# On the Quality of Deep Representations for Kepler Light Curves Using Variational Auto-Encoders
## 3 Experimental Setup and Results
### Results
#### 3.3.2 Quality Evaluation
On the other hand, the Mandel-Agl model residuals show that the reconstruction errors are related to the positive values, as the function models that the measured light could not be greater than the regular/normal star's light intensity (without objects in front of the observer), i.e., it is limited by the model itself. In Table 3, we present the disentanglement of the representation based on the feature dependence. Here, it can be seen that learning-based methods (AEs) obtain features with less information duplicity than the metadata features obtained by Kepler, i.e., the learned features are more disentangled. Minimizing the correlation and mutual information could simplify the task of identifying independent linear and non-linear processes in the system, respectively. We computed an F-PCA representation from the whole (unfolded) raw measurements and from the folded representation. Both obtained components were linearly independent between them based on the orthogonality of the PCA formulation. However, the F-PCA method over the fold representation produces less MI, as an example of optimal independence for the problem. The closer values to F-PCA (_in the folded curve_) are from the proposed model with re-scaling (S-VRAE\({}_{t}\)) showing the good impact of including the _F-std_ into the model. It is worth noting that the variational proposed models (VRAE\({}_{t}\) and S-VRAE\({}_{t}\)) learn a space with more independent components (linearly and based on mutual information) than the deterministic counterpart RAE\({}_{t}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Config.**} & \multicolumn{2}{c}{**Reconstruction**} & \multicolumn{2}{c}{**Denoising**} & \multirow{2}{*}{**Residual Noise**} \\  & & **RMSE \(\downarrow\)** & & **MAE \(\downarrow\)** & & **Auto-C \(\uparrow\)** & **Diff-M \(\downarrow\)** & **Spectral-H \(\uparrow\)** \\ \hline \multicolumn{2}{c}{Light Curve} & - & - & - & 0.273 & 0.784 & 0.840 \\ \hline \multirow{3}{*}{Passband} & 1-500 & 1.081 & 0.624 & 0.968 & 0.047 & 0.824 \\  & 50–1500 & 1.041 & 0.655 & 0.831 & 0.200 & 0.842 \\  & 50–2500 & 0.959 & 0.640 & 0.670 & 0.363 & 0.846 \\ \hline \multirow{3}{*}{Moving avg} & 3 & 0.719 & 0.461 & 0.704 & 0.274 & 0.876 \\  & 5 & 0.841 & 0.513 & 0.784 & 0.170 & 0.860 \\  & 10 & 0.937 & 0.553 & 0.843 & 0.089 & 0.843 \\ \hline M-A fit & ktransit & 0.799 & 0.514 & 0.693 & 0.028 & 0.873 \\ \hline RAE\({}_{t}\) & 16 & 0.680 & 0.475 & 0.502 & 0.125 & 0.895 \\ \hline
**VRAE\({}_{t}\)** & 16 & 0.688 & 0.484 & 0.594 & 0.068 & 0.901 \\
**S-VRAE\({}_{t}\)** & 16 & 0.724 & 0.489 & 0.611 & 0.064 & 0.898 \\ \hline \end{tabular}
\end{table} 
Table 2: **Reconstruction validation**. Reconstruction and denoising results with the associated metrics on different methods. The configuration of the passband corresponds to low and high-pass filters, respectively, while for moving average corresponds to window size. For the Mandel–Aglot it indicates the library used for the fit, while deep auto-encoder methods have the dimension of the encoder representation. The \(\uparrow/\downarrow\) symbols mean that a higher/lower value is better on that task respectively. Figure 5: Examples of the reconstructed and simulated light curves by different methods in (**b-d**) of the corresponding light curves in (**a**). The red line with stars is the residual generated from the methods with respect to the original curves in (**a**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Representation** & **Pcorr** & **Pcorr-A** & **MI** & **N-MI** \\ \hline Metadata & 0.064 & 0.162 & 0.275 & 0.044 \\ \hline (Raw) F-PCA & 0.000 & 0.000 & 0.210 & 0.027 \\ (Fold) F-PCA & 0.000 & 0.000 & 0.061 & 0.008 \\ \hline RAE\({}_{t}\) & 0.057 & 0.277 & 0.255 & 0.033 \\
**VRAE\({}_{t}\)** & 0.012 & 0.168 & 0.122 & 0.016 \\
**S-VRAE\({}_{t}\)** & \(-\)0.003 & 0.138 & 0.072 & 0.009 \\ \hline \hline \end{tabular}
\end{table}