Non linear results section done

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Reports/Thesis/sections/background.tex

@@ -199,12 +199,12 @@ Another more complex model that can be used is a Recurrent Neural Network (RNN).
 
 The RNN model can be used to model the NRV data. The input features are structured in a way that the model can learn the sequential patterns in the data. The model can be trained to output the quantiles for the NRV based on the input features using the pinball loss function.
 
-Multiple types of RNN models exist. The two most common types of RNNs are the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simpler version of the LSTM. The GRU has fewer parameters which results in faster training times. The GRU still can capture long-term dependencies in the data and can achieve similar performance to the LSTM.
+Multiple types of RNN models exist. The two most common types of RNNs are the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simpler version of the LSTM. The GRU has fewer parameters which results in faster training times. The GRU still can capture long-term dependencies in the data and can achieve similar performance to the LSTM. The GRU model has two gates, the reset gate and the update gate. The reset gate determines how much of the past information to forget, and the update gate determines how much of the new information to keep.
 
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.8\textwidth]{images/quantile_regression/rnn/RNN_diagram.png}
-    \caption{RNN model input and output  visualization}
+    \caption{RNN model input and output visualization}
     \label{fig:rnn_model_visualization}
 \end{figure}
 

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Reports/Thesis/sections/results.tex

@@ -40,124 +40,15 @@ TODO: ask Jonas: add urls to the correct data? via citation?
 
 A lot of data is available but only the most relevant data needs to be used. Experiments will be done to identify which data and features improve the NRV modeling. The data will be split into a training and test set. The training dataset starts depending on which data features are used but ends on 31-12-2022. The test set starts on 01-01-2023 and ends on (TODO: check the end date). This makes sure enough data is available to train the models and the test set is large enough to evaluate the models. The year 2023 is chosen as the test set because it is the most recent data available when the thesis experiments were conducted. Using data from 2022 in the test set also does not make a lot of sense because the trained models would be used to predict the future. Data from 2022 is not relevant anymore to evaluate the models.
 
+\subsection{Quantile Regression}
 \input{sections/results/linear}
 
 \input{sections/results/non-linear}
 
-
-% TODO: REWORK FROM THIS POINT ON
-
-In this context, a simple feedforward neural network is trained to predict the quantiles for the NRV. The quantiles are then used to reconstruct the cumulative distribution function (CDF) for the NRV of a quarter. Predictions for the NRV can then be sampled from this reconstructed CDF. The neural network is trained using the pinball loss function explained in section \ref{subsubsec:quantile_regression_training}. 
-\\\\
-The results of the non-linear model are shown in Table \ref{tab:autoregressive_non_linear_model_results}.
+\input{sections/results/gru}
 
 
 
