# Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets
## 5 Discussion  
We conducted a comprehensive evaluation of datasets across various domains, employing our proposed LDP scheme based on BRR, across various scenarios involving \(k=2,3,4,5\) with a privacy budget set at 0.1. Regrettably, direct comparison with the study conducted by [PERSON] et al. [2] is not feasible, although both methods employ LDP. Their main objective revolves around improving accuracy in machine learning models, whereas our emphasis is on estimating the joint probability distribution with minimal error.  
Our proposed method consistently outperforms LOPUB and LOCOP across various datasets, considering differences in size, attribute composition, and the average absolute Pearson correlation coefficient (AAR). The AAR serves as a valuable tool for scrutinizing datasets prior to publication and evaluating the performance of synthetic data algorithms. This preventive approach helps avoid the release or sharing of datasets containing highly correlated attributes, thereby safeguarding the privacy of users within the dataset. For instance, this paper assesses the performance using the Nursery and Cirrhosis datasets, showcasing the lowest and highest AAR values, respectively. Our findings indicate that as \(k\) increases, more highly correlated attributes become available for estimating the joint probability distribution, posing a risk, especially in the absence of a small privacy budget, which implies robust privacy protection.  
Particularly noteworthy is a specific dataset (the dataset with a lower AAR) where our method achieved a remarkable decrease in the average variant distance compared to LOPUB and LOCOP. Additionally, for the other datasets, our proposed method outperformed the well-known LOPUB and LOCOP algorithms, both based on randomized response and the LASSO algorithm, with a privacy budget set at 0.1 per attribute and \(k=5\).  
Continuing our experiments, we employ the R-squared metric to assess the performance of LASSO and Bayesian Ridge Regression. The findings reveal that BRR consistently outperforms both LOPUB and LOCOP, both of which are based on LASSO regression. These results illustrate how BRR exhibits greater stability across various \(k\)-way evaluations, privacy budgets, and AAR compared to LASSO, owing to its effective handling of multicollinearity. In summary, our study unveils the nuanced performance of our proposed method, LOPUB, and LOCOP across diverse datasets, emphasizing the crucial influence of AAR on their efficacy. These findings underscore the necessity of aligning algorithmic choices with the unique characteristics of datasets to achieve optimal results. These insights  
Figure 6: Correlation matrix for the Cirrhosis dataset.  
hold significant implications for applications such as healthcare, where precise predictions and considerations of attribute correlations are paramount. Importantly, our study underscores the importance of avoiding high correlation among attributes in datasets, as revealed by our results.  
Highly correlated attributes in a dataset present two risks. Firstly, information from one attribute can be inferred from another, compromising the privacy guarantees provided by local differential privacy, especially when working with a high privacy budget value. Secondly, when employing a small privacy budget value in a dataset with highly correlated attributes, introducing noise to one attribute can cause the noise to propagate to other attributes. This propagation of noise results in a further decline in data utility. It becomes challenging to accurately estimate joint probability distributions, particularly for higher values of \(k\)-way.