## 2 Related Works
### Previous Work
#### 2.4.2 The Previous Method
The effectiveness of our approach was already verified through the experiments in [7]. Therefore, the proposed TT-VFDL-ST consists of four stages according to our approach in [7]. The overall progress of TT-VFDL-ST is also summarized in Figure 3:

1. **The Constructing Partial Tasks Stage** * It is a groundwork before the distributed learning, which derives model structures of each partial and the merging task by the model split technique proposed in [7]. * Also, input-output pairs for the training of each partial task, which are called \"similar feature spaces\" in [7] are also created by the data augmentation technique proposed in [7]. 2. **The Partial Task Training Stage** * Each univariate partial task is trained as the pre-training of the aimed task * The newly proposed self-transfer partial training mechanism organizes the created similar feature spaces for the two-phased transfer learning of each univariate partial task. 3. **The Single Communication Stage** * Features from each partial task are transferred to the host party with only a single step of communication. 4. **The Merging Task Training Stage** * Concatenating each task-driven feature and training the multivariate task (merging task), the aimed task is fine-tuned on the host party. As a result, in TT-VFDL-ST, two types of transfer learning mechanisms are both performed unlike our previous method [7]. One is performed for training the aimed task itself, and the other is performed for training each partial task, which is a pre-training for the aimed task. With the form of objective functions using formulation in Table 1, the proposed TT-VFDL-ST including the newly proposed self-transfer partial training is summarized in Table 2. Capital R denotes raw data stored in each guest party. Capital D denotes decoded data that reproduce each guest party's raw data. \begin{table}
\begin{tabular}{c c} \hline \hline
**Formulation** & **Description** \\ \hline \(f^{k}_{P}\) & Pre-trained model on guest party \(k\) \\ \hline \(f^{k}\) & Fine-tuned model on guest party \(k\) \\ \(f^{k}\) & Trained model on the host party (when \(k=0\)) \\ \hline \(\omega^{k}_{P}\) & Parameter of \(f^{k}_{P}\) on guest party \(k\) \\ \hline \(\omega^{k}\) & Parameter of \(f^{k}\) on guest party \(k\) or the host party (when \(k=0\)) \\ \hline \(L\) & Loss function \\ \hline \(X^{k}_{i}\) & _i-th_ input on guest party \(k\) \\ \hline \(Y_{i}\) & _i-th_ output on the host party \\ \hline \(XD^{k}_{i}\) & _i-th_ input reproduced utilizing LSTM-AE on guest party \(k\) \\ \hline \(YD_{i}\) & _i-th_ output reproduced utilizing LSTM-AE on guest party \(k\) \\  & LSTM-AE-based reproduced output for regression task on the host party (when \(k=0\)) \\ \hline \(F^{k}_{i}\) & _i-th_ feature on guest party \(k\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The formulation used for the description of TT-VFDL-ST.

\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Guest Party** & **Host Party** \\ \hline \begin{tabular}{c} **Pre-Training** \\ **for the Aimed Task** \\ \end{tabular}  & \begin{tabular}{c} **[2-Phased training]** \\ **Self-transfer Partial Training** \\ \end{tabular}  & \begin{tabular}{c} **Fine-tuning** \\ **for the** \\ **aimed task** \\ \end{tabular}  & Merging Task Training \\ \hline \ \begin{tabular}{c} **Objective** \\ **Function** \\ **For** \\ **Represent** \\ \end{tabular}  &
\begin{tabular}{c} **[1-Phase: Pre-training (DD)]** \\ \(\underset{\omega^{k}}{\operatorname{argmin}}\underset{l}{\operatorname{argmin}} \underset{l}{\operatorname{argmin}}\underset{l



### The Self-Transfer Partial Training Mechanism

Self-transfer partial training mechanism trains each partial task in two-phased, leveraging transfer learning. In particular, each task-driven features are trained through a transfer learning between two feature spaces similar to each other, on the same model structure. The purpose of introducing a transfer learning mechanism even in training of univariate partial tasks is as follows:

1.