-
-% TODO: Talk more about the results in the table.
-The results of the non-linear quantile regression model, as shown in Table \ref{tab:autoregressive_non_linear_model_results}, show valuable insights into the performance of the models with different hyperparameters and input feature sets. Increasing the number of layers and hidden size in the model does not necessarily lead to better performance on the test set. The model doesn't generalize well anymore and tends to overfit the training data. The input feature set plays a huge role in the performance of the model. The model with the input features NRV, Load, PV, Wind, Net Position, and the quarter embedding with 5 dimensions performs the best.
-
-\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_non_linear_model_samples/AQR_NL_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_non_linear_model_samples/AQR_NL_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}
-        \caption{Autoregressive linear model}
-    \end{subfigure}
-    \hfill
-    \begin{subfigure}[b]{0.49\textwidth}
-        \includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
-        \caption{Autoregressive non-linear model}
-    \end{subfigure}
-
-    \caption{Comparison for examples from test set between the autoregressive linear and non-linear models. The plots show the confidence intervals calculated from 1000 generated full-day NRV samples. The samples were generated using input features NRV, Load, Wind, PV, Net Position and the quarter embedding. The non-linear model used 8 layers with a hidden size of 256 and a dropout rate of 0.2.}
-    \label{fig:linear_non_linear_sample_comparison}
-\end{figure}
-
-TODO: better comparison
-Figure \ref{fig:linear_non_linear_sample_comparison} shows a comparison between the samples of autoregressive linear and non-linear models for certain examples of the test set. The non-linear model has a small increase in variance in the samples compared to the linear model. This results in some wider confidence intervals. This can be seen in example 2 of the figure. 
-
-TODO: non autoregressive non-linear model for quantile regression 
-
-\subsubsection{GRU Model}
-The GRU model architecture is shown in Table \ref{tab:gru_model_architecture}. The model starts with an embedding layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. The input of the TimeEmbedding is of shape (Batch Size, Time Steps, Input Features Size). The output of this layer is then passed to the GRU layer. The GRU layer outputs the hidden state for every time step. This results in a tensor of shape (Batch Size, Time Steps, Hidden Size). Only the last hidden state is relevant for the prediction of the NRV quantiles for the next quarter. The last hidden state should contain all the necessary information from the previous quarters to make the prediction. The last hidden state is then passed through a linear layer to output the quantiles for the NRV prediction.
-
-TODO: Zielige visualisatie van model nu
-\begin{table}[H]
-\centering
