Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generation

Core Concepts

The authors propose using Neural Tangent Kernels (NTKs) for differentially private data generation, showing that the expressiveness of untrained e-NTK features rivals pre-trained perceptual features. This approach improves the privacy-accuracy trade-off without relying on public data.

Abstract

The study introduces DP-NTK, leveraging NTKs for privacy-preserving data generation. By comparing various models and datasets, they demonstrate the effectiveness of their method in generating high-quality synthetic data while maintaining privacy. The research highlights the importance of kernel selection and its impact on generative model behavior. The study begins by discussing differential privacy mechanisms and Maximum Mean Discrepancy (MMD) as a distance metric for data distribution. It explores the use of NTKs, particularly e-NTKs, to improve privacy in generative modeling. The authors emphasize the role of appropriate kernels in enhancing model performance. By analyzing theoretical aspects and experimental results on image datasets like MNIST and CelebA, as well as tabular datasets, the study showcases DP-NTK's superiority over existing methods. They address challenges in generating diverse and realistic synthetic data while preserving privacy constraints. Through comparisons with other models like DP-MERF and DP-GAN, the study illustrates how DP-NTK outperforms in terms of image quality and accuracy metrics. The research also delves into varying levels of privacy parameters to evaluate model robustness across different datasets. Overall, the study provides valuable insights into leveraging NTKs for privacy-preserving data generation, showcasing promising results across multiple domains.

Stats

Maximum Mean Discrepancy (MMD) is a useful distance metric for differentially private data generation. The expressiveness of untrained e-NTK features is comparable to pre-trained perceptual features. DP-MERF uses random Fourier features for Gaussian kernels. Hermite polynomial features provide a better trade-off in DP-HP. Neural Tangent Kernels (NTKs) converge to a fixed kernel independent of weights during optimization.

Quotes

"The expressiveness of untrained e-NTK features is comparable to that of pre-trained perceptual features." "Our method improves the privacy-accuracy trade-off compared to other state-of-the-art methods." "Choosing an appropriate kernel has a strong influence on the final behavior of a generative model."

Key Insights Distilled From

Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generation

by Yilin Yang,K... at arxiv.org 02-29-2024

https://arxiv.org/pdf/2303.01687.pdf

Deeper Inquiries

How can incorporating infinite NTK improve the performance of DP-NTK

Incorporating infinite NTK in DP-NTK can potentially improve its performance by leveraging the benefits of the NTK's behavior as networks become wider. The convergence of e-NTK to a fixed kernel, known as "the NTK," independent of network weights, allows for more stable and consistent representations of data. With an infinite-width network, the e-NTK converges to a function that depends on architecture but not specific weights, providing a more robust and generalizable model. This convergence ensures that training deep networks with stochastic gradient descent corresponds to kernel regression with the NTK, leading to better optimization and learning capabilities. By utilizing the properties of infinite NTKs, DP-NTK could achieve higher accuracy and efficiency in privacy-preserving data generation tasks.

What are potential implications of using public data for pre-training in comparison to solely relying on private data

Using public data for pre-training offers several advantages compared to solely relying on private data for differentially private generative modeling. Firstly, public datasets often contain diverse and extensive samples that can enhance model generalization and performance by capturing broader patterns present in real-world data. Pre-training on public datasets allows models to learn meaningful features before fine-tuning on sensitive private data, reducing overfitting risks and improving overall model stability. Additionally, leveraging public data enables researchers to benefit from existing labeled information without compromising individual privacy or requiring large amounts of private labeled data for effective training. However, there are potential ethical considerations regarding consent and proper handling of public datasets when used in conjunction with private information.

How might advancements in kernel selection impact future developments in differentially private generative modeling

Advancements in kernel selection have significant implications for future developments in differentially private generative modeling. The choice of kernel plays a crucial role in determining how distributions are compared during training processes like MMD minimization or feature extraction. Improved kernels can lead to better representation learning from limited or noisy datasets while maintaining privacy guarantees through differential privacy mechanisms. By exploring novel kernels tailored specifically for generative tasks or incorporating insights from neural tangent kernels (NTKs), researchers can enhance model expressiveness, capture complex relationships within data distributions more effectively, and improve overall model performance. Moreover, advancements in kernel selection may also contribute towards developing more efficient algorithms for measuring distances between distributions accurately under differential privacy constraints—leading to enhanced privacy-preserving techniques across various machine learning applications beyond generative modeling.