{"ID":2826027,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.18932","arxiv_id":"2512.18932","title":"DPSR: Differentially Private Sparse Reconstruction via Multi-Stage Denoising for Recommender Systems","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 $p \u003c 0.05$, most $p \u003c 0.001$). 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.","short_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 Priva...","url_abs":"https://arxiv.org/abs/2512.18932","url_pdf":"https://arxiv.org/pdf/2512.18932v1","authors":"[\"Sarwan Ali\"]","published":"2025-12-22T00:43:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CR\"]","methods":"[]","has_code":false}