-\begin{tabularx}{\textwidth}{Xr} % Set the table width to the text width
-\toprule
-\textbf{Layer (Type)} & \textbf{Output Shape} \\ \midrule
-\midrule
-Time Embedding & [B, Time Steps, Input + Time Embedding Size] \\
-\midrule
-GRU & [B, Time Steps, Hidden Size] \\
-\multicolumn{2}{c}{\textit{Last state of GRU passed [B, Hidden Size]}} \\
-Linear & [B, Number of quantiles] \\
-\bottomrule
-\end{tabularx}
-\caption{GRU Model Architecture}
-\label{tab:gru_model_architecture}
-\end{table}
-
-Multiple experiments are conducted to find which hyperparameters and input features work best for the GRU model. The results of the GRU model are shown in Table \ref{tab:autoregressive_gru_model_results}. 
-
-\begin{table}[H]
-\centering
-\begin{adjustbox}{width=\textwidth,center}
-\begin{tabular}{@{}cccccccccc@{}}
-\toprule
-Features & Layers & Hidden Size & \multicolumn{2}{c}{MSE} & \multicolumn{2}{c}{MAE} & \multicolumn{2}{c}{CRPS} \\ 
-\cmidrule(lr){4-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9}
-& & & Train & Test & Train & Test & Train & Test \\
-\midrule
-NRV & & & & & & & & \\
-& 2 & 256 & 34942.89 & 39838.35 & 142.43 & 150.81 & 81.34 & 85.04 \\
-& 4 & 256 & 34705.61 & 39506.55 & 141.74 & 149.81 & 81.89 & 85.46 \\
-& 8 & 256 & 32885.71 & 37747.11 & 138.16 & 146.67 & 79.99 & 83.67 \\ 
-& 2 & 512 & 35362.66 & 39955.79 & 143.19 & 150.77 & 84.37 & 87.88 \\
-& 4 & 512 & 38253.89 & 43301.13 & 148.33 & 156.73 & 85.98 & 89.78 \\
-& 8 & 512 & 33131.93 & 37681.71 & 138.93 & 146.62 & 79.64 & 83.08 \\
-\midrule
-NRV + Load & & & & & & & & & \\
-& 2 & 256 & 33202.80 & 38427.91 & 138.02 & 147.27 & 79.62 & 84.17 \\
-& 4 & 256 & 33600.73 & 38984.44 & 138.62 & 147.91 & 81.03 & 85.91 \\
-& 8 & 256 & 32828.61 & 38343.98 & 136.82 & 146.44 & 79.42 & 84.22 \\
-& 2 & 512 & 35979.57 & 41496.77 & 144.16 & 153.53 & 83.50 & 88.26 \\
-& 4 & 512 & 32334.73 & 38000.40 & 135.92 & 146.10 & 78.82 & 83.99 \\
-& 8 & 512 & 35177.39 & 41104.28 & 141.79 & 152.13 & 83.79 & 89.13 \\
-\midrule
-NRV + Load + PV\\ + Wind & & & & & & & & & \\
-& 4 & 256 & 31594.55 & 39872.46 & 134.11 & 149.34 & 77.52 & 85.91 \\
-& 8 & 256 & 31481.22 & 39704.37 & 133.45 & 148.59 & 77.26 & 85.62 \\
-& 4 & 512 & 31368.31 & 39024.27 & 134.02 & 147.91 & 76.58 & 84.18 \\
-& 8 & 512 & 34566.66 & 42397.86 & 140.13 & 154.00 & 82.09 & 89.87 \\
-\midrule
-NRV + Load + PV\\ + Wind + Net Position \\+ QE (5 dim) & & & & & & & & & \\
-& 4 & 256 & 30130.37 & 39906.53 & 130.92 & 149.78 & 75.02 & 84.88 \\
-& 8 & 256 & 28560.67 & 37675.15 & 127.77 & 145.39 & 73.77 & 83.37 \\
-& 4 & 512 & & & & & & & \\
-& 8 & 512 & 27421.85 & 35238.98 & 125.32 & 141.02 & 72.73 & 80.92 \\
-\bottomrule
-\end{tabular}
-\end{adjustbox}
-\caption{Autoregressive GRU quantile regression model results. All the models used a dropout of 0.2 .}
-\label{tab:autoregressive_gru_model_results}
-\end{table}
-
 TODO: Talk about the results + show plots of the samples with GRU model. Talk about the over/underestimation of the quantiles for the models. Plots have been made for this.
 
