## 3 Methodology
### Bayesian Truth Serum  
The ensemble learning approach in this paper is primarily based on Bayesian Truth Serum (BTS), a mechanism design method grounded in information theory, which incentivizes participants to report truthful information without external validation. Originally proposed by [PERSON] in 2004 [6], BTS aims to address certain information asymmetry issues, such as in surveys or prediction markets. The core of this method involves asking participants two questions:  
* **The participant's own answer to the question.**
* **The participant's prediction of how others will answer the question.**  
Then, Bayesian statistical methods are used to calculate the consistency between each participant's answer and their prediction of others' responses. This approach can identify  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Field** & **Year** & **Model** & **Dataset** & **Learning** \\  & & & & Homogeneous ensemble: & & **Paradigms** \\ \hline \begin{tabular}{c} Parallel learning, \\ Sequential \\ learning [19] \\ \end{tabular} & Slope & 2021 & \begin{tabular}{c} Homogeneous ensemble: \\ DT, SVM, ANN, KNN. \\ Heterogeneous ensemble: \\ KNN, SVM, SGD, GP, \\ QDA, GNB, DT, ANN. \\ \end{tabular} & 153 slope cases. & Supervised. \\ \begin{tabular}{c} Bagging, \\ AdaBoost [20] \\ \end{tabular} & \begin{tabular}{c} Fake \\ Reviews \\ \end{tabular} & 2020 & \begin{tabular}{c} DT, RF, SVM, XGBT, MLP. \\ \end{tabular} & Restaurant Dataset. & Supervised. \\ \begin{tabular}{c} Sequential \\ learning [21] \\ \end{tabular} & \begin{tabular}{c} Image \\ Denoising \\ \end{tabular} & 2020 & \begin{tabular}{c} Local base denoiser, \\ Nonlocal base denoiser. \\ \end{tabular} & \begin{tabular}{c} 400 cropped images of \\ size 180 \(\times\) 180 from \\ the Berkeley \\ segmentation dataset, \\ BSD68. \\ \end{tabular} & Supervised. \\ \begin{tabular}{c} MKEL [22] \\ \end{tabular} & \begin{tabular}{c} Software \\ defect \\ prediction \\ Alzheimer’s \\ disease \\ classification \\ \end{tabular} & 2016 & SVM. & \begin{tabular}{c} Datasets from NASA \\ MDP. \\ \end{tabular} & Supervised. \\ \begin{tabular}{c} DELearning [23] \\ \end{tabular} & \
\begin{tabular}{c} Alzheimer’s \\ disease \\ classification \\ \end{tabular} & 2020 &
\begin{tabular}{c} Bayes, \\ J48 and so on, DBN, RBM. \\ \end{tabular} & UDS. & Supervised. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Different studies in specific fields.  
participants who not only provide the correct answer but also accurately predict others' responses, thereby rewarding them. This process encourages participants to provide more truthful and accurate information.  
The basic steps of BTS are as follows:  
**Collect answer**: Participants answer a question and provide a probability distribution of how likely they think others will choose each option.
**Calculate prior probability**: Calculate the prior probability for each answer option, typically the average distribution of responses provided by all participants.  
\[P_{k}=\frac{\sum_{i=1}^{N}I_{i,k}}{N} \tag{3}\]  
Here, \(I_{i,k}\) is an indicator function where the i-th participant chooses the k-th option, and N represents the number of participants.
**Calculate posterior probability**: Calculate each participant's posterior probability based on their report and the prior probability.  
\[Q_{i,k}=\frac{P_{k}y_{i,k}}{\sum_{j=1}^{N}P_{j}y_{i,j}} \tag{4}\]  
Here, \(y_{i,k}\) is the probability that the i-th participant believes others will choose the k-th option.
**Scoring Mechanism**: Calculate a score based on each participant's posterior probability and their provided confidence; a higher score indicates that their answer is more likely to be close to the truth.