You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Differentially Private Data Publishing and Analysis: A Survey 
Chapter Title:  Summary of the Non-Interactive Setting 
1. Abstract of Cited Paper (BIB001):  Releasing high-dimensional data enables a wide spectrum of data mining tasks. Yet, individual privacy has been a major obstacle to data sharing. In this paper, we consider the problem of releasing high-dimensional data with differential privacy guarantees. We propose a novel solution to preserve the joint distribution of a high-dimensional dataset. We first develop a robust sampling-based framework to systematically explore the dependencies among all attributes and subsequently build a dependency graph. This framework is coupled with a generic threshold mechanism to significantly improve accuracy. We then identify a set of marginal tables from the dependency graph to approximate the joint distribution based on the solid inference foundation of the junction tree algorithm while minimizing the resultant error. We prove that selecting the optimal marginals with the goal of minimizing error is NP-hard and, thus, design an approximation algorithm using an integer programming relaxation and the constrained concave-convex procedure. Extensive experiments on real datasets demonstrate that our solution substantially outperforms the state-of-the-art competitors.

Literature Review:
High sensitivity presents a big challenge in non-interactive settings. Batch query publishing methods can only publish limited types of queries. Publishing a synthetic dataset seems appealing because, in some scenarios, people require details of the attributes to determine further analysis methods. The research on synthetic data publishing, however, is still in its early stages and there are many open problems in this area. The essential problem is efficiency. Given most publishing mechanisms need to sample datasets from the entire data universe, it is hard to search for a suitable dataset in polynomial time. Another problem is that synthetic dataset publishing can only publish datasets for particular purposes. For example, an anonymization dataset focuses on a decision tree algorithm, the published dataset obtains an acceptable result for decision tree tasks, yet the proposed method does not guarantee the performance for other types of tasks. Learning-based methods have the same disadvantage, or worse, as they only guarantee learning performance for a particular class. Publishing a dataset for multiple purposes needs further investigation. The third problem is dealing with high-dimensional datasets. Even though BIB001 and BIB002 have undertaken some initial work, they both consume too much of the privacy budget when building the distribution model, making the results less accurate than that of lower-dimensional datasets.