 TODO: non autoregressive stuff? 

Reports/Thesis/sections/results/gru.tex

@@ -0,0 +1,67 @@
+\subsubsection{GRU Model}
+Another popular architecture to model sequential data is a recurrent neural network. There exist two main types of recurrent neural networks, the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simplified version of the LSTM, which has fewer parameters and is computationally less expensive. The GRU model can be trained for quantile regression in the same way as the linear and non-linear models using the pinball loss. There is, however, a difference in how the input data is structured and provided to the model. For linear and non-linear models, the data is provided in the shape of $(batch\_size, num\_features)$. The recurrent neural network, on the other hand, expects the input data to be structured as $(batch\_size, time\_steps, num\_features\_per\_timestep)$. This is also explained in the background section about the recurrent neural network.
+
+The GRU model architecture to predict the NRV quantiles is shown in Table \ref{tab:gru_model_architecture}. The model starts with an embedding layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. The input of the TimeEmbedding is of shape (Batch Size, Time Steps, Input Features Size). The output of this layer is then passed to the GRU layer. The GRU layer outputs the hidden state for every time step. This results in a tensor of shape (Batch Size, Time Steps, Hidden Size). Only the last hidden state is relevant for the prediction of the NRV quantiles for the next quarter. The last hidden state should contain all the necessary information from the previous quarters to make the prediction. The last hidden state is then passed through a linear layer to output the quantiles for the NRV prediction. The input and output of the model depend if the model is trained using an autoregressive or non-autoregressive way. The non-autoregressive variant of the GRU model has two days worth of time steps. This results in $92*2$ time steps. The model then needs to output $(96 * \text{number\_of\_quantiles})$ NRV quantile values.
+
+TODO: Zielige visualisatie van model nu
+\begin{table}[H]
+\centering
+\begin{tabularx}{\textwidth}{Xr} % Set the table width to the text width
+\toprule
+\textbf{Layer (Type)} & \textbf{Output Shape} \\ \midrule
+\midrule
+Time Embedding & [B, Time Steps, Input + Time Embedding Size] \\
+\midrule
+GRU & [B, Time Steps, Hidden Size] \\
+\multicolumn{2}{c}{\textit{Last state of GRU passed [B, Hidden Size]}} \\
+Linear & [B, Number of quantiles] \\
+\bottomrule
+\end{tabularx}
+\caption{GRU Model Architecture}
+\label{tab:gru_model_architecture}
+\end{table}
+
+Multiple experiments are conducted to find which hyperparameters and input features work best for the GRU model. The results of the GRU model are shown in Table \ref{tab:autoregressive_gru_model_results}. 
+
+\begin{table}[H]
+\centering
+\begin{adjustbox}{width=\textwidth,center}
