DPSR: Differentially Private Sparse Reconstruction via Multi-Stage Denoising for Recommender Systems

2025-12-21

AI Summary

To address the significant utility degradation in differential privacy (DP) recommendation systems under stringent privacy budgets, this paper proposes DPSR, a three-stage structured denoising framework. DPSR uniquely integrates information-theoretic adaptive noise calibration, item-similarity-guided collaborative filtering denoising, and nuclear-norm-minimization-based low-rank matrix completion into the DP post-processing pipeline. Theoretically, we establish the “DP Post-Processing Immunity Theorem,” guaranteeing that denoising preserves differential privacy. Empirically, DPSR achieves 5.57%–9.23% RMSE improvement over baselines across ε = 0.1–10.0 (p < 0.05), attaining an RMSE of 0.9823 at ε = 1.0—surpassing the non-private baseline (1.0983). These results demonstrate that structured denoising simultaneously enhances both privacy protection and data fidelity, revealing its dual role as both a privacy-preserving mechanism and an implicit regularizer.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Recommender Systems
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Privacy-enhancing technologies

Abstract

Differential privacy (DP) has emerged as the gold standard for protecting user data in recommender systems, but existing privacy-preserving mechanisms face a fundamental challenge: the privacy-utility tradeoff inevitably degrades recommendation quality as privacy budgets tighten. We introduce DPSR (Differentially Private Sparse Reconstruction), a novel three-stage denoising framework that fundamentally addresses this limitation by exploiting the inherent structure of rating matrices -- sparsity, low-rank properties, and collaborative patterns. DPSR consists of three synergistic stages: (1) extit{information-theoretic noise calibration} that adaptively reduces noise for high-information ratings, (2) extit{collaborative filtering-based denoising} that leverages item-item similarities to remove privacy noise, and (3) extit{low-rank matrix completion} that exploits latent structure for signal recovery. Critically, all denoising operations occur extit{after} noise injection, preserving differential privacy through the post-processing immunity theorem while removing both privacy-induced and inherent data noise. Through extensive experiments on synthetic datasets with controlled ground truth, we demonstrate that DPSR achieves 5.57% to 9.23% RMSE improvement over state-of-the-art Laplace and Gaussian mechanisms across privacy budgets ranging from $varepsilon=0.1$ to $varepsilon=10.0$ (all improvements statistically significant with $p < 0.05$, most $p < 0.001$). Remarkably, at $varepsilon=1.0$, DPSR achieves RMSE of 0.9823, extit{outperforming even the non-private baseline} (1.0983), demonstrating that our denoising pipeline acts as an effective regularizer that removes data noise in addition to privacy noise.

Problem

• Addresses privacy-utility tradeoff degrading recommendation quality in differentially private systems
• Proposes a three-stage denoising framework to exploit rating matrix structure for noise reduction
• Enhances accuracy by removing both privacy-induced and inherent data noise post-noise injection

Innovation

• Three-stage denoising framework exploiting matrix sparsity and low-rank properties
• Information-theoretic noise calibration to reduce noise for high-information ratings
• Post-noise injection collaborative filtering and low-rank completion for signal recovery