This is enabled through a new theoretical technique to analyze the Rényi Differential Privacy (RDP) of the sub-sampled shuffle model.

Mean estimation under differential privacy is a fundamental problem, but worst-case optimal mechanisms do not offer meaningful utility guarantees in practice when the global sensitivity is very large.

Conformal prediction (CP) provides sets of candidate classes with a guaranteed probability of containing the true class. However, it typically relies on a calibration set with clean labels. We address privacy-sensitive scenarios where the aggregator is untrusted and can only access a perturbed version of the true labels. We propose two complementary approaches under local differential privacy (LDP). In the first approach, users do not access the model but instead provide their input features and a perturbed label using a k-ary randomized response. In the second approach, which enforces stricter privacy constraints, users add noise to their conformity score by binary search response. This method requires access to the classification model but preserves both data and label privacy. Both approaches compute the conformal threshold directly from noisy data without accessing the true labels. We prove finite-sample coverage guarantees and demonstrate robust coverage even under severe randomization. This approach unifies strong local privacy with predictive uncertainty control, making it well-suited for sensitive applications such as medical imaging or large language model queries, regardless of whether users can (or are willing to) compute their own scores.

We study a setting of collecting and learning from private data distributed across end users. In the shuffled model of differential privacy, the end users partially protect their data locally before sharing it, and their data is also anonymized during its collection to enhance privacy. This model has recently become a prominent alternative to central DP, which requires full trust in a central data curator, and local DP, where fully local data protection takes a steep toll on downstream accuracy. Our main technical result is a shuffled DP protocol for privately estimating the kernel density function of a distributed dataset, with accuracy essentially matching central DP . We use it to privately learn a classifier from the end user data, by learning a private density function per class. Moreover, we show that the density function itself can recover the semantic content of its class, despite having been learned in the absence of any unprotected data. Our experiments show the favorable downstream performance of our approach, and highlight key downstream considerations and trade-offs in a practical ML deployment of shuffled DP . Collecting statistics on end user data is commonly required in data analytics and machine learning. As it could leak private user information, privacy guarantees need to be incorporated into the data collection pipeline. Differential Privacy (DP) (Dwork et al., 2006) currently serves as the gold standard for privacy in machine learning. Most of its success has been in the central DP model, where a centralized data curator holds the private data of all the users and is charged with protecting their privacy. However, this model does not address how to collect the data from end users in the first place. The local DP model (Kasiviswanathan et al., 2011), where end users protect the privacy of their data locally before sharing it, is often used for private data collection (Erlingsson et al., 2014; Ding et al., 2017; Apple, 2017). However, compared to central DP, local DP often comes at a steep price of degraded accuracy in downstream uses of the collected data. The shuffled DP model (Bittau et al., 2017; Cheu et al., 2019; Erlingsson et al., 2019) has recently emerged as a prominent intermediate alternative. In this model, the users partially protect their data locally, and then entrust a centralized authority--called the "shuffler"--with the single operation of shuffling (or anonymizing) the data from all participating users.

We explore the use of distributed differentially private computations across multiple servers, balancing the tradeoff between the error introduced by the differentially private mechanism and the computational efficiency of the resulting distributed algorithm. We introduce the linear-transformation model, where clients have access to a trusted platform capable of applying a public matrix to their inputs. Such computations can be securely distributed across multiple servers using simple and efficient secure multiparty computation techniques. The linear-transformation model serves as an intermediate model between the highly expressive central model and the minimal local model. In the central model, clients have access to a trusted platform capable of applying any function to their inputs. However, this expressiveness comes at a cost, as it is often expensive to distribute such computations, leading to the central model typically being implemented by a single trusted server. In contrast, the local model assumes no trusted platform, which forces clients to add significant noise to their data. The linear-transformation model avoids the single point of failure for privacy present in the central model, while also mitigating the high noise required in the local model. We demonstrate that linear transformations are very useful for differential privacy, allowing for the computation of linear sketches of input data. These sketches largely preserve utility for tasks such as private low-rank approximation and private ridge regression, while introducing only minimal error, critically independent of the number of clients. Previously, such accuracy had only been achieved in the more expressive central model.

In data-driven applications, preserving user privacy while enabling valuable computations remains a critical challenge. Technologies like Differential Privacy (DP) have been pivotal in addressing these concerns. The shuffle model of DP requires no trusted curators and can achieve high utility by leveraging the privacy amplification effect yielded from shuffling. These benefits have led to significant interest in the shuffle model. However, the computation tasks in the shuffle model are limited to statistical estimation, making the shuffle model inapplicable to real-world scenarios in which each user requires a personalized output. This paper introduces a novel paradigm termed Private Individual Computation (PIC), expanding the shuffle model to support a broader range of permutation-equivariant computations. PIC enables personalized outputs while preserving privacy, and enjoys privacy amplification through shuffling. We propose a concrete protocol that realizes PIC. By using one-time public keys, our protocol enables users to receive their outputs without compromising anonymity, which is essential for privacy amplification. Additionally, we present an optimal randomizer, the Minkowski Response, designed for the PIC model to enhance utility. We formally prove the security and privacy properties of the PIC protocol. Theoretical analysis and empirical evaluations demonstrate PIC's capability in handling non-statistical computation tasks, and the efficacy of PIC and the Minkowski randomizer in achieving superior utility compared to existing solutions.

We study the problem of private vector mean estimation in the shuffle model of privacy where $n$ users each have a unit vector $v^{(i)} \in\mathbb{R}^d$. We propose a new multi-message protocol that achieves the optimal error using $\tilde{\mathcal{O}}\left(\min(n\varepsilon^2,d)\right)$ messages per user. Moreover, we show that any (unbiased) protocol that achieves optimal error requires each user to send $\Omega(\min(n\varepsilon^2,d)/\log(n))$ messages, demonstrating the optimality of our message complexity up to logarithmic factors. Additionally, we study the single-message setting and design a protocol that achieves mean squared error $\mathcal{O}(dn^{d/(d+2)}\varepsilon^{-4/(d+2)})$. Moreover, we show that any single-message protocol must incur mean squared error $\Omega(dn^{d/(d+2)})$, showing that our protocol is optimal in the standard setting where $\varepsilon = \Theta(1)$. Finally, we study robustness to malicious users and show that malicious users can incur large additive error with a single shuffler.

We study a protocol for distributed computation called shuffled check-in, which achieves strong privacy guarantees without requiring any further trust assumptions beyond a trusted shuffler. Unlike most existing work, shuffled check-in allows clients to make independent and random decisions to participate in the computation, removing the need for server-initiated subsampling. Leveraging differential privacy, we show that shuffled check-in achieves tight privacy guarantees through privacy amplification, with a novel analysis based on R{\'e}nyi differential privacy that improves privacy accounting over existing work. We also introduce a numerical approach to track the privacy of generic shuffling mechanisms, including Gaussian mechanism, which is the first evaluation of a generic mechanism under the distributed setting within the local/shuffle model in the literature. Empirical studies are also given to demonstrate the efficacy of the proposed approach.