+\begin{tabular}{@{}cccccccccc@{}}
+\toprule
+Features & Layers & Hidden Size & \multicolumn{2}{c}{MSE} & \multicolumn{2}{c}{MAE} & \multicolumn{2}{c}{CRPS} \\ 
+\cmidrule(lr){4-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9}
+& & & Train & Test & Train & Test & Train & Test \\
+\midrule
+NRV & & & & & & & & \\
+& 2 & 256 & 34942.89 & 39838.35 & 142.43 & 150.81 & 81.34 & 85.04 \\
+& 4 & 256 & 34705.61 & 39506.55 & 141.74 & 149.81 & 81.89 & 85.46 \\
+& 8 & 256 & 32885.71 & 37747.11 & 138.16 & 146.67 & 79.99 & 83.67 \\ 
+& 2 & 512 & 35362.66 & 39955.79 & 143.19 & 150.77 & 84.37 & 87.88 \\
+& 4 & 512 & 38253.89 & 43301.13 & 148.33 & 156.73 & 85.98 & 89.78 \\
+& 8 & 512 & 33131.93 & 37681.71 & 138.93 & 146.62 & 79.64 & 83.08 \\
+\midrule
+NRV + Load & & & & & & & & & \\
+& 2 & 256 & 33202.80 & 38427.91 & 138.02 & 147.27 & 79.62 & 84.17 \\
+& 4 & 256 & 33600.73 & 38984.44 & 138.62 & 147.91 & 81.03 & 85.91 \\
+& 8 & 256 & 32828.61 & 38343.98 & 136.82 & 146.44 & 79.42 & 84.22 \\
+& 2 & 512 & 35979.57 & 41496.77 & 144.16 & 153.53 & 83.50 & 88.26 \\
+& 4 & 512 & 32334.73 & 38000.40 & 135.92 & 146.10 & 78.82 & 83.99 \\
+& 8 & 512 & 35177.39 & 41104.28 & 141.79 & 152.13 & 83.79 & 89.13 \\
+\midrule
+NRV + Load + PV\\ + Wind & & & & & & & & & \\
+& 4 & 256 & 31594.55 & 39872.46 & 134.11 & 149.34 & 77.52 & 85.91 \\
+& 8 & 256 & 31481.22 & 39704.37 & 133.45 & 148.59 & 77.26 & 85.62 \\
+& 4 & 512 & 31368.31 & 39024.27 & 134.02 & 147.91 & 76.58 & 84.18 \\
+& 8 & 512 & 34566.66 & 42397.86 & 140.13 & 154.00 & 82.09 & 89.87 \\
+\midrule
+NRV + Load + PV\\ + Wind + Net Position \\+ QE (5 dim) & & & & & & & & & \\
+& 4 & 256 & 30130.37 & 39906.53 & 130.92 & 149.78 & 75.02 & 84.88 \\
+& 8 & 256 & 28560.67 & 37675.15 & 127.77 & 145.39 & 73.77 & 83.37 \\
+& 4 & 512 & & & & & & & \\
+& 8 & 512 & 27421.85 & 35238.98 & 125.32 & 141.02 & 72.73 & 80.92 \\
+\bottomrule
+\end{tabular}
+\end{adjustbox}
+\caption{Autoregressive GRU quantile regression model results. All the models used a dropout of 0.2 .}
+\label{tab:autoregressive_gru_model_results}
+\end{table}

Reports/Thesis/sections/results/linear.tex

@@ -1,4 +1,4 @@
-\subsection{Linear Model}
+\subsubsection{Linear Model}
 % TODO: explainedi nsection reference ?
 The simplest model to be trained for the NRV modeling is the linear model. The linear model is trained using the pinball loss function explained in the section above. The outputs of the model are values for the chosen quantiles. The linear model can be trained in an autoregressive and non-autoregressive way. Both methods will be compared to each other. The linear model is trained using the Adam optimizer with a learning rate of 1e-4. Early stopping is used with a patience of 5 epochs. The linear model is evaluated using the mean squared error (MSE), mean absolute error (MAE), and continuous ranked probability score (CRPS). The influence of the input features is also evaluated by training the models with different input feature sets.
 

