## 2 Related Works
### Previous Work
#### 2.4.2 The Previous Method
11 Pre-trained Partial Task Input: \(XD_{i}^{k}\gets d_{DA}^{k}(e_{DA}^{k}(X_{i}^{k};\delta_{e}^{k});\delta_{e} ^{k})\)
12 Pre-trained Partial Task Output: \(Y_{i}\) // prepared in the previous Preparation step
13 Fine-tuned Partial Task Input: \(X_{i}^{k}\)
14 Fine-tuned Partial Task Output: \(Y_{i}\) // prepared in the previous Preparation step
15 Self-transfer Partial Training
16 1-Phase: Pre-training (DR) Train the Partial Task with objective function as \(\underset{i}{\text{argmin}}\sum\limits_{\omega_{i}^{0}}L\big{(}f_{P}^{k} \big{(}\omega_{P}^{k};XD_{i}^{k}\big{)},Y_{i}\big{)}\)
17 2-Phase: Fine-tuning (RR) Set the initial weight as pre-trained weight: \(\omega^{k}\leftarrow\omega_{P}^{k}\)
18 Train the Partial Task with objective function as \(\underset{i}{\text{argmin}}\sum\limits_{\omega^{k}}L\big{(}f^{k}\big{(}\omega ^{k};X_{i}^{k}\big{)},Y_{i}\big{)}\)
19 Get Feature Data \(F_{i}^{k}\leftarrow\epsilon_{FE}^{k}(X_{i}^{k};\theta^{k})\)
20 Send Feature Data \(F_{i}^{k}\) the Host Party
21  TT-VPD-ST: Fine-tuning for the Target Task (Merging Task Training) Host Party
22 Receive Feature Data \(F_{i}^{k}\) from each Guest Party
23 24 Merging Task Construction
25 By DFS Model Split, get the model structure of the Merging Task \(f^{0}\) consist of FM part of the target task
26 Set input of Merging Task as the received each Guest Party's Feature Data \(F_{i}^{1},\ldots,F_{i}^{K}\)
27 Set output of Merging Task as \(Y_{i}\)
28 Merging Task Training
29 Train the Merging Task with objective function as \(\underset{i}{\text{argmin}}\sum\limits_{\omega^{0}}L\big{(}f^{0}\big{(} \omega^{0};F_{i}^{1},\ldots,F_{i}^{K}\big{)},Y_{i}\big{)}\)
```

**Algorithm 4** TT-VPD-ST for Classification

On the other hand, for classification tasks, the host party directly sends its encoded label dataset \(Y\) to each guest party without reconstruction in the partial task construction stage, since it is relatively less sensitive than raw time-series data. In the partial task construction stage, each guest party reconstructs the decoded dataset \(X\) from the raw dataset \(X\) it held while directly receiving the encoded label dataset \(Y\). It is the same as in regression tasks that \(XD\) and \(X\) are used as input for pre-training and fine-tuning, respectively, in the next self-transfer partial training stage. Also, the received encoded label dataset \(Y\) is directly used as output for the self-transfer partial training stage. After the partial task construction stage, which prepares input and output for the self-transfer partial training stage, operations occurring in each guest party and the host party are the same in both regression and classification tasks. Figure 6: Description of TT-VFDL-ST for regression with an example data pattern. ### Considerations When Applying to Real-World Scenarios

In Figure 7 and Algorithm 4 for classification tasks, we assume that the host party holds only an encoded label dataset. From some points of view, it might be considered that the resource of the host party is wasted. However, the reason for that assumption is that we consider the most generalized system architecture from the perspective of theory. When applied to a real-world scenario, the host party can hold one of the multivariate inputs, both with an encoded label dataset for output. In addition, there are some points to be considered when applying TT-VFDL-ST to real-world scenarios. In this section, we briefly discuss such considerations. Figure 7: Description of TT-VFDL-ST for classification with an example data pattern. #### 3.4.1 Design of the Target Task Model

TT-VFDL-ST supports the generalized structures of deep learning models for multivariate time-series analysis described in Figure 2 of Section 2.1 as the target task model. As summarized in Section 2.1, we derived generalized structures in Figure 2 based on existing studies about multivariate time-series analysis using deep learning.