ABC: Numerical Data Collection under Local Differential Privacy without Prior Knowledge

Local Differential Privacy (LDP) provides strong privacy guarantees for collecting numerical data. A fundamental challenge, however, is that existing LDP mechanisms require a predefined data domain, which is often unknown in practice. This lack of prior knowledge creates a critical dilemma for the data collector: if the chosen domain is too narrow, values outside the range are clipped, leading to information loss. Conversely, if the domain is too wide, excessive noise is added during the privatization process, which degrades the quality of collected data. This highlights the need for methods that can dynamically estimate the data domain. In this work, we propose an adaptive LDP framework that addresses this problem. In our method, each user sends two pieces of information: their perturbed numerical data, and a privatized signal indicating if their original value was clipped by the current domain. By aggregating these signals, our proposed method, Adaptive Bounding of Clipping regions (ABC) method, iteratively adjusts the domain to fit the underlying data distribution without prior knowledge. Our theoretical analysis shows that the estimated data domain converges to an appropriate range. In the empirical evaluation, the results demonstrate that our framework significantly improves the quality of numerical data collection across various datasets and underlying LDP mechanisms. We also show that the estimated range successfully converges in practice and our approach is robust to its hyperparameters through comprehensive ablation studies.

SSTQ:Privacy-Preserving Vector Quantization via Subsampled Stochastic TurboQuant

Achieving local differential privacy in distributed optimization while maintaining low communication cost remains challenging. Existing vector quantization methods, such as vqSGD, use high-dimensional geometric constructions but incur unfavorable dimension-dependent variance. In this work, we propose Subsampled Stochastic TurboQuant (SSTQ), a framework that combines overcomplete equal-norm tight frames, coordinate subsampling, and privacy-aware one-dimensional quantization. SSTQ includes two variants: a Flat Randomized Response version and a Metric-Aware Laplace version, the latter being better suited to higher codebook bit-width regimes. We show that SSTQ achieves optimal mean squared error scaling while using only $\lceil \log_2 N \rceil + b$ bits per client, where $N = Θ(d)$ is the frame size. We also derive a surrogate privacy-aware codebook objective that reduces the codebook-dependent MSE scaling from $O(4^b)$ to $O(2^b)$. Finally, we empirically evaluate SSTQ against established baselines on federated learning tasks using CIFAR-10 and Fashion-MNIST, demonstrating favorable utility and communication efficiency.

Robust Estimation of Sparse Numerical Vectors under Local Differential Privacy

Local differential privacy (LDP) protocols are vulnerable to poisoning attacks. Existing research have proposed efficient defense strategies for single-item users. However, in practice, a user may possess multiple items. The defense against poisoning attacks for multi-item users is challenging, because due to larger output spaces, the adversary can conduct more powerful attacks without being detected. In this paper, we address the robust sparse vector mean estimation problem, in which each user has a vector with $m$ nonzero coordinates. We propose Randomized Projection with Clipping (RPC). Firstly, the server sends a random binary vector to each user. The user then projects its local data on the vector, and clip the value to restrict the attacker's capability. To handle clipping bias, we propose a correction method based on a careful analysis that gives an exact expression of the bias. As a result, bias-variance tradeoff is no longer needed, thus the clipping threshold can be further reduced to shrink the output space and enhance robustness. We provide a rigorous theoretical guarantee of the estimation error under all possible attacks. Numerical experiments show that under trusted environments, our new method achieves comparable or better performance than existing methods, indicating that our method is already an efficient estimator in its own right. Under untrusted environments, our method is also significantly more robust to poisoning attacks.

Locally Private Online Quantile Regression: Estimation and Inference

We study estimation and inference for online quantile regression under a one-report user-level $\eps$-locally differentially private ($\eps$-LDP) protocol. The main difficulty is that the standard quantile-regression estimating-equation contribution couples covariates with a residual comparison, so a server that receives only privatized reports cannot form the usual online update. We address this by developing a finite-alphabet channel in which each user computes the contribution locally, applies support-aware stochastic quantization and randomized response to one selected-block category, and sends one report. A public decoder corrects the randomized-response distortion and reconstructs a server-side estimating-equation input with the correct conditional mean. These decoded inputs are then used in projected Polyak-Ruppert averaging. For fixed finite channel designs, we establish local privacy, decoder unbiasedness, consistency, asymptotic normality, and Hessian-free self-normalized inference for prespecified scalar contrasts. Simulations and a New York City taxi-trip illustration show that the private trajectory approaches the nonprivate online reference as the privacy budget grows and outperforms direct Laplace and face-exponential geometric releases in the reported regimes.

Towards Personalized Differentially Private Learning for Decentralized Local Graphs

Graph-structured data is increasingly generated and stored in decentralized environments, such as social platforms, mobile applications, and edge networks, where users maintain control over their local graph data. However, collecting and analyzing such decentralized graph data for downstream learning tasks raises significant privacy concerns, as nodes and their attributes often contain sensitive personal information. Local Differential Privacy (LDP) has emerged as a promising solution for privacy-preserving data collection without relying on trusted servers. Nevertheless, existing LDP-based graph learning methods typically assume uniform privacy requirements across users, ignoring the heterogeneous and personalized privacy preferences commonly observed in real-world systems. This uniform treatment leads to inflexible noise injection at the data collection stage, resulting in substantial distortion of graph data and degraded utility in subsequent analysis. To address this limitation, we propose PPGNN, a personalized differentially private framework for decentralized graph data. PPGNN enables user-specific privacy budgets during local perturbation while preserving analytical utility. To handle heterogeneous privacy levels and noise distortion, we design a two-stage solution consisting of a Personalized Perturbation Mechanism (PPM) and a weighted calibration strategy, FlexProp. Extensive experiments on six real-world graph datasets demonstrate that PPGNN effectively balances personalized privacy protection and data utility in decentralized graph learning scenarios.

Unveiling the Non-Monotonic Effect of Privacy on Generalization under Byzantine Robustness

Recent work has established a fundamental trilemma between Byzantine robustness, local differential privacy (LDP), and optimization error in distributed learning. We show that this trilemma does not universally extend to generalization error, but instead depends critically on the privacy regime. Specifically, in the high-noise regime (strong privacy), we prove that increasing privacy reduces the generalization error, i.e., there is no tension between robustness and privacy. In the low-noise regime (weaker privacy), however, the tension between robustness and privacy reappears and increasing privacy indeed degrades generalization. Our theory explains this surprising non-monotonic behavior of the generalization error via matching lower and upper bounds on the algorithmic stability of Byzantine-robust distributed learning under LDP constraints. We corroborate and further analyze these theoretical findings with empirical evaluations.