Differential privacy representation geometry for medical image analysis
Authors: Soroosh Tayebi Arasteh, Marziyeh Mohammadi, Sven Nebelung, Daniel Truhn
Organizations: Lab for AI in Medicine, RWTH Aachen University, Aachen, Germany · Department of Diagnostic and Interventional Radiology, University Hospital RWTH Aachen, Aachen, Germany · INDA Institute, RWTH Aachen University, Aachen, Germany
Abstract
Differential privacy (DP)'s effect in medical imaging is typically evaluated only through end-to-end performance, leaving the mechanism of privacy-induced utility loss unclear. We introduce Differential Privacy Representation Geometry for Medical Imaging (DP-RGMI), a framework that interprets DP as a structured transformation of representation space and decomposes performance degradation into encoder geometry and task-head utilization. Geometry is quantified by representation displacement from initialization and spectral effective dimension, while utilization is measured as the gap between linear-probe and end-to-end utility. Across over 594,000 images from four chest X-ray datasets and multiple pretrained initializations, we show that DP is consistently associated with a utilization gap even when linear separability is largely preserved. At the same time, displacement and spectral dimension exhibit non-monotonic, initialization- and dataset-dependent reshaping, indicating that DP alters representation anisotropy rather than uniformly collapsing features. Correlation analysis reveals that the association between end-to-end performance and utilization is robust across datasets but can vary by initialization, while geometric quantities capture additional prior- and dataset-conditioned variation. These findings position DP-RGMI as a reproducible framework for diagnosing privacy-induced failure modes and informing privacy model selection.
The ever-increasing collection of personal data has created mounting pressure to develop technologies that protect sensitive aspects of individual identity. Differential privacy (DP) provides a principled framework with strong formal guarantees and has already achieved practical success. However, releasing high-dimensional data, such as images, has remained elusive: releasing uncompressed privatized data requires significant storage. At the same time, no effective data compression scheme exists that can compress high-resolution data with privacy guarantees. We address this challenge with DP-DiPP, a compression pipeline that combines stochastic codes with diffusion models. DP-DiPP is highly flexible: the practitioner has direct control over the compression rate-privacy-utility tradeoff. As the theoretical backbone, we extend the Poisson private representation (PPR) to encode the outputs of privacy mechanisms. We then combine it with DiffC, a diffusion-based lossy data compression method, to obtain a differentially private image compressor. Our experiments on privatized image classification on CIFAR-10 demonstrate that DP-DiPP significantly outperforms the baseline, achieving a 10-30 times better compression while retaining comparable privacy guarantees and utility.
Medical image segmentation is widely used for disease detection but relies on sensitive data, raising privacy concerns as trained models can leak information. Differential privacy, typically implemented via Differential Private Stochastic Gradient Descent (DPSGD), provides a solution, though at the cost of reduced utility. Recent DPSGD variants, including Automatic clipping (Auto-S), Normalised SGD with perturbation (NSGD), and Per-sample adaptive clipping (PSAC), have shown promise in image classification, but their behavior in medical segmentation remains underexplored. We evaluate these methods across binary and multi-class tasks and analyze gradient alignment, showing that prior assumptions, particularly for PSAC, do not consistently hold. We further demonstrate that combining clipping strategies with morphological refinement improves segmentation quality under privacy constraints. Finally, we propose an adaptive DP-Morph variant that captures class-specific structures and enhances performance in multi-class settings.
Differential privacy (DP) has become the gold standard for ensuring the privacy protection of machine learning and statistical algorithms in recent decades. A plethora of algorithms and methods have been developed to enhance the utility of DP algorithms while maintaining the same level of DP. However, these are often overly complex or computationally ineffective. We propose a novel approach focusing on denoising the output of the simple additive Gaussian mechanism by adopting the idea of \textit{empirical Bayes estimation}. We highlight that the empirical Bayes approach can reduce the mean-squared error solely by taking the output of the Gaussian mechanism as input. Our numerical studies show that this simple yet powerful approach can be applied to improve upon various statistical problems, including histogram release, principal component analysis, and linear regression, often outperforming existing private algorithms.