# Training from Zero: Forecasting of Radio Frequency Machine Learning Data Quantity
## 3 Results and Discussion  
The prior sections made use of all data points taken in order to establish the best predictions for data quantity with their given metric. As these are estimates that are intended to predict the data quantity needed to achieve high-performance systems through the increase in available data alone, certifying any result in particular is beyond the scope of this work, as the expected predicted quantities will far exceed the available data acquired. Instead, the focus shifts to how having fewer data available during training relatively affects the prediction capability for each metric in comparison to greater quantities of available data. Due to the performance of the synthetic dataset stagnating, further analysis will ignore this case going forward. For the purpose of finding how well the log-linear regression with each metric is able to predict the data quantity needed, the data quantities provided in Table 5, with preference for a quantity estimate given by the GoF in Table 4, will be used such that the metric that achieved the best GoF will be used as the truth for the problem space. Therefore, predictions of the models making use of \(\Omega_{C}\) will use the LEEP metric's quantity prediction for \(\Phi_{3}\) and \(\Phi_{5}\) but will make use of the NCE prediction for \(\Phi_{10}\), while the predictions for \(\Omega_{A}\) will all make use of the LogME metric, and these quantity prediction are summarized in Table 6. The predictions for each metric can be seen in Figure 8, where the top row shows the predictions when using the \(\Omega_{C}\) dataset, while the bottom shows the predictions for the \(\Omega_{A}\) dataset. The columns consist of waveform spaces {\(\Phi_{3}\),\(\Phi_{5}\),\(\Phi_{10}\)} from left to right. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\Phi\)} & \multirow{2}{*}{\(\alpha\)} & \multirow{2}{*}{\(\mathbf{NCE}\)} & \multirow{2}{*}{\(\mathbf{LEEP}\)} & \multirow{2}{*}{\(\mathbf{LogME}\)} & \multirow{2}{*}{\(\Omega\)} & \multirow{2}{*}{\(\mathbf{\kappa}\)} & \multirow{2}{*}{\(\mathbf{NCE}\)} & \multirow{2}{*}{\(\mathbf{LEEP}\)} & \multirow{2}{*}{\(\mathbf{LogME}\)} \\  & & & & & & & & & \\ \hline \multirow{2}{*}{\(\Phi_{3}\)} & \multirow{2}{*}{0.999990} & \multirow{2}{*}{\(-1.275\times 10^{-4}\)} & \multirow{2}{*}{\(-2.668\times 10^{-3}\)} & & \(\Omega_{C}\) & \(48.7\times 10^{6}\) & \(237\times 10^{6}\) & \(88.5\times 10^{6}\) & \(2.46\times 10^{12}\) \\  & & & & & \(\Omega_{5}\) & \(6.42\times 10^{224}\) & \(1.64\times 10^{106}\) & \(1.38\times 10^{158}\) & \(\infty\) \\  & & & & & \(\Omega_{A}\) & \(72.8\times 10^{6}\) & \(291\times 10^{6}\) & \(144\times 10^{10}\) & \(3.47\times 10^{15}\) \\ \hline \multirow{2}{*}{\(\Phi_{5}\)} & \multirow{2}{*}{0.999990} & \multirow{2}{*}{\(-1.272\times 10^{-4}\)} & \multirow{2}{*}{\(-2.972\times 10^{-3}\)} & & \(\Omega_{C}\) & \(394\times 10^{6}\) & \(135\times 10^{6}\) & \(4.45\times 10^{100}\) & \(2.57\times 10^{159}\) \\  & & & & & \(\Omega_{5}\) & \(\infty\) & \(9.15\times 10^{6}\) & \(6.57\times 10^{100}\) & \(\infty\) \\  & & & & & \(\Omega_{A}\) & \(181\times 10^{6}\) & \(3.60\times 10^{6}\) & \(1.11\times 10^{9}\) & \(2.41\times 10^{121}\) \\ \hline \multirow{2}{*}{\(\Phi_{10}\)} & \multirow{2}{*}{0.999990} & \multirow{2}{*}{\(-1.289\times 10^{-4}\)} & \multirow{2}{*}{\(-3.963\times 10^{-3}\)} & & \(\Omega_{C}\) & \(34.2\times 10^{6}\) & \(514\times 10^{6}\) & \(430\times 10^{6}\) & \(1.61\times 10^{11}\) \\  & & & & & \(\Omega_{S}\) & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) \\  & & & & & \(\Omega_{A}\) & \(29.3\times 10^{6}\) & \(337\times 10^{6}\) & \(233\times 10^{6}\) & \(1.57\times 10^{23}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The performance of Accuracy (\(\alpha\)), NCE, LEEP, and LogME for the label whitening procedure proposed in Section 2 for a desired error \(\epsilon=10^{-5}\). Additionally, the data quantity needed per metric for the log-linear regression of the metric with the data quantity used during training is provided.