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

arXiv: https://arxiv.org/abs/2512.18932 · HTML: https://mlsanity.com/paper/2512.18932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 5 of 5)

- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Privacy-Preserving Machine Learning: Methods, Challenges and Directions](https://mlsanity.com/paper/2108.04417/) (2021)
- [Leveraging Public Data for Practical Private Query Release](https://mlsanity.com/paper/2102.08598/) (2021)
- [Privacy Odometers and Filters: Pay-as-you-Go Composition](https://mlsanity.com/paper/1605.08294/) (2016)

## Abstract (arXiv)

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) textitinformation-theoretic noise calibration that adaptively reduces noise for high-information ratings, (2) textitcollaborative filtering-based denoising that leverages item-item similarities to remove privacy noise, and (3) textitlow-rank matrix completion that exploits latent structure for signal recovery. Critically, all denoising operations occur textitafter 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, textitoutperforming 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.