Local Differential Privacy (LDP) has become a widely adopted paradigm for collecting and analyzing sensitive data from user devices. Personalized LDP (PLDP) extends LDP by enabling users to operate under different privacy budgets, better reflecting users' diverse privacy preferences that arise in practice. While PLDP provides greater flexibility, it introduces new challenges for the data collector, particularly in how estimates obtained from users with different privacy budgets should be combined and post-processed to maximize utility. In particular, while post-processing methods have been explored in LDP, similar studies remain lacking for PLDP. In this paper, we present a systematic study of combination and post-processing methods under PLDP. We consider two combination strategies: Simple Averaging (SA) and Inverse Variance Weighting (IVW), as well as three end-to-end post-processing architectures (No-PP, Combine-First, PP-First) that differ in whether post-processing is applied before combination, after combination, or not at all. Through extensive experiments, we show that IVW consistently outperforms SA. We further demonstrate that applying post-processing at the group level before aggregation (PP-First) generally yields higher utility than alternative architectures, although the gap narrows when IVW is used. Our results also reveal that no single post-processing method is universally optimal under PLDP; however, normalization-based methods such as Norm-Sub and Norm-Mul provide strongest performance. Finally, we analyze the impact of population-level privacy preferences and show how the distribution of privacy budgets affects overall utility and user incentives. Together, our results and findings provide practical guidance for designing effective pipelines that improve utility under PLDP.

Bayesian networks are widely used for causal discovery and probabilistic modeling across diverse domains including healthcare, multi-dimensional data analysis, environmental modeling, and industrial processes. Although previous work has studied the learning of Bayesian networks under centralized differential privacy, to the best of our knowledge, the problem of learning Bayesian networks under local differential privacy (LDP) remains open. In this paper, we address this problem by proposing two solution methods for learning Bayesian networks under LDP: LDP-BN and LDP-BN+. Our first solution called LDP-BN utilizes a novel algorithm for computing mutual information values necessary for building a Bayesian network under LDP, but it suffers from high utility loss since the privacy budget needs to be divided into many pairs of attributes and candidate parent sets. To reduce the amount of noise, we propose LDP-BN+ which utilizes a novel density-aware covering design algorithm that ensures all necessary mutual information values will be computed while the privacy budget is used more effectively. We experimentally evaluate LDP-BN and LDP-BN+ using multiple utility metrics and datasets. Results show that LDP-BN+ outperforms LDP-BN and enables the generation of high-utility Bayesian networks that can be used in practice.