One Step to Efficient Synthetic Data (2006.02397v7)

Abstract: A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true distribution. Motivated by this, we propose a general method of producing synthetic data, which is widely applicable for parametric models, has asymptotically efficient summary statistics, and is both easily implemented and highly computationally efficient. Our approach allows for the construction of both partially synthetic datasets, which preserve certain summary statistics, as well as fully synthetic data which satisfy the strong guarantee of differential privacy (DP), both with the same asymptotic guarantees. We also provide theoretical and empirical evidence that the distribution from our procedure converges to the true distribution. Besides our focus on synthetic data, our procedure can also be used to perform approximate hypothesis tests in the presence of intractable likelihood functions.

• The paper presents a novel synthetic data generation method that ensures summary statistics converge asymptotically to true parameters.
• It offers a computationally efficient process, making it suitable for large-scale applications and complex parametric models.
• The approach supports differential privacy, enabling both partially and fully synthetic datasets for robust statistical inference.

The paper "One Step to Efficient Synthetic Data" addresses the challenges related to generating synthetic data that is both statistically efficient and computationally feasible. The conventional method of generating synthetic data often involves sampling from a fitted model. However, the authors argue that this method can lead to the generation of data with inefficient estimators and inconsistencies with the true underlying distribution.

To overcome these limitations, the authors propose a novel method for synthetic data generation that is designed to be more versatile and reliable. This method is applicable across a wide range of parametric models and offers several key advantages:

1. Asymptotic Efficiency: The new method ensures that the summary statistics of the synthetic data are asymptotically efficient. This implies that as the sample size increases, the synthetic data's summary statistics converge to the true population parameters.
2. Computational Efficiency: The proposed synthetic data generation process is designed to be computationally efficient, making it feasible for large-scale applications.
3. Differential Privacy: Notably, their method can be adapted to produce synthetic data that meets the stringent requirements of differential privacy (DP). This adaptation applies to both partially synthetic datasets, which retain specific summary statistics, and fully synthetic datasets, which adhere strictly to differential privacy regulations.
4. Theoretical and Empirical Validation: The authors provide both theoretical justifications and empirical evidence to support the efficacy of their approach. They demonstrate that the data generated using their method converges to the true distribution, addressing concerns of consistency and representativeness.

Additionally, the paper discusses the extended applicability of their method beyond synthetic data generation. Specifically, it can be utilized for performing approximate hypothesis tests in scenarios where the likelihood functions are intractable, offering a robust tool for statistical inference under complex model conditions.

In summary, this paper presents a significant advancement in the field of synthetic data generation, offering a method that balances statistical efficiency, computational feasibility, and privacy considerations.