# SPriFed-OMP: A Differentially Private Federated Learning Algorithm for Sparse Basis Recovery

arXiv: https://arxiv.org/abs/2402.19016 · HTML: https://mlsanity.com/paper/2402.19016/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 16 of 16)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Private Stochastic Convex Optimization: Optimal Rates in ℓ1 Geometry](https://mlsanity.com/paper/2103.01516/) (2021)
- [Non-Euclidean Differentially Private Stochastic Convex Optimization: Optimal Rates in Linear Time](https://mlsanity.com/paper/2103.01278/) (2021)
- [High Dimensional Differentially Private Stochastic Optimization with Heavy-tailed Data](https://mlsanity.com/paper/2107.11136/) (2021)
- [SurvSet: An open-source time-to-event dataset repository](https://mlsanity.com/paper/2203.03094/) (2022)
- [Identification, Amplification and Measurement: A bridge to Gaussian Differential Privacy](https://mlsanity.com/paper/2210.09269/) (2022)
- [High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent](https://mlsanity.com/paper/2207.01560/) (2022)

## Abstract (arXiv)

Sparse basis recovery is a classical and important statistical learning problem when the number of model dimensions p is much larger than the number of samples n. However, there has been little work that studies sparse basis recovery in the Federated Learning (FL) setting, where the client data's differential privacy (DP) must also be simultaneously protected. In particular, the performance guarantees of existing DP-FL algorithms (such as DP-SGD) will degrade significantly when p gg n, and thus, they will fail to learn the true underlying sparse model accurately. In this work, we develop a new differentially private sparse basis recovery algorithm for the FL setting, called SPriFed-OMP. SPriFed-OMP converts OMP (Orthogonal Matching Pursuit) to the FL setting. Further, it combines SMPC (secure multi-party computation) and DP to ensure that only a small amount of noise needs to be added in order to achieve differential privacy. As a result, SPriFed-OMP can efficiently recover the true sparse basis for a linear model with only n = O(√p) samples. We further present an enhanced version of our approach, SPriFed-OMP-GRAD based on gradient privatization, that improves the performance of SPriFed-OMP. Our theoretical analysis and empirical results demonstrate that both SPriFed-OMP and SPriFed-OMP-GRAD terminate in a small number of steps, and they significantly outperform the previous state-of-the-art DP-FL solutions in terms of the accuracy-privacy trade-off.