New Sampling-Free Privacy Accounting Method Improves Matrix Mechanism Guarantees

Global: New Sampling-Free Privacy Accounting Method Improves Matrix Mechanism Guarantees

Researchers Jan Schuchardt and Nikita Kalinin submitted a paper titled “Sampling-Free Privacy Accounting for Matrix Mechanisms under Random Allocation” to arXiv on 29 Jan 2026. The work proposes a sampling‑free approach to privacy accounting for matrix factorization mechanisms that operate under a random‑allocation (balls‑in‑bins) model. According to the abstract, the method leverages Rényi divergence and conditional composition to derive privacy amplification bounds without relying on Monte Carlo sampling.

Background on Differential Privacy and Matrix Mechanisms

Differential privacy provides a formal framework for limiting the information disclosed about any individual in a dataset. Matrix mechanisms, a class of linear queries, are frequently employed in machine‑learning model training and statistical analysis. When queries are allocated randomly across data partitions, the resulting privacy guarantees can be amplified, a phenomenon that prior research has sought to quantify.

Limitations of Prior Sampling‑Based Approaches

Earlier work by Choquette‑Choo et al. (2025) introduced a Monte Carlo method to estimate amplification parameters. That technique required a large number of samples—proportional to the inverse of the privacy parameter δ—to achieve (ε,δ)‑DP, and its guarantees held only with high probability or demanded random abstention by the mechanism. These constraints motivated the search for deterministic bounds.

Sampling‑Free Bounds via Rényi Divergence

The authors derive sampling‑free privacy bounds by analyzing Rényi divergence between the output distributions of the mechanism under neighboring datasets. By applying conditional composition theorems, they obtain tighter guarantees for small ε values where Rényi‑based approximations tend to be conservative. This theoretical development eliminates the need for stochastic estimation.

Dynamic Programming Implementation

To make the Rényi‑based bounds computationally tractable, the paper presents a dynamic‑programming formulation that efficiently evaluates the required divergence terms for both banded and non‑banded matrices. The algorithm scales with the size of the matrix and the number of allocation bins, enabling practical use in real‑world settings.

Empirical Evaluation

Numerical experiments compare the new sampling‑free bounds against the Monte Carlo approach across a variety of matrix mechanisms commonly employed in research and industry. The results, as summarized in the abstract, demonstrate that the proposed method achieves comparable or stronger privacy guarantees while reducing computational overhead.

Implications and Future Work

The sampling‑free framework broadens the toolkit available to practitioners designing differentially private systems that rely on matrix mechanisms. By removing dependence on random sampling, the approach may simplify compliance audits and improve reproducibility. The authors suggest extending the methodology to other allocation models and exploring tighter composition theorems as avenues for further research.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.