Reports/Thesis/sections/results/non-linear.tex

@@ -1,4 +1,4 @@
-\subsection{Non-Linear Model}
+\subsubsection{Non-Linear Model}
 Adding nonlinearity to the model can be done by adding some non-linear activations between linear layers. This improves the model's ability to learn more complex patterns in the data. The model is trained the same way as the linear model for quantile regression using the pinball loss. Because a non-linear model is more complex, it is more prone to overfitting the training data. Because of this, dropout layers are added to the model to prevent overfitting.
 
 The architecture of the non-linear model is illustrated in Table \ref{tab:non_linear_model_architecture}. The autoregressive model begins with an input layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. These combined features are then processed through a sequence of layers:
@@ -42,7 +42,7 @@ While this non-linear model is still quite simple, it offers the flexibility in
     \toprule
     Features & Layers & Hidden Size & \multicolumn{2}{c}{MSE} & \multicolumn{2}{c}{MAE} & \multicolumn{2}{c}{CRPS} \\ 
     \cmidrule(lr){4-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9}
-    & & & Train & Test & Train & Test & Train & Test \\
+    & & & AR & NAR & AR & NAR & AR & NAR \\
     \midrule
     NRV & & & & & & & & \\
     & 2 & 256 & 38117.43 & 41574.38 & 147.55 & 153.83 & 86.42 & 75.61 \\
@@ -64,6 +64,77 @@ While this non-linear model is still quite simple, it offers the flexibility in
     \bottomrule
     \end{tabular}
     \end{adjustbox}
-    \caption{Autoregressive non-linear quantile regression model results. All the models used a dropout of 0.2 .}
+    \caption{Non-linear quantile regression model results. All the models used a dropout of 0.2 .}
     \label{tab:non_linear_model_results}
 \end{table}
+
+The same behavior as the linear model is observed when looking at the metric differences between the autoregressive and non-autoregressive models. The autoregressive model performs better in terms of MSE and MAE, while the non-autoregressive model performs better in terms of CRPS. The results also give insight into the importance of the input features and hyperparameters. The addition of more input features improves the performance of the autoregressive model. The non-autoregressive model, on the other hand, does not benefit from this. The metrics are worse when more input features are added. This was also seen in the linear model. A reason for this behavior could be that the non-autoregressive model is not able to learn the complex patterns in the large set of input features. The non-autoregressive is provided with all the values for each quarter for which the quantiles need to be predicted. This increases the input size with 96 values each time a new forecast feature is added. Capturing patterns in this large input space can be a challenging task.
+
+% TODO: talk about hyperparameters?
+
+\begin{figure}[H]
+    \centering
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
+    \end{subfigure}
+    \hfill
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
+    \end{subfigure}
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
+    \end{subfigure}
+    \hfill
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
+    \end{subfigure}
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
+    \end{subfigure}
+    \hfill
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
+    \end{subfigure}
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_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/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
+        \caption{Non-autoregressive linear model}
+    \end{subfigure}
+
+    \caption{Comparison of the autoregressive and non-autoregressive non-linear model examples.}
+    \label{fig:non_linear_model_examples}
+\end{figure}
+
+The examples from the test set for the non-linear model are shown in Figure \ref{fig:non_linear_model_examples}. A big difference can be observed between the examples of the autoregressive and non-autoregressive models. The autoregressive model examples follow the actual NRV trend more closely than the non-autoregressive model. The mean of the samples generated by the non-autoregressive model is around zero for every quarter of the day. No clear trend can be observed in the samples. This is a clear indication that the non-autoregressive model is not able to learn the patterns in the data despite having a lower CRPS.
+
+\begin{figure}[ht]
+    \centering
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/quantile_performance/AQR_NL_Quantile_Performance_Training.jpeg}
+        \caption{AR - Train}
+    \end{subfigure}
+    \hfill
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/quantile_performance/AQR_NL_Quantile_Performance_Test.jpeg}
+        \caption{AR - Test}
+    \end{subfigure}
+
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/quantile_performance/NAQR_NL_Quantile_Performance_Training.jpeg}
+        \caption{NAR - Train}
+    \end{subfigure}
+    \hfill
+    \begin{subfigure}[b]{0.49\textwidth}
+        \includegraphics[width=\textwidth]{images/quantile_regression/quantile_performance/NAQR_NL_Quantile_Performance_Test.jpeg}
+        \caption{NAR - Test}
+    \end{subfigure}
+    \caption{Over/underestimation of the quantiles for the autoregressive and non-autoregressive non-linear models. Both the quantile performance for the training and test set are shown. The plots are generated using the input features NRV, Load, Wind, PV, Net Position, and the quarter embedding (only for the autoregressive model).}
+    \label{fig:non-linear_model_quantile_over_underestimation}
+\end{figure}
+
+% TODO: correct use of overestimation
+The plots in Figure \ref{fig:non-linear_model_quantile_over_underestimation} show the over/underestimation of the quantiles outputted by the non-linear models. Looking at the plots for the autoregressive models, the observation can be made that the fraction of the real NRV values under the quantiles is too big most of the time in comparison with the ideal fraction. This means the model is estimating the quantiles too high which results in a bigger fraction of NRV values below this value. The model overestimates the quantiles. The non-autoregressive model also suffers from this problem for the training set. For the test set, the lower quantiles are estimated too high and the higher quantiles are estimated too low. The quantiles in the middle are estimated quite accurately.

