non-autoregressive models, however, have a higher \ac{MSE} and \ac{MAE} error. The model outputs a distribution for each quarter of the day. The full-day NRV sample is then generated by sampling from each of the distributions. The sampled values are independent of each other. This can result in unrealistic samples with large peaks which impact the \ac{MSE} and \ac{MAE} metrics.
Comparing the Linear model with the GRU model, the GRU model has a better performance when only using the NRV data. The autoregressive linear quantile regression model, however, outperforms the model using all available features. Some examples of the test set are shown in \ref{fig:ar_linear_gru_comparison}. A comparison is made between the autoregressive linear and GRU models. A clear difference in the confidence intervals can be observed. The confidence intervals almost have the same width over the whole day. This is not the case for the GRU model. The confidence intervals are wider in the middle of the day. This gives a more realistic insight into the uncertainty.
\begin{figure}[H]
\centering
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{Autoregressive linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{Autoregressive GRU model}
\end{subfigure}
\caption{Comparison of the autoregressive linear and GRU model}
\label{fig:ar_linear_gru_comparison}
\end{figure}
% other conclusion:

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Reports/Thesis/sections/results/policies/nrv_samples_policy.tex
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@@ -5,5 +5,4 @@ The generated full-day samples can be used to improve the profit of the policy.
% TODO: Compare with baselines
% TODO: explain further
An observation that can be made is that the metrics used to evaluate the NRV predictions, do not necessarily correlate with the profit that can be made using the predictions. This means the best model in terms of the metrics does not necessarily result in the best profit. During the training, the profit should be used as a metric to evaluate the models but this becomes computationally expensive.
An observation that can be made is that the metrics used to evaluate the NRV predictions, do not necessarily correlate with the profit that can be made using the predictions. This means the best model in terms of the metrics does not necessarily result in the best profit. During the training, the profit should be used as a metric to evaluate the models but this becomes computationally expensive. Because of this, the policy now will only be evaluated after the training is done. The profit can give a better insight if the model improves the profit compared to the baselines.

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Reports/Thesis/verslag.aux
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@@ -101,25 +101,27 @@
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Reports/Thesis/verslag.toc
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