## 3 Materials and Methods
### Design of Proposed Framework  
We briefly describe our proposed system model and technique in this section. Additionally, in this section, we provide a comprehensive overview of the federated matchedaveraging (FedMA) algorithm and M-ABC-based optimization for optimal feature selection and classification. The proposed system model is illustrated in Figure 1 below. We assume that there are five healthcare client sites and one cloud server, this setting can be scaled up for generalization. Our proposed framework consists of heart disease data collection devices that are located inside a healthcare site. Initially, a global model is disseminated by the global cloud towards the healthcare sites, after receiving the model from the cloud, the sites perform feature selection and classification using an M-ABC optimizer, after that perform training on the local data using the received model and then the healthcare sites upload their local model updates to the cloud. On receiving multiple updates of local models, a new global model is computed using FedMA, and this new model is then disseminated among the healthcare sites. In this way, all the training data remains on the device and the privacy concerns are overcome with increased prediction accuracy and less classification errors. The working of the proposed framework is illustrated in Algorithm 2. FedMA calculates the Maximum Aposteriori Estimate (MAE) of a Bayesian nonparametric model using the Beta Bernoulli process (BBP) using equation 6 below. The \(w_{\parallel}\) be \(l^{\text{th}}\) neuron studied on the dataset \(j\) and \(c(..)\) be an appropriate function of similarity. In case the client data sizes are imbalanced, then weighted averaging can be used instead of uniform. The similarity function \(c\) (\(w_{jl}\), \(\theta_{i}\)) is the subsequent posterior probability of \(j^{\text{th}}\) client neuron \(l\) generated from a Gaussian with mean \(\theta_{i}\). Due to the nonparametric aspect, their BBP-MAP inference approach allows a number of neurons in the federated model to mildly grow in comparison to the client model sizes. This matched averaging-based global cloud model helps in reducing the communication size to reach the target accuracy and the overall convergence rate of the model is also improved. \[\min_{\{\pi_{\parallel}^{j}\}}\sum_{i=1}^{\text{L}}\sum_{j,l}\min_{\theta_{1}} \pi_{\tilde{h}}^{j}c(w_{jl})\text{s.t.}\sum_{i}\pi_{\tilde{h}}^{j}=1\forall j,l;\;\sum_{l}\pi_{\tilde{h}}^{j}=1\forall i,\;j \tag{6}\]  
Figure 1: Overview of proposed framework. ```
Input: Data from various healthcare users {\(U_{I}\), \(U_{2}\), - - -, \(U_{N}\)} Output: Privacy-aware personalized model for each IoMT user \(\omega_{k}\)// Processing at the global cloud end:
1: Initialize a global cloud model \(\omega_{o}\)
2:for every round \(r\) = 1, 2,...do (i) \(r\leftarrow\) 210 _maximum of (\(K\), 1)_ (ii) \(S_{t}\leftarrow\) (\(r\) is random number of clients)
3:for every client \(k\in S_{r}\)do in parallel (i) \(\left\{\prod\limits_{r}^{k}\right\}\leftarrow\) BBP-MAP (\(\left\{k\), \(C_{n}\), \(\omega_{r}\))//call BBP-MAE to solve Equation (6) (ii) \(\omega_{k}\leftarrow\frac{1}{K}\sum\limits_{k=1}^{K}\omega_{r}^{k}\prod_{r}^{k}\) (iii) \(\omega_{r+1}\leftarrow\prod\limits_{r}^{k}\omega_{k}\)//permutate the next weights 4: Distribute \(\omega_{k}\) among all users 5: Repeat above steps with every evolving user data // Working at Client End (\(k\), \(\omega\)):
1:for each client in \(k\) (i) \(\beta\leftarrow\) (fragment each \(P_{k}\) to groups of \(\beta\) size) (ii) Compute candidate solution \(C_{n}\) using M-ABC Optimizer using Equations (2), (3), and (5) 2:for every local round \(i=1\ldots E\)do (i) for group \(b\in\beta\)do (a) \(\omega\)\(\leftarrow\)\(\omega\)\(\leftarrow\)\(\omega\)\(\rightarrow\)\(\eta\
abla l\) (\(\omega\);b) 3: return \(\omega\) to the cloud
```  
**Algorithm 2**Learning method of proposed framework for healthcare.