Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognition

In this study, we apply the information-theoretic Privacy Funnel (PF) model to the domain of face recognition, developing a novel method for privacy-preserving representation learning within an end-to-end training framework. Our approach addresses the trade-off between obfuscation and utility in data protection, quantified through logarithmic loss, also known as self-information loss. This research provides a foundational exploration into the integration of information-theoretic privacy principles with representation learning, focusing specifically on the face recognition systems. We particularly highlight the adaptability of our framework with recent advancements in face recognition networks, such as AdaFace and ArcFace. In addition, we introduce the Generative Privacy Funnel ($\mathsf{GenPF}$) model, a paradigm that extends beyond the traditional scope of the PF model, referred to as the Discriminative Privacy Funnel ($\mathsf{DisPF}$). This $\mathsf{GenPF}$ model brings new perspectives on data generation methods with estimation-theoretic and information-theoretic privacy guarantees. Complementing these developments, we also present the deep variational PF (DVPF) model. This model proposes a tractable variational bound for measuring information leakage, enhancing the understanding of privacy preservation challenges in deep representation learning. The DVPF model, associated with both $\mathsf{DisPF}$ and $\mathsf{GenPF}$ models, sheds light on connections with various generative models such as Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and Diffusion models. Complementing our theoretical contributions, we release a reproducible PyTorch package, facilitating further exploration and application of these privacy-preserving methodologies in face recognition systems.