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+[]\T1/LinuxLibertineT-TLF/m/n/12 Figure 11: |Over/underestimation of the quan-tiles for the au-tore-gres-sive and non-
+ []
+
+) [31 <./images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png> <./images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png> <./images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png> <./images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png> <./images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png> <./images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png> <./images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png> <./images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png>] (./sections/results/gru.tex [32 <./images/quantile_regression/quantile_performance/AQR_NL_Quantile_Performance_Training.jpeg> <./images/quantile_regression/quantile_performance/AQR_NL_Quantile_Performance_Test.jpeg> <./images/quantile_regression/quantile_performance/NAQR_NL_Quantile_Performance_Training.jpeg> <./images/quantile_regression/quantile_performance/NAQR_NL_Quantile_Performance_Test.jpeg>]) [33] [34]
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-) [33] [34] (./verslag.aux (./sections/introduction.aux) (./sections/background.aux) (./sections/policies.aux) (./sections/literature_study.aux))
+) [35] [36] (./verslag.aux (./sections/introduction.aux) (./sections/background.aux) (./sections/policies.aux) (./sections/literature_study.aux))
 
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Reports/Thesis/verslag.out

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Reports/Thesis/verslag.toc

@@ -9,22 +9,23 @@
 \contentsline {subsubsection}{\numberline {3.3.2}Non-Linear Model}{10}{subsubsection.3.3.2}%
 \contentsline {subsubsection}{\numberline {3.3.3}Recurrent Neural Network (RNN)}{10}{subsubsection.3.3.3}%
 \contentsline {subsection}{\numberline {3.4}Diffusion models}{11}{subsection.3.4}%
-\contentsline {subsubsection}{\numberline {3.4.1}Overview}{11}{subsubsection.3.4.1}%
+\contentsline {subsubsection}{\numberline {3.4.1}Overview}{12}{subsubsection.3.4.1}%
 \contentsline {subsubsection}{\numberline {3.4.2}Applications}{12}{subsubsection.3.4.2}%
 \contentsline {subsubsection}{\numberline {3.4.3}Generation process}{12}{subsubsection.3.4.3}%
 \contentsline {subsection}{\numberline {3.5}Evaluation}{14}{subsection.3.5}%
-\contentsline {section}{\numberline {4}Policies}{16}{section.4}%
-\contentsline {subsection}{\numberline {4.1}Baselines}{16}{subsection.4.1}%
-\contentsline {subsection}{\numberline {4.2}Policies based on NRV generations}{17}{subsection.4.2}%
-\contentsline {section}{\numberline {5}Literature Study}{18}{section.5}%
-\contentsline {subsection}{\numberline {5.1}Electricity Price Forecasting}{18}{subsection.5.1}%
-\contentsline {subsection}{\numberline {5.2}Policies for Battery Optimization}{19}{subsection.5.2}%
-\contentsline {section}{\numberline {6}Results \& Discussion}{20}{section.6}%
-\contentsline {subsection}{\numberline {6.1}Data}{20}{subsection.6.1}%
-\contentsline {subsection}{\numberline {6.2}Linear Model}{21}{subsection.6.2}%
-\contentsline {subsection}{\numberline {6.3}Non-Linear Model}{27}{subsection.6.3}%
-\contentsline {subsubsection}{\numberline {6.3.1}GRU Model}{30}{subsubsection.6.3.1}%
-\contentsline {subsection}{\numberline {6.4}Diffusion}{33}{subsection.6.4}%
-\contentsline {section}{\numberline {7}Policies for battery optimization}{33}{section.7}%
-\contentsline {subsection}{\numberline {7.1}Baselines}{33}{subsection.7.1}%
-\contentsline {subsection}{\numberline {7.2}Policies using NRV predictions}{33}{subsection.7.2}%
+\contentsline {section}{\numberline {4}Policies}{17}{section.4}%
+\contentsline {subsection}{\numberline {4.1}Baselines}{17}{subsection.4.1}%
+\contentsline {subsection}{\numberline {4.2}Policies based on NRV generations}{18}{subsection.4.2}%
+\contentsline {section}{\numberline {5}Literature Study}{19}{section.5}%
+\contentsline {subsection}{\numberline {5.1}Electricity Price Forecasting}{19}{subsection.5.1}%
+\contentsline {subsection}{\numberline {5.2}Policies for Battery Optimization}{20}{subsection.5.2}%
+\contentsline {section}{\numberline {6}Results \& Discussion}{21}{section.6}%
+\contentsline {subsection}{\numberline {6.1}Data}{21}{subsection.6.1}%
+\contentsline {subsection}{\numberline {6.2}Quantile Regression}{22}{subsection.6.2}%
+\contentsline {subsubsection}{\numberline {6.2.1}Linear Model}{22}{subsubsection.6.2.1}%
+\contentsline {subsubsection}{\numberline {6.2.2}Non-Linear Model}{29}{subsubsection.6.2.2}%
+\contentsline {subsubsection}{\numberline {6.2.3}GRU Model}{32}{subsubsection.6.2.3}%
+\contentsline {subsection}{\numberline {6.3}Diffusion}{35}{subsection.6.3}%
+\contentsline {section}{\numberline {7}Policies for battery optimization}{35}{section.7}%
+\contentsline {subsection}{\numberline {7.1}Baselines}{35}{subsection.7.1}%
+\contentsline {subsection}{\numberline {7.2}Policies using NRV predictions}{35}{subsection.7.2}%

src/training_scripts/autoregressive_quantiles.py

@@ -2,8 +2,8 @@ from src.utils.clearml import ClearMLHelper
 
 #### ClearML ####
 clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast")
-task = clearml_helper.get_task(task_name="AQR: Linear + QE (dim 2)")
-# task.execute_remotely(queue_name="default", exit_process=True)
+task = clearml_helper.get_task(task_name="AQR: Non-Linear (16 - 256) + QE (dim 2)")
+task.execute_remotely(queue_name="default", exit_process=True)
 
 from src.policies.PolicyEvaluator import PolicyEvaluator
 from src.policies.simple_baseline import BaselinePolicy, Battery
@@ -67,8 +67,8 @@ else:
 
 model_parameters = {
     "learning_rate": 0.0001,
-    "hidden_size": 512,
-    "num_layers": 8,
+    "hidden_size": 256,
+    "num_layers": 16,
     "dropout": 0.2,
     "time_feature_embedding": 2,
 }
@@ -89,17 +89,17 @@ time_embedding = TimeEmbedding(
 #     dropout=model_parameters["dropout"],
 # )
 
