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

TL;DR

DPSR introduces a three-stage denoising framework that enhances the utility of differentially private recommender systems by exploiting matrix structures, significantly improving recommendation accuracy even at strict privacy levels.

Contribution

The paper presents DPSR, a novel multi-stage denoising approach that leverages matrix sparsity, low-rank properties, and collaborative patterns to improve privacy-utility tradeoff in recommender systems.

Findings

DPSR achieves 5.57% to 9.23% RMSE improvement over state-of-the-art mechanisms.

At privacy level ε=1.0, DPSR outperforms non-private baseline.

DPSR effectively removes both privacy and inherent data noise.

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) \textit{information-theoretic noise calibration} that adaptively reduces noise for high-information ratings, (2) \textit{collaborative filtering-based denoising} that leverages item-item similarities to remove privacy noise, and (3) \textit{low-rank matrix completion} that exploits latent structure for signal recovery. Critically, all denoising operations occur \textit{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, \textit{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.