Zeyu Ding

Guanlin He, Yingtai Xiao, Jiamu Bai et al.

Matrix mechanisms are often used to provide unbiased differentially private query answers when publishing statistics or creating synthetic data. Recent work has developed matrix mechanisms, such as ResidualPlanner and Weighted Fourier Factorizations, that scale to high dimensional datasets while providing optimality guarantees for workloads such as marginals and circular product queries. They operate by adding noise to a linearly independent set of queries that can compactly represent the desired workloads. In this paper, we present QuerySmasher, an alternative scalable approach based on a divide-and-conquer strategy. Given a workload that can be answered from various data marginals, QuerySmasher splits each query into sub-queries and re-assembles the pieces into mutually orthogonal sub-workloads. These sub-workloads represent small, low-dimensional problems that can be independently and optimally answered by existing low-dimensional matrix mechanisms. QuerySmasher then stitches these solutions together to answer queries in the original workload. We show that QuerySmasher subsumes prior work, like ResidualPlanner (RP), ResidualPlanner+ (RP+), and Weighted Fourier Factorizations (WFF). We prove that it can dominate those approaches, under sum squared error, for all workloads. We also experimentally demonstrate the scalability and accuracy of QuerySmasher.

Zeyu Ding, Katja Ickstadt, Nadja Klein et al.

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. Our approach yields substantial data reduction via importance sampling. It ensures with high probability that the log-likelihood remains within multiplicative error bounds of $(1\pm\varepsilon)$ and thereby maintains statistical model accuracy. Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability, particularly in scenarios where complex distributions and non-linear relationships are present, but not fully understood. To address numerical problems associated with normalizing logarithmic terms, we follow a geometric approximation based on the convex hull of input data. This ensures feasible, stable, and accurate inference in scenarios involving large amounts of data. Numerical experiments demonstrate substantially improved computational efficiency when handling large and complex datasets, thus laying the foundation for a broad range of applications within the statistics and machine learning communities.

Andrew Cascio, KinChin Tong, Daniel Kifer et al.

The plausible deniability model of differential privacy for single-table datasets is well-understood. However, applying differential privacy to relational databases is much trickier: each application needs flexibility in specifying the pieces of information about an entity, spread across multiple relations, that require plausible deniability guarantees. Existing differentially private SQL systems only support rigid privacy policies. Even seemingly small changes, such as specifying that some tables need to protect the existence of records while others only need to protect the record contents, require significant manual effort in updating their privacy accountants and proving their correctness. One example of a challenge is the presence of partially public data. Public columns in a table (e.g., faculty names in a university dataset and partial course enrollment information) can cause some queries to require more noise (compared to fully private data), while others require less noise. This kind of reasoning is not supported in existing systems. Another example is when different parts of records (e.g., demographics, financial data) require different levels of privacy protection. Again, existing differentially private SQL systems need to rewrite their rules for calculating query stability in order to support such a feature. This paper presents DP4SQL, a differentially private SQL system that allows data curators to better customize the plausible deniability requirements for their relational databases. This avoids the drawbacks of the "one-size-fits-all" systems that would either underprotect the data or inject too much noise into query answers.

Yuxin Wang, Zeyu Ding, Yingtai Xiao et al.

Differential privacy has become a de facto standard for releasing data in a privacy-preserving way. Creating a differentially private algorithm is a process that often starts with a noise-free (non-private) algorithm. The designer then decides where to add noise, and how much of it to add. This can be a non-trivial process -- if not done carefully, the algorithm might either violate differential privacy or have low utility. In this paper, we present DPGen, a program synthesizer that takes in non-private code (without any noise) and automatically synthesizes its differentially private version (with carefully calibrated noise). Under the hood, DPGen uses novel algorithms to automatically generate a sketch program with candidate locations for noise, and then optimize privacy proof and noise scales simultaneously on the sketch program. Moreover, DPGen can synthesize sophisticated mechanisms that adaptively process queries until a specified privacy budget is exhausted. When evaluated on standard benchmarks, DPGen is able to generate differentially private mechanisms that optimize simple utility functions within 120 seconds. It is also powerful enough to synthesize adaptive privacy mechanisms.

Zeyu Ding, Daniel Kifer, Sayed M. Saghaian N. E. et al.

The permute-and-flip mechanism is a recently proposed differentially private selection algorithm that was shown to outperform the exponential mechanism. In this paper, we show that permute-and-flip is equivalent to the well-known report noisy max algorithm with exponential noise.

Zeyu Ding, Yuxin Wang, Yingtai Xiao et al.

Private selection algorithms, such as the Exponential Mechanism, Noisy Max and Sparse Vector, are used to select items (such as queries with large answers) from a set of candidates, while controlling privacy leakage in the underlying data. Such algorithms serve as building blocks for more complex differentially private algorithms. In this paper we show that these algorithms can release additional information related to the gaps between the selected items and the other candidates for free (i.e., at no additional privacy cost). This free gap information can improve the accuracy of certain follow-up counting queries by up to 66%. We obtain these results from a careful privacy analysis of these algorithms. Based on this analysis, we further propose novel hybrid algorithms that can dynamically save additional privacy budget.

Zeyu Ding, Yuxin Wang, Danfeng Zhang et al.

Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer among a set of queries. We show that it can also release for free the noisy gap between the approximate maximizer and runner-up. This free information can improve the accuracy of certain subsequent counting queries by up to 50%. Sparse Vector is used to return a set of queries that are approximately larger than a fixed threshold. We show that it can adaptively control its privacy budget (use less budget for queries that are likely to be much larger than the threshold) in order to increase the amount of queries it can process. These results follow from a careful privacy analysis.