## 2 Related Works
### Previous Work
#### 2.4.2 The Previous Method
#### 3.4.5 Feature Selection in Each Guest Party

With a separate training loop for each guest party, the overall performance of the proposed TT-VFDL-ST also might be affected by the performance of each guest party. The feature selection problem could be roughly dealt with before starting the training in the host party by suggesting the empirical lower bound predicting the performance of further training in the host party. The empirical lower bound for the performance of further training in the host party is the average performance of all guest parties. In our experiments in Section 4, in most cases except only a few, the final performance of TT-VFDL-ST in the host party was higher than the highest performance among all guest parties. Also, for all cases, the final performance of TT-VFDL-ST in the host party was higher than the average performance of all guest parties. Therefore, before starting the training in the host party, it might be considered whether additional performance improvements are needed in guest parties. However, the feature selection problem originates from the characteristics of data in each guest party. Moreover, the final performance is determined by all combined multivariate features in the host party. Therefore, the feature selection problem can be finely dealt with by the host party, considering the effects that all guest parties' performances on the training, once the training is finished. We are working on developing a method, that could be performed on the host party, to consider which guest party needs to be more trained. #### 3.4.6 Data and Model Sharing

Another advantage of the separate training loop for each party is that all sent feature data are not directly involved in the middle of the model training phase. Therefore, the feature data of each guest party, which is sent after each guest party's training, might be simply encrypted by traditional data encryption methods if it needs to be shared securely. The compressed data for regression output sent from the host party to each guest party in the partial task construction stage also might be encrypted by traditional data encryption methods for secure sharing. In TT-VFDL-ST, weight matrices are sent from the host party to each guest party for model sharing. To share the FM part structure, the host party sends weight matrices of the FM part initialized with dummy or random values. Also, to share the decoder reconstructing compressed regression output, the host party sends weight matrices of the decoder part of the trained LSTM-AE to each guest party. These weight matrices sent from the host party to each guest party for model sharing also might be encrypted using traditional data encryption methods for secure data sharing. It is not too overhead since the weight matrices are data in very small sizes and sent only once. #### 3.4.7 Analysis from the Perspective of Privacy

Including the proposed TT-VFDL-ST and our previous work [7], most of the current vertical federated learning methods preserve privacy by preventing the exposure of raw data of each party. However, due to the characteristics of each distributed learning mechanism, the type of exposed intermediate data is different from each vertical federated learning method. In [8; 9; 10; 11] taking a data-driven transfer approach, only the feature data of each guest party is exposed. In the proposed TT-VFDL-ST and our previous work [7], not only the feature data of each guest party but also the weight matrices of the host party for model sharing are exposed. However, these feature data and weight matrices are exposed only once since the proposed TT-VFDL-ST, our previous work [7], and refs. [8; 9; 10; 11] have separate training loops on each party. On the other hand, in [12; 13; 14; 15], the feature data of each guest party and the gradients of the host party are continuously exposed at every iteration of the training loop.