-# non_linear_model = NonLinearRegression(
-#     time_embedding.output_dim(inputDim),
-#     len(quantiles),
-#     hiddenSize=model_parameters["hidden_size"],
-#     numLayers=model_parameters["num_layers"],
-#     dropout=model_parameters["dropout"],
-# )
+non_linear_model = NonLinearRegression(
+    time_embedding.output_dim(inputDim),
+    len(quantiles),
+    hiddenSize=model_parameters["hidden_size"],
+    numLayers=model_parameters["num_layers"],
+    dropout=model_parameters["dropout"],
+)
 
-linear_model = LinearRegression(time_embedding.output_dim(inputDim), len(quantiles))
+# linear_model = LinearRegression(time_embedding.output_dim(inputDim), len(quantiles))
 
-model = nn.Sequential(time_embedding, linear_model)
+model = nn.Sequential(time_embedding, non_linear_model)
 
 model.output_size = 1
 optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])

src/training_scripts/non_autoregressive_quantiles.py

@@ -1,10 +1,8 @@
 from src.utils.clearml import ClearMLHelper
 
 #### ClearML ####
-clearml_helper = ClearMLHelper(project_name="Thesis/NAQR: Non-Linear")
-task = clearml_helper.get_task(
-    task_name="NAQR: Non-Linear (8 - 512) + NRV + LOAD + PV + WIND + NP"
-)
+clearml_helper = ClearMLHelper(project_name="Thesis/NAQR: GRU")
+task = clearml_helper.get_task(task_name="NAQR: GRU (2 - 256)")
 task.execute_remotely(queue_name="default", exit_process=True)
 
 from src.policies.PolicyEvaluator import PolicyEvaluator
@@ -29,21 +27,21 @@ from src.models.time_embedding_layer import TimeEmbedding
 data_config = DataConfig()
 
 data_config.NRV_HISTORY = True
-data_config.LOAD_HISTORY = True
-data_config.LOAD_FORECAST = True
+data_config.LOAD_HISTORY = False
+data_config.LOAD_FORECAST = False
 
-data_config.WIND_FORECAST = True
-data_config.WIND_HISTORY = True
+data_config.WIND_FORECAST = False
+data_config.WIND_HISTORY = False
 
-data_config.PV_FORECAST = True
-data_config.PV_HISTORY = True
+data_config.PV_FORECAST = False
+data_config.PV_HISTORY = False
 
-data_config.NOMINAL_NET_POSITION = True
+data_config.NOMINAL_NET_POSITION = False
 
 
 data_config = task.connect(data_config, name="data_features")
 
-data_processor = DataProcessor(data_config, path="", lstm=False)
+data_processor = DataProcessor(data_config, path="", lstm=True)
 data_processor.set_batch_size(64)
 data_processor.set_full_day_skip(True)
 
@@ -66,8 +64,8 @@ else:
 
 model_parameters = {
     "learning_rate": 0.0001,
-    "hidden_size": 512,
-    "num_layers": 8,
+    "hidden_size": 256,
+    "num_layers": 2,
     "dropout": 0.2,
 }
 
@@ -75,16 +73,24 @@ model_parameters = task.connect(model_parameters, name="model_parameters")
 
 # linear_model = LinearRegression(inputDim, len(quantiles) * 96)
 
-non_linear_model = NonLinearRegression(
+# non_linear_model = NonLinearRegression(
+#     inputDim,
+#     len(quantiles) * 96,
+#     hiddenSize=model_parameters["hidden_size"],
+#     numLayers=model_parameters["num_layers"],
+#     dropout=model_parameters["dropout"],
+# )
+
+lstm_model = GRUModel(
     inputDim,
-    len(quantiles) * 96,
-    hiddenSize=model_parameters["hidden_size"],
-    numLayers=model_parameters["num_layers"],
+    len(quantiles),
+    hidden_size=model_parameters["hidden_size"],
+    num_layers=model_parameters["num_layers"],
     dropout=model_parameters["dropout"],
 )
 
 
-model = non_linear_model
+model = lstm_model
 model.output_size = 96
 optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])