Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique in data science and machine learning. Beyond computational benefits, this operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of \Renyi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.

Neural Information Processing Systems http://nips.cc/

Propose-Test-Release (PTR) is a differential privacy framework that works with local sensitivity of functions, instead of their global sensitivity. This framework is typically used for releasing robust statistics such as median or trimmed mean in a differentially private manner. While PTR is a common framework introduced over a decade ago, using it in applications such as robust SGD where we need many adaptive robust queries is challenging. This is mainly due to the lack of \Renyi Differential Privacy (RDP) analysis, an essential ingredient underlying the moments accountant approach for differentially private deep learning. In this work, we generalize the standard PTR and derive the first RDP bound for it.

We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively throughinteractions with a server from whom we need privacy. Motivated by stochastic optimization and the federated learning (FL) paradigm, we focus on the case where a small fraction of data samples are randomly sub-sampled in each round to participate in the learning process, which also enables privacy amplification. To obtain even stronger local privacy guarantees, we study this in the shuffle privacy model, where each client randomizes its response using a local differentially private (LDP) mechanism and the server only receives a random permutation (shuffle) of the clients' responses without theirassociation to each client. The principal result of this paper is a privacy-optimization performance trade-off for discrete randomization mechanisms in this sub-sampled shuffle privacy model. This is enabledthrough a new theoretical technique to analyze the Renyi Differential Privacy (RDP) of the sub-sampled shuffle model. We numerically demonstrate that, for important regimes, with composition our boundyields significant improvement in privacy guarantee over the state-of-the-art approximate Differential Privacy (DP) guarantee (with strong composition) for sub-sampled shuffled models. We also demonstrate numerically significant improvement in privacy-learning performance operating point using real data sets. Despite these advances, an open question is to bridge the gap between lower and upper privacy bounds in our RDP analysis.

Neural Information Processing Systems http://nips.cc/

We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively throughinteractions with a server from whom we need privacy. Motivated by stochastic optimization and the federated learning (FL) paradigm, we focus on the case where a small fraction of data samples are randomly sub-sampled in each round to participate in the learning process, which also enables privacy amplification. To obtain even stronger local privacy guarantees, we study this in the shuffle privacy model, where each client randomizes its response using a local differentially private (LDP) mechanism and the server only receives a random permutation (shuffle) of the clients' responses without theirassociation to each client. The principal result of this paper is a privacy-optimization performance trade-off for discrete randomization mechanisms in this sub-sampled shuffle privacy model. This is enabledthrough a new theoretical technique to analyze the Renyi Differential Privacy (RDP) of the sub-sampled shuffle model.

Propose-Test-Release (PTR) is a differential privacy framework that works with local sensitivity of functions, instead of their global sensitivity. This framework is typically used for releasing robust statistics such as median or trimmed mean in a differentially private manner. While PTR is a common framework introduced over a decade ago, using it in applications such as robust SGD where we need many adaptive robust queries is challenging. This is mainly due to the lack of \Renyi Differential Privacy (RDP) analysis, an essential ingredient underlying the moments accountant approach for differentially private deep learning. In this work, we generalize the standard PTR and derive the first RDP bound for it.